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Cardiovascular outcomes and the physical and chemical properties of metal ions found in particulate matter air pollution: a QICAR study.

Changes in the cardiovascular (CV) system may occur if particulate matter (PM) exposure initiates pulmonary oxidative stress and inflammation and/or pulmonary reflex responses. These responses can lead to adverse outcomes such as stroke, myocardial ischemia, and myocardial infarction [Brook et al. 2004, 2010; Chuang et al. 2007; Mills et al. 2007; U.S. Environmental Protection Agency (EPA) 2009; Zhang et al. 2009], as illustrated by the potential pathways for PM to affect the CV system (Figure 1). Oxidative stress occurs when the burden of reactive oxygen species [ROS (oxygen radicals and non-radical oxygen derivatives)] at a target site is larger than the target site's antioxidant reserve (Halliwell and Gutteridge 2007). Oxidative stress can lead to altered cell signaling, DNA injury, or apoptosis (U.S. EPA 2009). In PM experimental exposure studies of in vitro macrophage cytotoxicity (Becker et al. 2002; Hatch et al. 1985) and in vivo intratracheal instillation in mice, oxidative stress was associated more strongly with PM components such as metal ions than with PM mass. Oxidative stress induced by exposure to metal ions can occur directly or indirectly (Ercal et al. 2001). When occurring directly, oxidation-reduction (redox)-active metal ions in PM, such as iron (Fe) and copper (Cu), have been shown to cause ROS formation through experimental in vitro testing of normal human bronchial epithelial and alveolar macrophage cells (Becker et al. 2005), an electron paramagnetic resonance assay (Boogaard et al. 2012), and a dithiothreitol assay (Cho et al. 2005) to replicate oxidation in the lung. Redox-active metal ions in PM participate in the Fenton reaction to produce the hydroxyl radical (OH*), which is subsequently involved in ROS production (Cho et al. 2005; Shafer et al. 2010). Redox-inactive metal ions, such as cadmium (Cd) and lead (Pb), can reduce antioxidant levels in cells by forming complexes with antioxidants; this condition leaves the cell vulnerable to oxidation, as described by Ercal et al. (2001) and observed through imaging experiments employing hydrogen peroxide-specific and redox-specific fluorophores (Cheng et al. 2010). PM components, including metal ions, have been shown to move into the circulation in animal models (Nemmar et al. 2001; Oberdorster et al. 2002) and controlled human exposure studies (Nemmar et al. 2002), but it is unclear whether they remain free or become sequestered (Brook et al. 2004). The location of oxidative stress within the body can also be affected by other ion properties, such as solubility in lipids or epithelial lining fluid and electron exchange properties of metal ions, for both redox-active and redox-inactive metal ions (Miyata and van Eeden 2011). A rat inhalation study suggested that exposure to metal ions in PM may cause oxidative stress in the lung, leading to the production and release of proinflammatory cytokines and endothelin-1 into the circulatory system (Thomson et al. 2005). These mediators could then travel to the heart and blood vessels, where they may mediate downstream inflammatory effects (Brook et al. 2010). Alternatively, an epidemiology panel study of greater Boston-area coronary artery disease patients exhibiting ST segment depression suggested that exposure to both gaseous and particulate air pollutants may lead to the activation of pulmonary reflexes and local inflammation and subsequent alteration of the autonomic nervous system, and resulting heart rate variability changes (Chuang et al. 2008). Markers of inflammation and autonomic imbalance have also been associated with exposure to gaseous and particulate air pollutants in an epidemiology panel of healthy young adults in Taipei, China (Chuang et al. 2007). We hypothesize that relevant physical and chemical properties of metal ions can be used to predict adverse CV outcomes initiated by oxidative stress.

Quantitative ion character-activity relation-ships (QICARs) can be used to examine associations between biological end points and a set of physical and chemical properties describing inorganic metal ions present in exposures. Further, QICARs have been used to predict ecotoxicity of inorganic metal ions on the basis of a set of physical and chemical properties (e.g., McCloskey et al. 1996; Newman et al. 1998; Ownby and Newman 2003; Walker et al. 2003). For example, the lethal or effective concentrations for 50% of species have been predicted by the physical and chemical properties of metal ions such as softness ([[sigma].sub.p]) and the log of the first hydrolysis constant ([absolute value of log([K.sub.OH])]) (Mendes et al. 2010; Ownby and Newman 2003; Williams et al. 1982). QICAR is a powerful tool for evaluating chemical toxicity because it allows for examination across compounds to determine which properties are more strongly associated with adverse responses. In turn, analysis of these properties may provide key insights into the biological mechanisms and pathways or target receptor(s) affected by metal ions. As mentioned above, health end points for humans [e.g. CV disease (CVD)] could also be linked with the physical and chemical properties of the chemicals to which people are exposed. However, to our knowledge, QICAR has not been applied in any human health studies.

The goal of this exploratory effort was to determine whether QICAR can be employed to study associations of adverse CVDs with human exposure to inorganic metal ions. QICAR appears to be a useful tool for elucidating important physical and chemical properties among redox-active and redox-inactive metal ions that may have adverse effects on CVD. In the present study, QICAR is applied to human health in the context of air pollution.

Methods

Data sources. Chemical and physical property data were obtained from physical chemistry reference handbooks for 17 metal ions commonly found in the atmosphere: lithium [Li(I)], sodium [Na(I)], potassium [K(I)], cesium [Cs(I)], magnesium [Mg(II)], calcium [Ca(II)], barium [Ba(II)], manganese [Mn(II)], iron [Fe(II)], cobalt [Co(II)], nickel [Ni(II)], silver [Ag(I)], copper [Cu(II)], zinc [Zn(II)], cadmium [Cd(II)], mercury [Hg(II)], and lead [Pb(II)] (James and Lord 1992; Kaye and Laby 1993). These physicochemical property data have been applied in several peer-reviewed QICAR studies (McCloskey et al. 1996; Mendes et al. 2010; Newman et al. 1998; Ownby and Newman 2003; Walker et al. 2003; Williams et al. 1982). Several of these metal ions (Pb, Hg, Mn, Ni) are well-known toxicants (Dreher et al. 1997; Ercal et al. 2001; Lippmann et al. 2006; Moriwaki et al. 2008). Properties included in this QICAR examination (Table 1) are related to the exchange of electrons and solubility of metal ions and, therefore, may be associated with ROS generation (Mendes et al. 2010; Walker et al. 2003). These properties include fundamental attributes of metal ions (e.g., ion mass, ion length scale) as well as solubility, softness, tendency of an ion to be oxidized, energy required for oxidation, oxidation state, oxidation energy, ability to produce hydroxyl ions (O[H.sup.-]), and abilities to form covalent and ionic bonds. The value of each property for each metal ion is provided in Supplemental Material, Table S1 (http://dx.doi.org/10.1289/ehp.1205793). In addition to evaluating associations with the properties of the individual metal ions, we evaluated associations according to two groups of metal ions. The s-block group comprised Li, Na, K, Cs, Mg, Ca, and Ba, which are from the s-block of the periodic table. The transition group included the transition metal ions Mn, Fe, Co, Ni, Ag, Cu, Zn, and Hg from the d-block of the periodic table, which can have multiple oxidation states. Although Pb is from the p-block of the periodic table, it was included with the transition metal ions for this analysis because it also has multiple oxidation states.
Table 1. The ROS generation-related properties of metal ions
used in the analysis.

Abbreviation              Description            Property
                                                affecting ROS
                                               generation (a)

AN                Atomic number               Ion mass

AR                Atomic radius               Ion length
                                              scale

r                 Pauling ionic radius        Ion length
                                              scale

[rho]             Density                     Ion mass and
                                              length scale

[BETA][E.sup.0]   Change in electrochemical   Tendency of an
                  potential from ion to its   ion to be
                  first reduced state         oxidized

[BETA]IP          Change in ionization        Energy required
                  potential from ion to its   for oxidation
                  first reduced state

Z                 Ion charge                  Oxidation state

AN/[BETA]IP       Atomic number:ionization    Oxidation
                  potential ratio             energy

log([K.sub.OH)    Logarithm of the first      Ability to
                  hydrolysis constant         produce hydroxyl
                                              ions

MP                Melting point               Solubility

P[K.sub.sp](CO3)  Solubility product of       Solubility
                  MCO3, where M = metal

[[sigma].sub.p]   Pearson softness            Softness
                  coefficient

[x.sub.m]         Electronegativity           Ability to form
                                              covalent bonds

[X.sub.m.sup.2]r  Covalent index              Ability to form
                                              covalent bonds

Z/AR              Ionic charge:atomic radius  Ability to form
                  ratio                       ionic bonds

[Z.sup.2]/r       Cation polarizing power     Ability to form
                                              ionic bonds

C[O.sub.3], carbonate.
(a) Data from McCloskey et al. (1996), Mendes et al. (2010),
Walker et al. (2003), and Wolterbeek and Verberg (2001).


Associations of CVDs with metal ion exposures examined in this analysis came from the publicly available Comparative Toxicogenomics Database (CTD; Davis et al. 2009, 2011). The CTD is a curated database of known interactions between chemicals and genes, genes and diseases, and infrequently, chemicals and diseases. Chemical-disease relationships are inferred in the CTD using established evidence of either chemical x gene and gene x disease interactions or chemical x disease interactions observed in curated laboratory studies within the CTD database. Chemical x gene or chemical x disease interactions curated in the CTD can include any study that demonstrates a chemical exposure can lead to a change in gene or disease status through any exposure pathway (Davis et al. 2009, 2011). The CTD data-base focuses on environmental chemicals and outcomes relevant to human health, but inferences may be based in part on information from animal studies if the animal contains a gene that is also present in humans and the study elucidates the effect of a chemical on the gene or a gene on a disease outcome.

Within the CTD, inference score is a measure of the degree of support for a given association between a disease and a chemical. An inference score is computed using principles of scale-free networks, where the probability (P) that a vertex in a large network interacts with another vertex decays according to a power law (Barabasi and Albert 1999). A vertex in the CTD can be a gene (G), chemical (C), or disease (D) with some number of connections (k) between them. For a set of [n.sub.G] genes, the inference score (Y) is computed as shown below (Li and Liang 2009):

Y = -ln[P(G associated with both C and D|k, nG) P(no other G connects C and D|k, nG)]. [1]

Each inference score used in this analysis is the log transform of the product of two probability functions: a) the probability that a gene is associated with both a chemical and a disease, and b) the probability that the chemical-gene-disease connection is unique. The CTD curates data for chemical x disease and gene x disease interactions for 27 disease categories, including CVDs. Within the CVD category, five end points were selected for this study based on the potential relevance of oxidative stress mechanisms to their development: cardiac arrhythmia, myocardial ischemia, myocardial infarction, stroke, and thrombosis (Godleski et al. 2000; Longhurst et al. 2001; U.S. EPA 2009). Inference score data for each CVD end pointmetal ion pair is provided in Supplemental Material, Table S2 (http://dx.doi.org/10.1289/ehp.1205793). Arrhythmia inference scores were available for 6 of 7 s-block metal ions and 7 of 10 transition metal ions, myocardial infarction inference scores were available for 5 s-block metal ions and 8 transition metal ions, myocardial ischemia inference scores were available for 5 s-block metal ions and 9 transition metal ions, and thrombosis and stroke inference scores were available for 5 s-block metal ions and 10 transition metal ions.

Statistical analysis. All statistical analyses were conducted with SAS version 9.1 (SAS Institute Inc., Cary, NC). For each CVD end point, least-trimmed squares (LTS) regression was used to estimate associations of log-transformed inference scores for a set of metal ions (s-block or transition) with their ion properties. LTS regression minimizes the influence of outliers on the model fit (Rousseeuw and Hubert 2011; Rousseeuw and Leroy 2003). Rather than minimize the sum of squared residuals for all data points included in ordinary least squares regression, LTS minimizes the sum of squared residuals for a subset of data points that minimizes the sum of squared residuals to remove the influence of outliers from the regression. Trimmed data points are those data points excluded from the minimized sum of squared residuals function, and the number of trimmed data points ([n.sub.trim]) is determined separately for each outcome and metal ion group model. The default approach provided by SAS (PROC ROBUSTREG) was employed to calculate LTS breakdown values to determine [n.sub.trim]. Breakdown values estimate the smallest proportion of data that, if erroneous, could bias the estimator. Breakdown values for the simulations ranged from 8 tto 20%.

The overall significance level was 0.05. Given that 16 properties were tested, the multiple comparisons design led to a Bonferroni-corrected significance level of 0.003 (or 0.05/16). Log transformation of the inference scores was applied to reduce heteroscedascity and more closely meet the statistical modeling assumptions.

Given collinearity between several ion properties, only one ion property was used in a univariate regression each time as a predictor (Table 2). Scatter plots were developed during exploratory analysis to visualize the data [Figure 2 shows an example for atomic number (AN)]. Examination of these scatter plots revealed that the properties tended to cluster around the type of metal ion (i.e., s-block or transition), with potentially different slopes for each group. Therefore, LTS regressions for each disease-property combination were performed separately for s-block and transition metal ions. Slopes obtained from the LTS regressions are presented both as 1-unit changes in properties and as standardized by the interquartile range (IQR) of the property distribution.
Table 2. Spearman correlation coefficients among the physical
and chemical properties across the metal ions included in
the QICAR models.

                          Z    AN     r      AR     [BETA]IP

Z                        1.0  0.24  -0.47  -0.49      0.50

AN                             1.0   0.48   0.13     -0.03

r                                     1.0   0.89     -0.71

AR                                           1.0     -0.75

[BETA]IP                                               1.0

[BETA][E.sup.0]

[X.sub.m]

log([K.sub.OH])

[[sigma].sub.p]

[X.sub.m.sup.2]r

[Z.sup.2]/r

AN/[BETA]IP

Z/AR

MP

[rho]

P[K.sub.sp](C[O.sub.3])

                         [BETA][E.sup.0]  [X.sub.m]  log([K.sub.OH])

Z                                  -0.50       0.48            -0.57

AN                                 -0.32       0.43            -0.36

r                                   0.50      -0.47             0.52

AR                                  0.80      -0.78             0.67

[BETA]IP                           -0.77       0.71            -0.83

[BETA][E.sup.0]                      1.0      -0.95             0.74

[X.sub.m]                                       1.0            -0.78

log([K.sub.OH])                                                  1.0

[[sigma].sub.p]

[X.sub.m.sup.2]r

[Z.sup.2]/r

AN/[BETA]IP

Z/AR

MP

[rho]

P[K.sub.sp](C[O.sub.3])

                         [[sigma].sub.p]  [X.sub.m.sup.2]r

Z                                  -0.54              0.26

AN                                 -0.50              0.71

r                                   0.35             -0.04

AR                                  0.65             -0.44

[BETA]IP                           -0.74              0.34

[BETA][E.sup.0]                     0.85             -0.74

[X.sub.m]                          -0.85              0.87

log([K.sub.OH])                     0.80             -0.56

[[sigma].sub.p]                      1.0             -0.71

[X.sub.m.sup.2]r                                       1.0

[Z.sup.2]/r

AN/[BETA]IP

Z/AR

MP

[rho]

P[K.sub.sp](C[O.sub.3])

                         [Z.sup.2]/r  AN/[BETA]IP  Z/AR     MP

Z                               0.88        -0.04   0.86   0.49

AN                             -0.07         0.85   0.15  -0.25

r                              -0.75         0.82  -0.69  -0.55

AR                             -0.71         0.58  -0.81  -0.55

[BETA]IP                        0.77        -0.42   0.73   0.67

[BETA][E.sup.0]                -0.61         0.14  -0.80  -0.48

[X.sub.m]                       0.55        -0.07   0.76   0.39

log([K.sub.OH])                -0.67         0.10  -0.74  -0.32

[[sigma].sub.p]                -0.54        -0.06  -0.66  -0.35

[X.sub.m.sup.2]r                0.16         0.30   0.47   0.06

[Z.sup.2]/r                      1.0        -0.39   0.92   0.66

AN/[BETA]IP                                   1.0  -0.26  -0.42

Z/AR                                                 1.0   0.59

MP                                                          1.0

[rho]

P[K.sub.sp](C[O.sub.3])

                         [rho]  P[K.sub.sp](C[O.sub.3])

Z                         0.46                    -0.45

AN                        0.62                    -0.58

r                        -0.27                    -0.09

AR                       -0.65                     0.23

[BETA]IP                  0.60                    -0.33

[BETA][E.sup.0]          -0.90                     0.66

[X.sub.m]                 0.94                    -0.63

log([K.sub.OH])          -0.76                     0.46

[[sigma].sub.p]          -0.91                     0.73

[X.sub.m.sup.2]r          0.86                    -0.65

[Z.sup.2]/r               0.44                    -0.31

AN/[BETA]IP               0.16                    -0.26

Z/AR                      0.67                    -0.53

MP                        0.30                    -0.34

[rho]                      1.0                    -0.74

P[K.sub.sp](C[O.sub.3])                             1.0


To evaluate whether the results were sensitive to specific regression methods, additional regression approaches were also used to examine the robustness of the LTS results. Other regression approaches included in the analysis were maximum likelihood type robust (M) estimation (Huber 1973), minimization of robust scale (S) estimation (Rousseeuw and Yohai 1984), and high breakdown/high efficiency robust (MM) estimation (Yohai 1987). For M estimation, a bisquare weight function was applied. For MM and S estimations, the SAS default parameters in PROC ROBUSTREG for the MM and S options, respectively, were employed.

Because the data set had small sample sizes (i.e., it was limited to the number of metal ions included in each group evaluated), robustness of the LTS results was further evaluated via Monte Carlo simulation. The log-transformed inference scores, [Y.sub.ij], were sampled once from the corresponding normal distribution with a mean of [[beta].sub.0,ikl] + [[beta].sub.1,iklxjk] and a standard deviation of [[sigma].sub.ikl] for the ith disease, jth metal ion, kth metal ion property, and lth group (s-block vs. transition metal ions). [[beta].sub.0] and [[beta].sub.1] are the regression coefficients (treated as fixed values in the simulation) between log-transformed inference scores and metal ion properties, x is the metal ion property (treated as a fixed value in the simulation), and [sigma] is the standard deviation of the regression residuals. The sampled [Y.sub.ij] were regressed on [x.sub.jk] with the LTS approach for each combination of health end points, metal ion properties, and metal ion groups. The number of outliers [defined as [Y.sub.ij] = ([[beta].sub.0,ikl] + [[beta].sub.1,ikl xjk]) [+ or -] 3[sigma]ikl] included in each simulated data set was greater than the number of outliers identified by LTS in the original data set. The procedure was repeated 1,000 times. Centrality and variability of the regression coefficients based on the original data sets were compared with the simulation results.

Model validation. Validation of selected models was performed where data were available in the CTD and properties databases. Because there are more transition metal ions than s-block metal ions, four cardiac arrhythmia models were chosen for validation: AN, [[sigma].sub.p], melting point (MP), and density ([rho]) (Dean 1999; Hammond 2003; James and Lord 1992; Kaye and Laby 1993). Relative [L.sub.2] error norms were computed to compare ln(Inference Score) predictions from the regression models input with property data for aluminum [Al(III)], chromium [Cr(VI)], and vanadium [V(V)]. In other words, the relative [L.sub.2] error norm approaches zero as the predicted ln(Inference Score) approaches that from the CTD. Relative [L.sub.2] error norm is computed as

[L.sub.2] = ([square root of ([summation][[ln Inference Score - prediction].sup.2])])/[square root of ([summation]ln [(Inference Score).sup.2])] [2]

Results and Discussion

All associations between inference scores and ion properties (robust univariate regressions) are summarized [see Supplemental Material, Tables S3-S7 (http://dx.doi.org/10.1289/ehp.1205793)]. A set of example scatter plots with LTS regression lines is provided for the AN property in Figure 2. Table 3 presents significant LTS regression results, with p-values of the slopes < 0.003. Table 3 also provides data for the number of metal ions included and trimmed from the robust model, SE, significance level, and coefficient of determination ([R.sup.2]). Table 4 displays a matrix illustrating statistically significant associations between inference scores and properties for each metal ion grouping (s-block or transition metal ions).
Table 3. The associations between the inference score relating
CVD to metal exposures with the physical and chemical properties
of metal ions using robust univariate regressions.

Disease     Group       Property          [n.sup.a]  [ntrim.sup.b]

Cardiac     Transition  [X.sub.m.sup.2]r          6              1
arrhythmia              AN                        6              1
                        [[sigma].sub.p]           6              1
                        [rho]                     6              1
                        MP                        6              1

Myocardial  s-Block     AN/[BETA]IP               4              1
infarction              AN                        4              1

Myocardial  s-Block     [X.sub.m.sup.2]r          4              1
ischemia                AN/[BETA]IP               4              1
                        r                         4              1
                        AR                        4              1
                        AN                        4              1
                        [X.sub.m]                 4              1

Stroke      s-Block     AN                        4              1
                        MP                        4              1
                        [[sigma].sub.p]           4              1
                        [X.sub.m.sup.2]r          4              1
                        Z                         4              1

Thrombosis  s-Block     [rho]                     4              1
                        [[sigma].sub.p]           4              1
            Transition  AR                        8              2
                        [[sigma].sub.p]           7              2
                        Z/AR                      8              2

Disease     Group       Property             Slope     Standardized
                                                       [slope.supc]

Cardiac     Transition  [X.sub.m.sup.2]r        0.177         0.112
arrhythmia              AN                     5.86 x        2.79 x
                                          [10.sup.-3]   [10.sup.-4]
                        [[sigma].sub.p]         -5.54          11.1
                        [rho]                  6.27 x        3.09 x
                                          [10.sup.-5]   [10.sup.-8]
                        MP                    -1.81 x       -1.72 x
                                          [10.sup.-4]   [10.sup.-7]

Myocardial  s-Block     AN/[BETA]IP             0.235        0.0375
infarction              AN                     0.0504        1.62 x
                                                        [10.sup.-3]

Myocardial  s-Block     [X.sub.m.sup.2]r         -2.6         -17.3
ischemia                AN/[BETA]IP             0.276        0.0441
                        r                         3.3          8.24
                        AR                       2.59          6.46
                        AN                     0.0584        1.89 x
                                                        [10.sup.-3]
                        [X.sub.m]               -1.82         -18.2

Stroke      s-Block     AN                     0.0381        1.23 x
                                                        [10.sup.-3]
                        MP                     3.73 x        5.74 x
                                          [10.sup.-4]   [10.sup.-7]
                        [[sigma].sub.p]         -9.63          -241
                        [X.sub.m.sup.2]r         2.53          16.9
                        Z                       0.260         0.260

Thrombosis  s-Block     [rho]                  0.36 x          1.20
                                          [10.sup.-3]
                        [[sigma].sub.p]         -19.7          -492
            Transition  AR                       2.21          11.0
                        [[sigma].sub.p]         -10.2          -204
                        Z/AR                    -2.60         -11.3

Disease     Group       Property              SE         p-Value

Cardiac     Transition  [X.sub.m.sup.2]r       0.0506      < 0.001
arrhythmia              AN                     8.95 x      < 0.001
                                          [10.sup.-4]
                        [[sigma].sub.p]          1.76        0.002
                        [rho]                  1.53 x      < 0.001
                                          [10.sup.-5]
                        MP                     4.84 x      < 0.001
                                          [10.sup.-5]

Myocardial  s-Block     AN/[BETA]IP             0.054      < 0.001
infarction              AN                     0.0147        0.001

Myocardial  s-Block     [X.sub.m.sup.2]r        0.262      < 0.001
ischemia                AN/[BETA]IP            0.0416      < 0.001
                        r                       0.514      < 0.001
                        AR                      0.519      < 0.001
                        AN                     0.0151      < 0.001
                        [X.sub.m]               0.567        0.001

Stroke      s-Block     AN                     7.35 x      < 0.001
                                          [10.sup.-3]
                        MP                     1.14 x       1.09 x
                                          [10.sup.-4]  [10.sup.-3]
                        [[sigma].sub.p]          1.33      < 0.001
                        [X.sub.m.sup.2]r       0.0828      < 0.001
                        Z                      0.0663      < 0.001

Thrombosis  s-Block     [rho]                  1.56 x      < 0.001
                                          [10.sup.-4]
                        [[sigma].sub.p]          3.71      < 0.001
            Transition  AR                      0.544      < 0.001
                        [[sigma].sub.p]          3.01      < 0.001
                        Z/AR                    0.572      < 0.001

Disease     Group       Property          [R.sup.2]

Cardiac     Transition  [X.sub.m.sup.2]r       0.48
arrhythmia              AN                     0.84
                        [[sigma].sub.p]         0.7
                        [rho]                  0.59
                        MP                     0.57

Myocardial  s-Block     AN/[BETA]IP             0.9
infarction              AN                     0.85

Myocardial  s-Block     [X.sub.m.sup.2]r       0.98
ischemia                AN/[BETA]IP            0.94
                        r                      0.92
                        AR                     0.87
                        AN                     0.84
                        [X.sub.m]              0.84

Stroke      s-Block     AN                     0.73
                        MP                     0.84
                        [[sigma].sub.p]        0.83
                        [X.sub.m.sup.2]r       0.99
                        Z                      0.88

Thrombosis  s-Block     [rho]                  0.84
                        [[sigma].sub.p]        0.60
            Transition  AR                     0.66
                        [[sigma].sub.p]        0.68
                        Z/AR                   0.65

Results reported are for the models with significant slopes
(p-values < 0.003). Properties are listed in descending
order of R2 within each disease and metal ion group
(a) Number of metals included in model. (b) Number of metals
trimmed from the robust model based on total number for which
data were available. (c) Standardized per IQR increase in
property. For complete results, see Supplemental Material,
Tables S3-S7 (http://dx.doi.org/10.1289/ehp.1205793).

Table 4. The statistically significant associations
(p < 0.003) between the CTD inference score relating CVD
to metal exposures, and the physical and chemical properties
of metal ions, by the groups of metal ions (s-block and
transition metal ions).

Property            Cardiac    Myocardial  Myocardial  Stroke
                  arrhythmia   infarction   ischemia

AN                Transition3  s-Block     s-Block     s-Block

AR                --           --          s-Block     --

[rho]             Transition   --          --          --

MP                Transition   --          --          s-Block

r                 --           --          s-Block     --

[[sigma].sub.p]   Transition   --          --          s-Block

[X.sub.m]         --           --          s-Block     --

AN/[BETA] IP      --           s-Block     s-Block     --

[X.sub.m.sup.2]r  Transition   --          s-Block     s-Block

Z                 --           --          --          s-Block

Z/AR              --           --          --          --

Property          Thrombosis

AN                --

AR                Transition

[rho]             s-Block

MP                --

r                 --

[[sigma].sub.p]   s-Block,
                  transition

[X.sub.m]         --

AN/[BETA] IP      --

[X.sub.m.sup.2]r  --

Z                 --

Z/AR              Transition

--, No statistically significant relationship between the
health outcome and property.
(a) Significant associations (p-values < 0.003 for
slopes and [R.sup.2] > 0.5 in the robust univariate
regression) between cardiac arrhythmia and AN for
transition metal ions


Evaluation of the LTS regression results through comparison with other robust estimation methods and Monte Carlo simulations to address small sample size lend confidence to the results. LTS regression produced slopes that were often comparable to those associated with the other robust estimation approaches [see Supplemental Material, Tables S8-S12 (http://dx.doi.org/10.1289/ehp.1205793)], with equivalent slopes produced by the four methods for 50% of the simulations and slopes within 20% of each other for 63% of the simulations. The Monte Carlo simulation results also confirmed the robustness of slopes (see Supplemental Material, Tables S13-S17) by predicting the model slopes within [+ or -] 3%, although the SE of the LTS results tended to underestimate the SE computed during the Monte Carlo simulations. The LTS approach is very robust to outliers (Nevitt and Tam 1998; You 1999).

The validation exercise produced [L.sub.2] error norms (i.e., the relative difference between the predicted inference score and the CTD inference score) for AN, [sigma], MP, and [rho] of 29%, 14%, 25%, and 41%, respectively. These [L.sub.2] error norms are high, but given that data from only three metals were used to validate the models, they suggest a reasonable fit.

Associations between health outcomes and properties varied among the diseases and metal ion groupings. Cardiac arrhythmia was not associated with any properties for the s-block elements (Tables 3 and 4). For the transition elements, cardiac arrhythmia was associated with ion mass and length scale (AN and [rho]), solubility (MP), softness ([[sigma].sub.p]), and the ability to form covalent bonds ([X.sub.m.sup.2]). Myocardial infarction was associated with two properties for the s-block element models and none for the transition metal ion models: ion mass (AN) and oxidation energy (AN/[DELTA]IP). Myocardial ischemia was associated with six properties for the s-block metal ion models and none for the transition metal ion models. For the s-block metal ions, associations were observed for ion size [AN, AR, r], oxidation energy (AN/[DELTA]IP), and ability to form covalent bonds ([X.sub.m], [X.sub.m.sup.2]). Stroke was associated with five properties for the s-block metal ion models and none for the transition metal ion models. For the s-block metal ions, associations were observed for ion mass (AN), solubility (MP), softness ([[sigma].sub.p]), ability to form covalent bonds ([X.sub.m.sup.2]), and ability to form ionic bonds (Z). Thrombosis was associated with two properties for the s-block metal ions, ion mass and length scale ([rho]) and softness ([[sigma].sub.p]), and three properties for the transition metal ions, ion length scale (AR), softness ([[sigma].sub.p]), and the ability to form ionic bonds (Z/AR). Thrombosis was the only end point for which both the s-block and transition metal ions had significant models.

Similarities and differences among the regression models are apparent for the health end points. The slopes, based on unit and IQR changes, were similar in magnitude and sign for myocardial ischemia and myocardial infarction for AN, AN/[DELTA]IP, log([K.sub.OH]), and [rho] [see Supplemental Material, Tables S4 and S5, respectively (http://dx.doi.org/10.1289/ehp.1205793)]. For example, the s-block model unit slopes for AN were 0.0504 and 0.0584 for myocardial infarction and myocardial ischemia, respectively. These observations, along with the finding that associations of myocardial ischemia and myocardial infarction were observed primarily for s-block elements (Table 3), suggest a common mechanistic pathway for both outcomes among the metal ions examined. Myocardial infarction is a severe potential consequence of myocardial ischemia, to which altered vasoreactivity, atherosclerotic plaque formation, and thrombosis may contribute (Figure 1). Estimated slopes for associations between cardiac arrhythmia and metal ion properties tended to differ from estimated slopes for other outcomes. For example, slopes for AN, AN/[DELTA]IP, and [rho] varied in magnitude between cardiac arrhythmia and myocardial ischemia [see Supplemental Material, Tables S3 and S5, respectively (http://dx.doi.org/10.1289/ehp.1205793)]. The s-block model unit slope for AN was an order of magnitude lower for cardiac arrhythmia (0.00583) compared with myocardial infarction (0.0504) and myocardial ischemia (0.0584). It is possible that these observed differences reflect the role of autonomic nervous system imbalance in the development of cardiac arrhythmia (see also Campese et al. 2004; Creason et al. 2001; Gold et al. 2000; He et al. 2010, 2011; Liao et al. 2009, 2010; Pope et al. 1999). Differences were observed between the statistically significant property-based models for thrombosis and stroke. It is possible that differences among the stroke and thrombosis models may relate to etiologic differences between strokes of hemorrhagic, rather than thromboembolic, origin. Previous epidemiologic studies have reported associations between PM, nitrogen dioxide, carbon monoxide, and ozone with ischemic (i.e., thromboembolic) but not hemorrhagic stroke (Hong et al. 2002; Wellenius et al. 2005). However, the models for softness ([[sigma].sub.p]) were statistically significant for stroke with s-block metal ions and for thrombosis with both s-block and transition metal ions.

Associations between CVD and transition metal ion exposure have been found in toxicological and epidemiologic studies. Farraj et al. (2011) exposed rats to a PM designed to mimic metal ion-containing residual oil fly ash by composing the PM of a mix of NiS[O.sub.4] (nickle sulfate), Fe2S[O.sub.4] [iron(II) sulfate], and NaV[O.sub.3] [sodium vanadate(V)] and observed cardiac arrhythmias with concurrent autonomic changes, with the magnitude of autonomic change corresponding to low, medium, or high exposure group and no effect for the no exposure group. Given that Farraj et al. (2011) studied only transition metal ions, this is somewhat consistent with the findings that the transition metal ion properties were significantly associated with cardiac arrhythmia. However, Farraj et al. (2011) did not look at associations between cardiac arrhythmia and individual metal ion compounds, so it is not possible to discern whether relative differences among the properties had differential effects on arrhythmogenesis. An epidemiologic study of hospital admissions for CVD among older adults (> 64 years of age) in Atlanta, Georgia, by Suh et al. (2011) reported significant associations between myocardial ischemia and transition metals in PM exposure, but did not study cardiac arrhythmias. However, our results indicate that for the transition metal ions, myocardial ischemia is not statistically significantly associated with any other properties examined. Hence, the results do not provide strong support for or negation of Suh et al.'s (2011) observations. Based on the results of the QICAR models, none of the CV health outcomes were associated with ionic exchange of electrons for transition metal ions, in contrast with with s-block metal ions, which were associated with myocardial ischemia and myocardial infarction. However, all five adverse CV health outcomes were associated with ion size for both transition and s-block metal ions. Ion size or mass may reflect greater reactivity, possibly resulting from stronger interatomic forces associated with complexes involving large ions (Walker et al. 2003). Softness ([[sigma].sub.p]) was found to be a statistically significant predictor of cardiac arrhythmia for transition metal ions (Table 3). Mendes et al. (2010) concluded that [[sigma].sub.p] caused covalent bonding of the metal ions to biological ligands in a study of fungi toxicity. [[sigma].sub.p] also provided the most statistically significant association with adverse species outcomes in several other ecotoxicology studies (McCloskey et al. 1996; Ownby and Newman 2003; Zhou et al. 2011).

There are several limitations of this work. First, the sample sizes were small because the number of s-block and transition metal ions is small in general, and only a subset is available in the CTD. Small sample size also limits the model validation, given that data from only three metal ions were available for validation. However, our analysis was intended to explore development of models potentially associating adverse CV end points and chemical and physical properties, rather than to establish definitive conclusions about these relationships. Furthermore, Monte Carlo simulations yielded slope estimates within [+ or -] 3%, which added confidence to the results. Second, the properties evaluated were moderately to highly correlated (Table 2), thus limiting the linear regression analyses to univariate regressions. More sophisticated multivariate approaches not constrained by collinearity (e.g., partial least square regressions) need to be tested to examine further the associations between disease outcomes and ion properties. Third, the CTD is likely subject to selection bias because the inference scores reflect both data availability and inference of association between each chemical-disease pair in question. Moreover, given that the CTD inferred associations between disease outcomes and chemical exposures, the CTD may not have been limited to inhalation exposures, which is the primary exposure pathway for air pollutants. However, the inference score calculated within the CTD was attractive to use as a health outcome metric because it incorporates probabilities of association in a consistent manner across health outcomes and outcome-property pairs. These limitations will be addressed as the methodology of applying QICAR to human health outcomes is refined.

Conclusions

In this exploratory, hypothesis-generating work, we used QICAR to link human CVD and the properties of metal ions commonly observed in ambient PM. Cardiac arrhythmia, myocardial infarction, myocardial ischemia, stroke, and thrombosis were associated with some ion properties related to ROS generation. This work supports the feasibility of using ion properties to predict CVD. QICAR has the potential to complement existing epidemiologic methods for estimating associations between CVDs and air pollutant exposures by providing clues about the underlying mechanisms that may explain these associations. More sophisticated approaches will be applied to extend work to study the associations between diseases and properties of organic and inorganic chemicals.

Supplemental Material

Cardiovascular Outcomes and the Physical and Chemical Properties of Metal Ions Found in Particulate Matter Air Pollution: a QICAR Study

BACKGROUND: This paper presents an application of quantitative ion character-activity relation-ships (QICAR) to estimate associations of human cardiovascular (CV) diseases (CVDs) with a set of metal ion properties commonly observed in ambient air pollutants. QICAR has previously been used to predict ecotoxicity of inorganic metal ions based on ion properties.

OBJECTIVES: The objective of this work was to examine potential associations of biological end points with a set of physical and chemical properties describing inorganic metal ions present in exposures using QICAR.

METHODS: Chemical and physical properties of 17 metal ions were obtained from peer-reviewed publications. Associations of cardiac arrhythmia, myocardial ischemia, myocardial infarction, stroke, and thrombosis with exposures to metal ions (measured as inference scores) were obtained from the Comparative Toxicogenomics Database (CTD). Robust regressions were applied to estimate the associations of CVDs with ion properties.

RESULTS: CVD was statistically significantly associated (Bonferroni-adjusted significance level of 0.003) with many ion properties reflecting ion size, solubility, oxidation potential, and abilities to form covalent and ionic bonds. The properties are relevant for reactive oxygen species (ROS) genera-tion, which has been identified as a possible mechanism leading to CVDs.

CONCLUSION: QICAR has the potential to complement existing epidemiologic methods for estimating associations between CVDs and air pollutant exposures by providing clues about the underlying mechanisms that may explain these associations.

KEY WORDS: air pollution, cardiovascular disease, multipollutant, QICAR, QSAR. Environ Health Perspect 121:558-564 (2013). http://dx.doi.org/10.1289/ehp.1205793 [Online 5 March 2013]

Address correspondence to J. Richmond-Bryant, 109 T.W. Alexander Dr., MC B243-01, Research Triangle Park, North Carolina 27711 USA. Telephone: (919) 541-4518. E-mail: richmond-bryant.jennifer@epa.gov

Supplemental Material is available online (http://dx.doi.org/10.1289/ehp.1205793).

We thank A. Farraj for his helpful comments in review of this manuscript.

The research and this manuscript have been reviewed in accordance with U.S. Environmental Protection Agency (EPA) policy and approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. The views expressed in this article are those of the authors and do not necessarily reflect the views or policies of the U.S. EPA.

The authors declare they have no actual or potential competing financial interests.

Received 19 July 2012; accepted 4 March 2013.

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Table of Contents

Table S1. Properties of metal ions included in the    S3
QICAR analysis.

Table S2. CTD inference scores, a measure of the      S4
degree of support for a given association between a
disease and a chemical based on known chemical-gene
and gene-disease interactions, for metal ions
included in the QICAR analysis, by CVD endpoint.

Table S3. The associations between inference score    S5
relating CVD to metal exposures with the physical
and chemical properties of metal ions using robust
univariate regressions for cardiac arrhythmia.

Table S4. The associations between inference score    S6
relating CVD to metal exposures with the physical
and chemical properties of metal ions using robust
univariate regressions for myocardial infarction.

Table S5. The associations between inference score    S7
relating CVD to metal exposures with the physical
and chemical properties of metal ions using robust
univariate regressions for myocardial ischemia.

Table S6. The associations between inference score    S8
relating CVD to metal exposures with the physical
and chemical properties of metal ions using robust
univariate regressions for thrombosis.

Table S7. The associations between inference score    S9
relating CVD to metal exposures with the physical
and chemical properties of metal ions using robust
univariate regressions for stroke.

Table S8. Comparisons of regression results from     S10
the various robust regression methods for cardiac
arrhythmia.

Table S9. Comparisons of regression results from     S11
the various robust regression methods for
myocardial infarction.

Table S10. Comparisons of regression results from    S12
the various robust regression methods for
myocardial ischemia.

Table S11. Comparisons of regression results from    S13
the various robust regression methods for stroke.

Table S12. Comparisons of regression results from    S14
the various robust regression methods for
thrombosis.

Table S13. Average results from 1000 Monte Carlo     S15
simulations of the LTS regression. Percent error
denotes the relative error between the LTS slope
from the data model fit compared with the LTS slope
from the Monte Carlo simulation for cardiac
arrhythmia.

Table S14. Average results from 1000 Monte Carlo     S16
simulations of the LTS regression. Percent error
denotes the relative error between the LTS slope
from the data model fit compared with the LTS slope
from the Monte Carlo simulation for myocardial
infarction.

Table S15. Average results from 1000 Monte Carlo     S17
simulations of the LTS regression. Percent error
denotes the relative error between the LTS slope
from the data model fit compared with the LTS slope
from the Monte Carlo simulation for myocardial
ischemia.

Table S16. Average results from 1000 Monte Carlo     S18
simulations of the LTS regression. Percent error
denotes the relative error between the LTS slope
from the data model fit compared with the LTS slope
from the Monte Carlo simulation for stroke.

Table S17. Average results from 1000 Monte Carlo     S19
simulations of the LTS regression. Percent error
denotes the relative error between the LTS slope
from the data model fit compared with the LTS slope
from the Monte Carlo simulation for thrombosis.

References                                           S20

Table S1. Properties of metal ions included in the QICAR analysis.

Metal       Z  AN   r   AR   [BETA]IP  [BETA][E.sup.0]  [X.sub.m]

s-block
Metals

Li (I)      1   3  0.7  1.5      5.39             3.05          1

Na (I)      1  11    1  1.9      5.14             2.71        0.9

K (I)       1  19  1.4  2.3      4.34             2.92        0.8

Cs (I)      1  55  1.7  2.6      3.89             2.92        0.8

Mg (II)     2  12  0.7  1.6      7.39             2.38        1.3

Ca (II)     2  20    1  1.9      5.76             2.76          1

Ba (II)     2  56  1.4  2.2      4.79              2.9        0.9

Transition
Metals

Mn (II)     2  25  0.8  1.3      8.21             1.03        1.6

Fe (II)     2  26  0.6  1.2      16.2             0.45        1.8

Co (II)     2  27  0.8  1.1      9.19             0.28        1.9

Ni (II)     2  28  0.7  1.3      10.5             0.23        1.9

Ag (I)      1  47  1.2  1.5      7.58              0.8        1.9

Cu (II)     2  29  0.7  1.4      12.6             0.16        1.9

Zn (II)     2  30  0.8  1.3      8.57             0.76        1.7

Cd (II)     2  48    1  1.5      7.91              0.4        1.7

Hg (II)     2  80    1  1.5      8.32             0.91          2

Pb (II)     2  82  1.2  1.5      7.61             0.13        2.3

Metal       log([K.sub.OH])  [[sigma].sub.p]  X[m.sup.2]r

s-block
Metals

Li (I)                 13.6             0.25         0.71

Na (I)                 14.2             0.21         0.88

K (I)                  14.5             0.23         0.93

Cs (I)                 14.9             0.22         1.06

Mg (II)                11.6             0.17         1.24

Ca (II)                12.7             0.18            1

Ba (II)                13.4             0.18         1.08

Transition
Metals

Mn (II)                10.6             0.13         1.99

Fe (II)                2.04               NA         2.04

Co (II)                 9.7             0.13         2.65

Ni (II)                 9.9             0.13         2.52

Ag (I)                   12             0.07         4.28

Cu (II)                   8              0.1         2.64

Zn (II)                   9             0.12         2.04

Cd (II)                10.1             0.08         2.71

Hg (II)                 3.4             0.07         4.08

Pb (II)                 7.7             0.13         6.41

Metal       [Z.sup.2]/r    AN/     Z/AR    MP      P
                           [BETA]IP

s-block
Metals

Li (I)             1.35      0.56  0.66  453.69    535

Na (I)             0.98      2.14  0.54  370.87    968

K (I)              0.72      4.38  0.43  336.53    856

Cs (I)             0.59     14.14  0.38  301.59   1879

Mg (II)            5.56      1.62  1.29     923   1738

Ca (II)               4      3.47  1.05    1115   1550

Ba (II)            2.92     11.69  0.92    1000   3510

Transition
Metals

Mn (II)            4.82      3.04  1.53    1519   7470

Fe (II)            6.55      1.61  1.61    1811   7874

Co (II)            5.33      2.94  1.79    1768   8900

Ni (II)             5.8      2.66   1.6    1728   8908

Ag (I)             0.87      6.21  0.66  1234.9  10490

Cu (II)            5.48      2.31  1.48  1357.8   8920

Zn (II)            5.33       3.5   1.6  692.68   7140

Cd (II)            4.21      6.07  1.35  594.22   8650

Hg (II)            3.92      9.62  1.35  234.32  13534

Pb (II)            3.39     10.78  1.61  600.61  11340

Metal       pKsp(C[O.sub.3])

s-block
Metals

Li (I)                 -1.60

Na (I)                    NA

K (I)                     NA

Cs (I)                 -8.47

Mg (II)                -7.46

Ca (II)                -8.42

Ba (II)                -8.29

Transition
Metals

Mn (II)               -10.74

Fe (II)               -10.49

Co (II)               -12.85

Ni (II)                -8.18

Ag (I)                -11.09

Cu (II)                -9.85

Zn (II)                -9.84

Cd (II)               -11.28

Hg (II)                   NA

Pb (II)               -13.13

NA: not available
Sources: Dean (1999); James and Lord (1992); Kaye and Laby (1993);
Lide (2003); Mendes et al. (2010); Wolterbeek and Verberg (2001)

Table S2. CTD inference scores, a measure of the degree of support
for a given association between a disease and a chemical based on
known chemical-gene and gene-disease interactions, for metal ions
included in the QICAR analysis, by CVD endpoint.

Metal         Cardiac   Myocardial  Myocardial  Thrombosis  Stroke
            Arrhythmia  Infarction   Ischemia

s-block
Metals

Li (I)            3.41        2.04        2.48        2.33    3.74

Na (I)            5.49        9.27        7.64        3.52    5.62

K (I)             5.49         5.7        6.39        2.99    6.41

Cs (I)            4.61          NA          NA          NA      NA

Mg (II)             NA        3.46        2.96        2.09    7.72

Ca (II)           3.32        4.05        6.12        8.85    7.85

Ba (II)           6.45          NA          NA          NA      NA

Transition
Metals

Mn (II)           2.49        3.31        3.22        2.83    7.64

Fe (II)           2.58        3.69        2.66        2.41   13.29

Co (II)           2.34        3.18         3.2        6.95   17.76

Ni (II)             NA          NA        3.78        3.46    7.24

Ag (I)              NA          NA          NA         4.2   10.15

Cu (II)            2.6        2.72        6.85        3.12    3.63

Zn (II)           2.09        2.23        2.61        2.43    9.41

Cd (II)           2.74        4.11        2.87        5.63    9.03

Hg (II)           3.44        2.44        3.09        4.38    7.22

Pb (II)             NA        3.48        3.31         2.1     3.4

NA: inference scores were not available in the CTD for this
disease-metal combination.
Source: The Comparative Toxicogenomics Database. http://ctdbase.org.
Accessed 21 February, 2013.

Table S3. The associations between inference score relating CVD to
metal exposures with the physical and chemical properties of metal
ions using robust univariate regressions for cardiac arrhythmia.

Property                 Group        N   [N.sub.trim]  Intercept
                                     (a)      (b)

AN                       s-block       5             1   1.38E+00

AN                       transition    6             1   7.55E-01

AN/[BETA]IP              s-block       5             1   1.40E+00

AN/[BETA]IP              transition    6             1   7.74E-01

AR                       s-block       5             1   8.21E-01

AR                       transition    6             1  -2.04E-01

[BETA][E.sup.0]          s-block       5             1   2.59E+00

[BETA][E.sup.0]          transition    6             1   9.58E-01

[rho]                    s-block       5             1   1.34E+00

[rho]                    transition    6             1   3.89E-01

[BETA]IP                 s-block       5             1   2.61E+00

[BETA]IP                 transition    6             1   8.13E-01

log([K.sub.OH])          s-block       5             1  -5.04E-01

log([K.sub.OH])          transition    6             1   1.13E+00

MP                       s-block       5             1   1.61E+00

MP                       transition    6             1   1.20E+00

[pK.sub.sp](C[O.sub.3])  transition    5             1   1.28E+00

r                        s-block       5             1   1.01E+00

r                        transition    6             1   3.60E-01

[[sigma].sub.p]          s-block       5             1   3.43E+00

[[sigma].sub.p]          transition    5             1   1.52E+00

[X.sub.m]                s-block       5             1   3.27E+00

[X.sub.m]                transition    6             1  -3.72E-02

X[m.sup.2]r              s-block       5             1   6.93E-01

X[m.sup.2]r              transition    6             1   4.90E-01

Z                        s-block       5             1   1.55E+00

Z/AR                     s-block       5             1   1.91E+00

Z/AR                     transition    6             1   2.03E+00

[Z.sup.2]/r              s-block       5             1   1.64E+00

[Z.sup.2]/r              transition    6             1   1.45E+00

Property                 Group       Slope (c)  Standardized     SE
                                                  Slope (d)

AN                       s-block      5.86E-03      1.89E-04  5.25E-03

AN                       transition   5.86E-03      2.79E-04  8.95E-04

AN/[BETA]IP              s-block      2.25E-02      3.60E-03  2.20E-02

AN/[BETA]IP              transition   4.23E-02      1.23E-02  1.58E-02

AR                       s-block      3.47E-01      8.67E-01  3.09E-01

AR                       transition   8.75E-01      4.37E+00  3.47E-01

[BETA][E.sup.0]          s-block     -3.65E-01     -2.15E+00  1.09E+00

[BETA][E.sup.0]          transition  -1.09E-01     -1.98E-01  1.38E-01

[rho]                    s-block      1.28E-04      1.13E-07  1.09E-04

[rho]                    transition   6.27E-05      3.09E-08  1.53E-05

[BETA]IP                 s-block     -2.19E-01     -2.71E-01  1.64E-01

[BETA]IP                 transition   8.50E-03      3.86E-03  1.40E-02

log([K.sub.OH])          s-block      1.47E-01      1.23E-01  1.53E-01

log([K.sub.OH])          transition  -2.36E-02     -1.04E-02  1.71E-02

MP                       s-block     -1.20E-04     -1.80E-07  3.72E-04

MP                       transition  -1.80E-04     -1.70E-07  4.84E-05

[pK.sub.sp](C[O.sub.3])  transition   3.13E-02      2.19E-02  2.36E-02

r                        s-block      4.36E-01      1.09E+00  3.31E-01

r                        transition   7.32E-01      2.44E+00  3.66E-01

[[sigma].sub.p]          s-block     -8.37E+00     -2.09E+02  3.25E+00

[[sigma].sub.p]          transition  -5.54E+00     -1.11E+02  1.76E+00

[X.sub.m]                s-block     -1.93E+00     -1.93E+01  1.29E+00

[X.sub.m]                transition   5.53E-01      2.76E+00  3.52E-01

X[m.sup.2]r              s-block      8.95E-01      5.97E+00  8.87E-01

X[m.sup.2]r              transition   1.77E-01      1.12E-01  5.06E-02

Z                        s-block     -8.18E-03     -8.18E-03  2.64E-01

Z/AR                     s-block     -7.08E-01     -1.47E+00  3.42E-01

Z/AR                     transition  -7.05E-01     -3.07E+00  3.07E-01

[Z.sup.2]/r              s-block     -5.63E-02     -2.06E-02  9.44E-02

[Z.sup.2]/r              transition  -9.77E-02     -6.74E-02  6.50E-02

Property                 Group       Lower CL   Upper CL   P-Value

AN                       s-block     -4.43E-03   1.62E-02  2.64E-01

AN                       transition   4.10E-03   7.61E-03  5.97E-11

AN/[BETA]IP              s-block     -2.07E-02   6.56E-02  3.07E-01

AN/[BETA]IP              transition   1.13E-02   7.33E-02  7.52E-03

AR                       s-block     -2.58E-01   9.52E-01  2.61E-01

AR                       transition   1.94E-01   1.56E+00  1.18E-02

[BETA][E.sup.0]          s-block     -2.51E+00   1.78E+00  7.38E-01

[BETA][E.sup.0]          transition  -3.79E-01   1.61E-01  4.29E-01

[rho]                    s-block     -8.60E-05   3.42E-04  2.42E-01

[rho]                    transition   3.27E-05   9.27E-05  4.14E-05

[BETA]IP                 s-block     -5.41E-01   1.03E-01  1.82E-01

[BETA]IP                 transition  -1.89E-02   3.59E-02  5.43E-01

log([K.sub.OH])          s-block     -1.53E-01   4.47E-01  3.37E-01

log([K.sub.OH])          transition  -5.71E-02   9.83E-03  1.66E-01

MP                       s-block     -8.40E-04   6.12E-04  7.54E-01

MP                       transition  -2.80E-04  -8.60E-05  1.89E-04

[pK.sub.sp](C[O.sub.3])  transition  -1.50E-02   7.75E-02  1.86E-01

r                        s-block     -2.13E-01   1.08E+00  1.88E-01

r                        transition   1.53E-02   1.45E+00  4.53E-02

[[sigma].sub.p]          s-block     -1.47E+01  -2.01E+00  9.97E-03

[[sigma].sub.p]          transition  -8.99E+00  -2.09E+00  1.67E-03

[X.sub.m]                s-block     -4.45E+00   6.01E-01  1.35E-01

[X.sub.m]                transition  -1.38E-01   1.24E+00  1.17E-01

X[m.sup.2]r              s-block     -8.44E-01   2.63E+00  3.13E-01

X[m.sup.2]r              transition   7.78E-02   2.76E-01  4.73E-04

Z                        s-block     -5.26E-01   5.09E-01  9.75E-01

Z/AR                     s-block     -1.38E+00  -3.71E-02  3.86E-02

Z/AR                     transition  -1.31E+00  -1.04E-01  2.15E-02

[Z.sup.2]/r              s-block     -2.41E-01   1.29E-01  5.51E-01

[Z.sup.2]/r              transition  -2.25E-01   2.97E-02  1.33E-01

Property                 Group       [R.sup.2]

AN                       s-block      2.48E-01

AN                       transition   8.35E-01

AN/[BETA]IP              s-block      1.66E-01

AN/[BETA]IP              transition   6.08E-01

AR                       s-block      2.36E-01

AR                       transition   3.99E-01

[BETA][E.sup.0]          s-block      4.02E-01

[BETA][E.sup.0]          transition   1.35E-01

[rho]                    s-block      4.03E-01

[rho]                    transition   5.90E-01

[BETA]IP                 s-block      4.31E-01

[BETA]IP                 transition   8.46E-02

log([K.sub.OH])          s-block      5.99E-01

log([K.sub.OH])          transition   3.29E-02

MP                       s-block      4.70E-01

MP                       transition   5.70E-01

[pK.sub.sp](C[O.sub.3])  transition   3.69E-01

r                        s-block      4.31E-01

r                        transition   1.14E-01

[[sigma].sub.p]          s-block      6.89E-01

[[sigma].sub.p]          transition   6.99E-01

[X.sub.m]                s-block      4.59E-01

[X.sub.m]                transition   3.69E-02

X[m.sup.2]r              s-block      5.41E-01

X[m.sup.2]r              transition   4.82E-01

Z                        s-block      3.57E-01

Z/AR                     s-block      5.73E-01

Z/AR                     transition   3.71E-01

[Z.sup.2]/r              s-block      4.90E-01

[Z.sup.2]/r              transition   2.59E-02

(a) Number of metals included in model; (b) number of metals
trimmed from the robust model based on total number for which data
were available; (c) slope given per unit change in property;
(d)standardized per interquartile range increase in property;
SE: standard error; CL: 95% confidence limit.

Table S4. The associations between inference score relating CVD
to metal exposures with the physical and chemical properties of
metal ions using robust univariate regressions for myocardial
infarction.

Property                 Group        N   [N.sub.trim]  Intercept
                                     (a)      (b)

AN                       s-block       4             1   5.94E-01

AN                       transition    6             2   1.14E+00

AN/[BETA]IP              s-block       4             1   6.85E-01

AN/[BETA]IP              transition    6             2   1.13E+00

AR                       s-block       4             1  -5.75E-01

AR                       transition    6             2   8.26E-01

[BETA][E.sup.0]          s-block       4             1   2.83E+00

[BETA][E.sup.0]          transition    6             2   1.24E+00

[rho]                    s-block       4             1   2.73E+00

[rho]                    transition    6             2   1.29E+00

[BETA]IP                 s-block       4             1   2.51E+00

[BETA]IP                 transition    6             2   1.03E+00

log([K.sub.OH])          s-block       4             1  -1.90E+00

log([K.sub.OH])          transition    6             2   1.07E+00

MP                       s-block       4             1   2.27E+00

MP                       transition    6             2   1.01E+00

[pK.sub.sp](C[O.sub.3])  transition    6             1   3.69E-01

r                        s-block       4             1   1.83E-01

r                        transition    6             2   1.02E+00

[[sigma].sub.p]          s-block       4             1  -4.62E-01

[[sigma].sub.p]          transition    6             2   9.63E-01

[X.sub.m]                s-block       4             1   2.65E+00

[X.sub.m]                transition    6             2   1.07E+00

X[m.sup.2]r              s-block       4             1   3.96E+00

X[m.sup.2]r              transition    6             2   1.09E+00

Z                        s-block       4             1   2.65E+00

Z/AR                     s-block       4             1   2.39E+00

Z/AR                     transition    6             2   1.07E+00

[Z.sup.2]/r              s-block       4             1   2.10E+00

[Z.sup.2]/r              transition    6             2   1.17E+00

Property                 Group       Slope (c)  Standardized     SE
                                                  Slope (d)

AN                       s-block      5.04E-02      1.62E-03  1.47E-02

AN                       transition  -3.30E-04     -1.60E-05  3.53E-03

AN/[BETA]IP              s-block      2.35E-01      3.75E-02  5.40E-02

AN/[BETA]IP              transition  -7.30E-04     -2.10E-04  2.47E-02

AR                       s-block      1.01E+00      2.54E+00  3.92E-01

AR                       transition   2.23E-01      1.12E+00  5.88E-01

[BETA][E.sup.0]          s-block     -4.95E-01     -2.91E+00  1.26E+00

[BETA][E.sup.0]          transition  -2.29E-01     -4.17E-01  2.32E-01

[rho]                    s-block     -8.50E-04     -7.50E-07  3.91E-04

[rho]                    transition  -1.80E-05     -8.70E-09  3.91E-05

[BETA]IP                 s-block     -1.87E-01     -2.31E-01  2.69E-01

[BETA]IP                 transition   9.54E-03      4.34E-03  2.83E-02

log([K.sub.OH])          s-block      2.68E-01      2.24E-01  1.26E-01

log([K.sub.OH])          transition   6.95E-03      3.06E-03  2.70E-02

MP                       s-block     -9.10E-04     -1.40E-06  4.57E-04

MP                       transition   1.05E-04      1.00E-07  1.34E-04

[pK.sub.sp](C[O.sub.3])  transition  -7.08E-02     -4.95E-02  5.98E-02

r                        s-block      1.32E+00      3.29E+00  9.51E-01

r                        transition   1.20E-01      3.99E-01  4.62E-01

[[sigma].sub.p]          s-block      1.07E+01      2.67E+02  7.33E+00

[[sigma].sub.p]          transition   1.29E+00      2.58E+01  3.69E+00

[X.sub.m]                s-block     -1.18E+00     -1.18E+01  1.65E+00

[X.sub.m]                transition   2.81E-02      1.40E-01  3.54E-01

X[m.sup.2]r              s-block     -2.28E+00     -1.52E+01  1.07E+00

X[m.sup.2]r              transition   1.11E-02      7.04E-03  5.68E-02

Z                        s-block     -6.64E-01     -6.64E-01  2.56E-01

Z/AR                     s-block     -8.86E-01     -1.85E+00  4.17E-01

Z/AR                     transition   3.95E-02      1.72E-01  5.84E-01

[Z.sup.2]/r              s-block     -1.60E-01     -5.83E-02  6.59E-02

[Z.sup.2]/r              transition  -8.35E-03     -5.76E-03  8.51E-02

Property                 Group       Lower CL   Upper CL   P-Value

AN                       s-block      2.16E-02   7.91E-02  6.07E-04

AN                       transition  -7.25E-03   6.60E-03  9.26E-01

AN/[BETA]IP              s-block      1.29E-01   3.41E-01  1.40E-05

AN/[BETA]IP              transition  -4.91E-02   4.77E-02  9.76E-01

AR                       s-block      2.47E-01   1.78E+00  9.59E-03

AR                       transition  -9.29E-01   1.38E+00  7.04E-01

[BETA][E.sup.0]          s-block     -2.96E+00   1.97E+00  6.93E-01

[BETA][E.sup.0]          transition  -6.84E-01   2.25E-01  3.23E-01

[rho]                    s-block     -1.61E-03  -8.00E-05  3.04E-02

[rho]                    transition  -9.40E-05   5.89E-05  6.50E-01

[BETA]IP                 s-block     -7.14E-01   3.39E-01  4.85E-01

[BETA]IP                 transition  -4.60E-02   6.50E-02  7.36E-01

log([K.sub.OH])          s-block      2.06E-02   5.16E-01  3.37E-02

log([K.sub.OH])          transition  -4.60E-02   5.99E-02  7.97E-01

MP                       s-block     -1.80E-03  -1.10E-05  4.73E-02

MP                       transition  -1.60E-04   3.68E-04  4.33E-01

[pK.sub.sp](C[O.sub.3])  transition  -1.88E-01   4.63E-02  2.36E-01

r                        s-block     -5.46E-01   3.18E+00  1.66E-01

r                        transition  -7.86E-01   1.03E+00  7.96E-01

[[sigma].sub.p]          s-block     -3.69E+00   2.51E+01  1.45E-01

[[sigma].sub.p]          transition  -5.94E+00   8.52E+00  7.27E-01

[X.sub.m]                s-block     -4.41E+00   2.06E+00  4.76E-01

[X.sub.m]                transition  -6.67E-01   7.23E-01  9.37E-01

X[m.sup.2]r              s-block     -4.38E+00  -1.76E-01  3.36E-02

X[m.sup.2]r              transition  -1.00E-01   1.22E-01  8.45E-01

Z                        s-block     -1.16E+00  -1.63E-01  9.42E-03

Z/AR                     s-block     -1.70E+00  -6.93E-02  3.35E-02

Z/AR                     transition  -1.11E+00   1.18E+00  9.46E-01

[Z.sup.2]/r              s-block     -2.89E-01  -3.07E-02  1.53E-02

[Z.sup.2]/r              transition  -1.75E-01   1.58E-01  9.22E-01

Property                 Group       [R.sup.2]

AN                       s-block      8.55E-01

AN                       transition   1.03E-01

AN/[BETA]IP              s-block      9.04E-01

AN/[BETA]IP              transition   1.20E-01

AR                       s-block      7.70E-01

AR                       transition   1.13E-01

[BETA][E.sup.0]          s-block      1.96E-01

[BETA][E.sup.0]          transition   3.37E-02

[rho]                    s-block      6.89E-01

[rho]                    transition   2.27E-01

[BETA]IP                 s-block      4.41E-01

[BETA]IP                 transition   2.94E-02

log([K.sub.OH])          s-block      6.80E-01

log([K.sub.OH])          transition   2.59E-01

MP                       s-block      6.49E-01

MP                       transition   5.38E-01

[pK.sub.sp](C[O.sub.3])  transition   5.10E-02

r                        s-block      7.08E-01

r                        transition   8.45E-02

[[sigma].sub.p]          s-block      4.96E-01

[[sigma].sub.p]          transition   4.26E-01

[X.sub.m]                s-block      4.23E-01

[X.sub.m]                transition   1.92E-02

X[m.sup.2]r              s-block      6.81E-01

X[m.sup.2]r              transition   4.49E-03

Z                        s-block      7.62E-01

Z/AR                     s-block      6.81E-01

Z/AR                     transition   3.29E-01

[Z.sup.2]/r              s-block      7.36E-01

[Z.sup.2]/r              transition   5.87E-02

(a) Number of metals included in model; (b) number of metals
trimmed from the robust model based on total number for which
data were available; (c) slope given per unit change in property;
(d) standardized per interquartile range increase in property;
SE: standard error; CL: 95% confidence limit.

Table S5. The associations between inference score relating CVD
to metal exposures with the physical and chemical properties of
metal ions using robust univariate regressions for myocardial
ischemia.

Property                 Group        N   [N.sub.trim]  Intercept
                                     (a)      (b)

AN                       s-block       4             1   6.26E-01

AN                       transition    7             2   1.09E+00

AN/[BETA]IP              s-block       4             1   7.24E-01

AN/[BETA]IP              transition    7             2   1.09E+00

AR                       s-block       4             1  -2.96E+00

AR                       transition    7             2   1.07E+00

[BETA][E.sup.0]          s-block       4             1  -2.50E+00

[BETA][E.sup.0]          transition    7             2   1.18E+00

[rho]                    s-block       4             1   2.66E+00

[rho]                    transition    7             2   9.55E-01

[BETA]IP                 s-block       4             1   3.31E+00

[BETA]IP                 transition    7             2   1.24E+00

log([K.sub.OH])          s-block       4             1  -1.84E+00

log([K.sub.OH])          transition    7             2   1.01E+00

MP                       s-block       4             1   1.68E+00

MP                       transition    7             2   1.07E+00

[pK.sub.sp](C[O.sub.3])  transition    6             2   3.78E-01

r                        s-block       4             1  -1.41E+00

r                        transition    7             2   1.02E+00

[[sigma].sub.p]          s-block       4             1  -3.59E-01

[[sigma].sub.p]          transition    6             2   9.53E-01

[X.sub.m]                s-block       4             1   3.55E+00

[X.sub.m]                transition    7             2   7.52E-01

X[m.sup.2]r              s-block       4             1   4.33E+00

X[m.sup.2]r              transition    7             2   1.04E+00

Z                        s-block       4             1   1.75E+00

Z/AR                     s-block       4             1   2.01E+00

Z/AR                     transition    7             2   9.22E-01

[Z.sup.2]/r              s-block       4             1   2.12E+00

[Z.sup.2]/r              transition    7             2   1.24E+00

Property                 Group       Slope (c)  Standardized     SE
                                                  Slope (d)

AN                       s-block      5.84E-02      1.89E-03  1.51E-02

AN                       transition   6.56E-04      3.13E-05  2.02E-03

AN/[BETA]IP              s-block      2.76E-01      4.41E-02  4.16E-02

AN/[BETA]IP              transition   5.49E-03      1.59E-03  1.43E-02

AR                       s-block      2.59E+00      6.46E+00  5.19E-01

AR                       transition   4.04E-02      2.02E-01  3.35E-01

[BETA][E.sup.0]          s-block      1.56E+00      9.18E+00  6.97E-01

[BETA][E.sup.0]          transition  -1.19E-01     -2.16E-01  1.41E-01

[rho]                    s-block     -7.50E-04     -6.70E-07  4.32E-04

[rho]                    transition   1.81E-05      8.93E-09  2.18E-05

[BETA]IP                 s-block     -2.85E-01     -3.52E-01  1.08E-01

[BETA]IP                 transition  -1.28E-02     -5.80E-03  1.69E-02

log([K.sub.OH])          s-block      2.67E-01      2.22E-01  1.11E-01

log([K.sub.OH])          transition   1.45E-02      6.37E-03  1.40E-02

MP                       s-block     -2.20E-04     -3.40E-07  8.12E-04

MP                       transition   4.53E-05      4.31E-08  7.47E-05

[pK.sub.sp](C[O.sub.3])  transition  -6.22E-02      1.89E-03  2.36E-02

r                        s-block      3.30E+00      3.13E-05  5.14E-01

r                        transition   1.25E-01      4.41E-02  2.58E-01

[[sigma].sub.p]          s-block      1.04E+01      1.59E-03  6.93E+00

[[sigma].sub.p]          transition   1.72E+00      6.46E+00  1.80E+00

[X.sub.m]                s-block     -1.82E+00      2.02E-01  5.67E-01

[X.sub.m]                transition   2.00E-01      9.18E+00  1.88E-01

X[m.sup.2]r              s-block     -2.60E+00     -2.16E-01  2.62E-01

X[m.sup.2]r              transition   2.57E-02     -6.70E-07  3.12E-02

Z                        s-block     -1.50E-01      8.93E-09  5.26E-01

Z/AR                     s-block     -5.91E-01     -5.80E-03  7.28E-01

Z/AR                     transition   1.29E-01      2.22E-01  3.37E-01

[Z.sup.2]/r              s-block     -1.49E-01      6.37E-03  6.78E-02

[Z.sup.2]/r              transition  -2.35E-02     -3.40E-07  4.68E-02

Property                 Group       Lower CL   Upper CL   P-Value

AN                       s-block      2.89E-02   8.80E-02  1.08E-04

AN                       transition  -3.31E-03   4.62E-03  7.46E-01

AN/[BETA]IP              s-block      1.94E-01   3.57E-01  3.51E-11

AN/[BETA]IP              transition  -2.25E-02   3.35E-02  7.01E-01

AR                       s-block      1.57E+00   3.60E+00  6.42E-07

AR                       transition  -6.17E-01   6.98E-01  9.04E-01

[BETA][E.sup.0]          s-block      1.94E-01   2.93E+00  2.52E-02

[BETA][E.sup.0]          transition  -3.95E-01   1.57E-01  3.98E-01

[rho]                    s-block     -1.60E-03   9.39E-05  8.14E-02

[rho]                    transition  -2.50E-05   6.09E-05  4.06E-01

[BETA]IP                 s-block     -4.97E-01  -7.28E-02  8.48E-03

[BETA]IP                 transition  -4.58E-02   2.03E-02  4.49E-01

log([K.sub.OH])          s-block      4.88E-02   4.84E-01  1.64E-02

log([K.sub.OH])          transition  -1.30E-02   4.20E-02  3.01E-01

MP                       s-block     -1.81E-03   1.37E-03  7.88E-01

MP                       transition  -1.00E-04   1.92E-04  5.44E-01

[pK.sub.sp](C[O.sub.3])  transition  -1.09E-01  -1.59E-02  8.42E-03

r                        s-block      2.29E+00   4.30E+00  1.46E-10

r                        transition  -3.81E-01   6.31E-01  6.28E-01

[[sigma].sub.p]          s-block     -3.20E+00   2.40E+01  1.34E-01

[[sigma].sub.p]          transition  -1.81E+00   5.25E+00  3.40E-01

[X.sub.m]                s-block     -2.93E+00  -7.12E-01  1.30E-03

[X.sub.m]                transition  -1.69E-01   5.69E-01  2.88E-01

X[m.sup.2]r              s-block     -3.11E+00  -2.09E+00  2.88E-23

X[m.sup.2]r              transition  -3.54E-02   8.69E-02  4.09E-01

Z                        s-block     -1.18E+00   8.80E-01  7.75E-01

Z/AR                     s-block     -2.02E+00   8.36E-01  4.17E-01

Z/AR                     transition  -5.31E-01   7.89E-01  7.02E-01

[Z.sup.2]/r              s-block     -2.82E-01  -1.63E-02  2.78E-02

[Z.sup.2]/r              transition  -1.15E-01   6.83E-02  6.16E-01

Property                 Group       [R.sup.2]

AN                       s-block      8.40E-01

AN                       transition   1.87E-01

AN/[BETA]IP              s-block      9.41E-01

AN/[BETA]IP              transition   2.44E-01

AR                       s-block      8.72E-01

AR                       transition   8.40E-02

[BETA][E.sup.0]          s-block      7.15E-01

[BETA][E.sup.0]          transition   1.48E-02

[rho]                    s-block      6.03E-01

[rho]                    transition   2.48E-01

[BETA]IP                 s-block      7.76E-01

[BETA]IP                 transition   2.91E-01

log([K.sub.OH])          s-block      7.42E-01

log([K.sub.OH])          transition   9.06E-02

MP                       s-block      2.72E-01

MP                       transition   3.56E-03

[pK.sub.sp](C[O.sub.3])  transition   6.34E-01

r                        s-block      9.21E-01

r                        transition   3.84E-01

[[sigma].sub.p]          s-block      5.29E-01

[[sigma].sub.p]          transition   3.70E-01

[X.sub.m]                s-block      8.38E-01

[X.sub.m]                transition   2.14E-01

X[m.sup.2]r              s-block      9.80E-01

X[m.sup.2]r              transition   3.36E-01

Z                        s-block      4.68E-01

Z/AR                     s-block      6.56E-01

Z/AR                     transition   9.23E-03

[Z.sup.2]/r              s-block      7.08E-01

[Z.sup.2]/r              transition   4.03E-01

(a) Number of metals included in model; (b) number of metals trimmed
from the robust model based on total number for which data were
available; (c) slope given per unit change in property;
(d) standardized per interquartile range increase in property;
SE: standard error; CL: 95% confidence limit.

Table S6. The associations between inference score relating CVD
to metal exposures with the physical and chemical properties of
metal ions using robust univariate regressions for thrombosis.

Property                 Group        N   [N.sub.trim]  Intercept
                                     (a)      (b)

AN                       s-block       4             1   8.31E-01

AN                       transition    8             2   1.28E+00

AN/[BETA]IP              s-block       4             1   8.18E-01

AN/[BETA]IP              transition    8             2   1.25E+00

AR                       s-block       4             1   2.07E-01

AR                       transition    8             2  -1.77E+00

[BETA][E.sup.0]          s-block       4             1   3.61E-01

[BETA][E.sup.0]          transition    8             2   1.25E+00

[rho]                    s-block       4             1   1.95E-02

[rho]                    transition    8             2   8.99E-01

[BETA]IP                 s-block       4             1   1.73E+00

[BETA]IP                 transition    8             2   1.65E+00

log([K.sub.OH])          s-block       4             1  -1.02E+00

log([K.sub.OH])          transition    8             2   9.51E-01

MP                       s-block       4             1   1.34E+00

MP                       transition    8             2   1.23E+00

[pK.sub.sp](C[O.sub.3])  transition    7             2  -6.76E-01

r                        s-block       4             1   4.68E-01

r                        transition    8             2   1.13E+00

[[sigma].sub.p]          s-block       4             1   5.63E+00

[[sigma].sub.p]          transition    8             2   2.26E+00

[X.sub.m]                s-block       4             1   1.84E+00

[X.sub.m]                transition    8             2   1.76E+00

X[m.sup.2]r              s-block       4             1   1.37E+00

X[m.sup.2]r              transition    8             2   7.40E-01

Z                        s-block       4             1   1.40E+00

Z/AR                     s-block       4             1   1.34E+00

Z/AR                     transition    8             2   5.08E+00

[Z.sup.2]/r              s-block       4             1   1.15E+00

[Z.sup.2]/r              transition    8             2   1.46E+00

Property                 Group       Slope (c)  Standardized     SE
                                                  Slope (d)


AN                       s-block      1.36E-02      4.38E-04  2.36E-02

AN                       transition  -6.42E-04     -3.10E-05  6.25E-03

AN/[BETA]IP              s-block      7.66E-02      1.22E-02  8.86E-02

AN/[BETA]IP              transition  -4.14E-04     -1.20E-04  4.32E-02

AR                       s-block      4.29E-01      1.07E+00  3.39E-01

AR                       transition   2.21E+00      1.10E+01  5.44E-01

[BETA][E.sup.0]          s-block      2.25E-01      1.33E+00  5.49E-01

[BETA][E.sup.0]          transition  -8.10E-03     -1.47E-02  4.16E-01

[rho]                    s-block      1.36E-03      1.20E-06  1.56E-04

[rho]                    transition   3.77E-05      1.86E-08  6.93E-05

[BETA]IP                 s-block     -1.35E-01     -1.66E-01  8.69E-02

[BETA]IP                 transition  -4.16E-02     -1.89E-02  4.77E-02

log([K.sub.OH])          s-block      1.49E-01      1.24E-01  7.34E-02

log([K.sub.OH])          transition   3.64E-02      1.60E-02  4.15E-02

MP                       s-block     -6.81E-04     -1.00E-06  3.80E-04

MP                       transition   2.06E-05      1.96E-08  2.39E-04

[pK.sub.sp](C[O.sub.3])  transition  -1.86E-01     -1.30E-01  8.77E-02

r                        s-block      5.35E-01      1.34E+00  3.88E-01

r                        transition   1.40E-01      4.66E-01  6.95E-01

[[sigma].sub.p]          s-block     -1.97E+01     -4.92E+02  3.71E+00

[[sigma].sub.p]          transition  -1.02E+01     -2.04E+02  3.01E+00

[X.sub.m]                s-block     -8.47E-01     -8.47E+00  5.19E-01

[X.sub.m]                transition  -2.73E-01     -1.36E+00  6.32E-01

X[m.sup.2]r              s-block     -4.08E-01     -2.72E+00  6.99E-01

X[m.sup.2]r              transition   2.04E-01      1.29E-01  1.44E-01

Z                        s-block     -3.29E-01     -3.29E-01  2.40E-01

Z/AR                     s-block     -4.82E-01     -1.00E+00  2.70E-01

Z/AR                     transition  -2.60E+00     -1.13E+01  5.72E-01

[Z.sup.2]/r              s-block     -7.73E-02     -2.82E-02  4.86E-02

[Z.sup.2]/r              transition  -4.57E-02     -3.15E-02  8.46E-02

Property                 Group       Lower CL   Upper CL   P-Value

AN                       s-block     -3.28E-02   5.99E-02  5.66E-01

AN                       transition  -1.29E-02   1.16E-02  9.18E-01

AN/[BETA]IP              s-block     -9.70E-02   2.50E-01  3.87E-01

AN/[BETA]IP              transition  -8.51E-02   8.43E-02  9.92E-01

AR                       s-block     -2.36E-01   1.09E+00  2.06E-01

AR                       transition   1.14E+00   3.27E+00  4.89E-05

[BETA][E.sup.0]          s-block     -8.51E-01   1.30E+00  6.81E-01

[BETA][E.sup.0]          transition  -8.23E-01   8.07E-01  9.84E-01

[rho]                    s-block      1.05E-03   1.66E-03  4.10E-18

[rho]                    transition  -9.81E-05   1.74E-04  5.86E-01

[BETA]IP                 s-block     -3.05E-01   3.57E-02  1.21E-01

[BETA]IP                 transition  -1.35E-01   5.19E-02  3.83E-01

log([K.sub.OH])          s-block      4.64E-03   2.92E-01  4.31E-02

log([K.sub.OH])          transition  -4.50E-02   1.18E-01  3.81E-01

MP                       s-block     -1.43E-03   6.45E-05  7.34E-02

MP                       transition  -4.48E-04   4.89E-04  9.31E-01

[pK.sub.sp](C[O.sub.3])  transition  -3.58E-01  -1.42E-02  3.38E-02

r                        s-block     -2.26E-01   1.29E+00  1.68E-01

r                        transition  -1.22E+00   1.50E+00  8.40E-01

[[sigma].sub.p]          s-block     -2.69E+01  -1.24E+01  1.14E-07

[[sigma].sub.p]          transition  -1.61E+01  -4.31E+00  6.93E-04

[X.sub.m]                s-block     -1.87E+00   1.71E-01  1.03E-01

[X.sub.m]                transition  -1.51E+00   9.66E-01  6.66E-01

X[m.sup.2]r              s-block     -1.78E+00   9.62E-01  5.59E-01

X[m.sup.2]r              transition  -7.87E-02   4.88E-01  1.57E-01

Z                        s-block     -8.00E-01   1.41E-01  1.70E-01

Z/AR                     s-block     -1.01E+00   4.69E-02  7.41E-02

Z/AR                     transition  -3.72E+00  -1.47E+00  5.75E-06

[Z.sup.2]/r              s-block     -1.73E-01   1.80E-02  1.12E-01

[Z.sup.2]/r              transition  -2.11E-01   1.20E-01  5.89E-01

Property                 Group       [R.sup.2]

AN                       s-block      1.42E-01

AN                       transition   3.30E-01

AN/[BETA]IP              s-block      2.72E-01

AN/[BETA]IP              transition   4.23E-01

AR                       s-block      4.45E-01

AR                       transition   6.62E-01

[BETA][E.sup.0]          s-block      7.77E-02

[BETA][E.sup.0]          transition   1.48E-01

[rho]                    s-block      8.43E-01

[rho]                    transition   2.54E-01

[BETA]IP                 s-block      5.46E-01

[BETA]IP                 transition   1.22E-01

log([K.sub.OH])          s-block      6.72E-01

log([K.sub.OH])          transition   2.08E-02

MP                       s-block      6.16E-01

MP                       transition   8.84E-02

[pK.sub.sp](C[O.sub.3])  transition   2.73E-01

r                        s-block      4.87E-01

r                        transition   4.15E-01

[[sigma].sub.p]          s-block      5.97E-01

[[sigma].sub.p]          transition   6.76E-01

[X.sub.m]                s-block      5.71E-01

[X.sub.m]                transition   1.16E-03

X[m.sup.2]r              s-block      1.46E-01

X[m.sup.2]r              transition   2.88E-01

Z                        s-block      4.85E-01

Z/AR                     s-block      6.15E-01

Z/AR                     transition   6.53E-01

[Z.sup.2]/r              s-block      5.58E-01

[Z.sup.2]/r              transition   1.91E-01

(a) Number of metals included in model; (b) number of metals
trimmed from the robust model based on total number for which
data were available; (c) slope given per unit change in property;
(d) standardized per interquartile range increase in property;
SE: standard error; CL: 95% confidence limit.

Table S7. The associations between inference score relating CVD
to metal exposures with the physical and chemical properties of
metal ions using robust univariate regressions for stroke.

Property                 Group        N   [N.sub.trim]  Intercept
                                     (a)      (b)

AN                       s-block       4             1   1.24E+00

AN                       transition    8             2   2.51E+00

AN/[BETA]IP              s-block       4             1   1.51E+00

AN/[BETA]IP              transition    8             2   2.40E+00

AR                       s-block       4             1   2.31E+00

AR                       transition    8             2   4.73E+00

[BETA][E.sup.0]          s-block       4             1   4.16E+00

[BETA][E.sup.0]          transition    8             2   2.57E+00

[rho]                    s-block       4             1   1.51E+00

[rho]                    transition    8             2   2.87E+00

[BETA]IP                 s-block       4             1   1.46E+00

[BETA]IP                 transition    8             2   1.84E+00

log([K.sub.OH])          s-block       4             1   3.23E+00

log([K.sub.OH])          transition    8             2   2.06E+00

MP                       s-block       4             1   1.67E+00

MP                       transition    8             2   1.68E+00

[pK.sub.sp](C[O.sub.3])  transition    7             2  -2.92E-02

r                        s-block       4             1   2.21E+00

r                        transition    8             2   2.86E+00

[[sigma].sub.p]          s-block       4             1   3.73E+00

[[sigma].sub.p]          transition    7             2   2.19E+00

[X.sub.m]                s-block       4             1   1.44E+00

[X.sub.m]                transition    8             2   4.19E+00

X[m.sup.2]r              s-block       4             1  -4.86E-01

X[m.sup.2]r              transition    8             2   2.66E+00

Z                        s-block       4             1   1.53E+00

Z/AR                     s-block       4             1   1.64E+00

Z/AR                     transition    8             2   2.06E+00

[Z.sup.2]/r              s-block       4             1   1.75E+00

[Z.sup.2]/r              transition    8             2   1.87E+00

Property                 Group       Slope (c)  Standardized     SE
                                                  Slope (d)

AN                       s-block      3.81E-02      1.23E-03  7.35E-03

AN                       transition  -1.04E-02     -5.00E-04  7.35E-03

AN/[BETA]IP              s-block      1.21E-01      1.94E-02  9.23E-02

AN/[BETA]IP              transition  -6.72E-02     -1.95E-02  5.16E-02

AR                       s-block     -2.04E-01     -5.11E-01  3.32E-01

AR                       transition  -1.96E+00     -9.80E+00  1.06E+00

[BETA][E.sup.0]          s-block     -8.55E-01     -5.03E+00  4.84E-01

[BETA][E.sup.0]          transition  -4.77E-01     -8.67E-01  3.78E-01

[rho]                    s-block      3.24E-04      2.88E-07  1.25E-04

[rho]                    transition  -8.55E-05     -4.20E-08  8.77E-05

[BETA]IP                 s-block      8.19E-02      1.01E-01  6.53E-02

[BETA]IP                 transition   2.37E-02      1.08E-02  6.51E-02

log([K.sub.OH])          s-block     -9.90E-02     -8.25E-02  4.54E-02

log([K.sub.OH])          transition   1.49E-03      6.54E-04  5.71E-02

MP                       s-block      3.73E-04      5.74E-07  1.14E-04

MP                       transition   3.44E-04      3.27E-07  2.90E-04

[pK.sub.sp](C[O.sub.3])  transition  -2.10E-01     -1.47E-01  1.10E-01

r                        s-block     -2.84E-01     -7.11E-01  3.66E-01

r                        transition  -9.10E-01     -3.03E+00  8.57E-01

[[sigma].sub.p]          s-block     -9.63E+00     -2.41E+02  1.33E+00

[[sigma].sub.p]          transition  -1.62E+00     -3.24E+01  7.40E+00

[X.sub.m]                s-block      4.75E-01      4.75E+00  4.19E-01

[X.sub.m]                transition  -1.13E+00     -5.67E+00  7.39E-01

X[m.sup.2]r              s-block      2.53E+00      1.69E+01  8.28E-02

X[m.sup.2]r              transition  -1.86E-01     -1.18E-01  1.11E-01

Z                        s-block      2.60E-01      2.60E-01  6.63E-02

Z/AR                     s-block      3.35E-01      6.98E-01  1.40E-01

Z/AR                     transition   9.38E-03      4.08E-02  5.86E-01

[Z.sup.2]/r              s-block      5.94E-02      2.17E-02  2.29E-02

[Z.sup.2]/r              transition   4.47E-02      3.08E-02  1.12E-01

Property                 Group       Lower CL   Upper CL    P-Value

AN                       s-block      2.37E-02   5.25E-02   2.18E-07

AN                       transition  -2.48E-02   3.95E-03   1.55E-01

AN/[BETA]IP              s-block     -5.95E-02   3.02E-01   1.88E-01

AN/[BETA]IP              transition  -1.68E-01   3.39E-02   1.93E-01

AR                       s-block     -8.54E-01   4.45E-01   5.37E-01

AR                       transition  -4.03E+00   1.13E-01   6.39E-02

[BETA][E.sup.0]          s-block     -1.80E+00   9.35E-02   7.73E-02

[BETA][E.sup.0]          transition  -1.22E+00   2.63E-01   2.07E-01

[rho]                    s-block      7.83E-05   5.70E-04   9.77E-03

[rho]                    transition  -2.57E-04   8.64E-05   3.30E-01

[BETA]IP                 s-block     -4.60E-02   2.10E-01   2.09E-01

[BETA]IP                 transition  -1.04E-01   1.51E-01   7.16E-01

log([K.sub.OH])          s-block     -1.88E-01  -9.89E-03   2.94E-02

log([K.sub.OH])          transition  -1.10E-01   1.13E-01   9.79E-01

MP                       s-block      1.49E-04   5.97E-04   1.09E-03

MP                       transition  -2.24E-04   9.12E-04   2.35E-01

[pK.sub.sp](C[O.sub.3])  transition  -4.27E-01   5.80E-03   5.65E-02

r                        s-block     -1.00E+00   4.32E-01   4.37E-01

r                        transition  -2.59E+00   7.71E-01   2.89E-01

[[sigma].sub.p]          s-block     -1.22E+01  -7.03E+00   4.11E-13

[[sigma].sub.p]          transition  -1.61E+01   1.29E+01   8.27E-01

[X.sub.m]                s-block     -3.45E-01   1.30E+00   2.56E-01

[X.sub.m]                transition  -2.58E+00   3.14E-01   1.25E-01

X[m.sup.2]r              s-block      2.37E+00   2.69E+00  4.51E-205

X[m.sup.2]r              transition  -4.05E-01   3.21E-02   9.46E-02

Z                        s-block      1.30E-01   3.90E-01   8.74E-05

Z/AR                     s-block      6.02E-02   6.10E-01   1.69E-02

Z/AR                     transition  -1.14E+00   1.16E+00   9.87E-01

[Z.sup.2]/r              s-block      1.46E-02   1.04E-01   9.43E-03

[Z.sup.2]/r              transition  -1.75E-01   2.64E-01   6.90E-01

Property                 Group       [R.sup.2]

AN                       s-block      7.33E-01

AN                       transition   1.60E-01

AN/[BETA]IP              s-block      4.37E-02

AN/[BETA]IP              transition   2.09E-01

AR                       s-block      1.60E-01

AR                       transition   2.85E-01

[BETA][E.sup.0]          s-block      1.85E-01

[BETA][E.sup.0]          transition   2.10E-01

[rho]                    s-block      7.69E-01

[rho]                    transition   7.06E-02

[BETA]IP                 s-block      4.41E-01

[BETA]IP                 transition   1.38E-01

log([K.sub.OH])          s-block      7.03E-01

log([K.sub.OH])          transition   7.25E-03

MP                       s-block      8.42E-01

MP                       transition   2.29E-01

[pK.sub.sp](C[O.sub.3])  transition   5.48E-01

r                        s-block      2.32E-01

r                        transition   9.57E-02

[[sigma].sub.p]          s-block      8.26E-01

[[sigma].sub.p]          transition   8.46E-02

[X.sub.m]                s-block      3.92E-01

[X.sub.m]                transition   1.43E-01

X[m.sup.2]r              s-block      9.92E-01

X[m.sup.2]r              transition   3.22E-01

Z                        s-block      8.85E-01

Z/AR                     s-block      7.41E-01

Z/AR                     transition   6.14E-02

[Z.sup.2]/r              s-block      7.71E-01

[Z.sup.2]/r              transition   3.24E-02

(a) Number of metals included in model; (b) number of metals
trimmed from the robust model based on total number for which
data were available; (c) slope given per unit change in property;
(d) standardized per interquartile range increase in property;
SE: standard error; CL: 95% confidence limit.

Table S8. Comparisons of regression results from the various
robust regression methods for cardiac arrhythmia.

                                            M
                                        estimation

Property                 Group       N       Slope     SE     P-Value

AN                       s-block     6      0.0059  0.005      0.2645

AN                       transition  7      0.0065  0.002      0.0003

AN/[BETA]IP              s-block     6      0.0225  0.022      0.3072

AN/[BETA]IP              transition  7      0.0423  0.016      0.0075

AR                       s-block     6      0.3469  0.309      0.2609

AR                       transition  7      0.8748  0.347      0.0118

[BETA][E.sup.0]          s-block     6     -0.3654  1.093      0.7381

[BETA][E.sup.0]          transition  7      0.0855  0.204      0.6746

[BETA]IP                 s-block     6     -0.2192  0.164      0.1825

[BETA]IP                 transition  7     -0.0025  0.022      0.9085

[rho]                    s-block     6      0.0001  1E-04      0.2423

[rho]                    transition  7      0.0001      0      <.0001

MP                       s-block     6     -0.0001  4E-04      0.7543

MP                       transition  7     -0.0002      0      0.0002

[X.sub.m]                s-block     6     -1.9266   1.29      0.1353

[X.sub.m]                transition  7      0.5525  0.352      0.1167

X[m.sup.2]r              s-block     6      0.8951  0.888      0.3132

X[m.sup.2]r              transition  7       0.177  0.051      0.0005

Z                        s-block     6     -0.0082  0.264      0.9753

[Z.sup.2]/r              s-block     6     -0.0563  0.094      0.5507

[Z.sup.2]/r              transition  7     -0.0977  0.065      0.1328

Z/AR                     s-block     6     -0.2793  0.485      0.5646

Z/AR                     transition  7     -0.3303  0.079      <.0001

log([K.sub.OH])          s-block     6       0.147  0.153      0.3366

log([K.sub.OH])          transition  7     -0.0236  0.017      0.1663

[pK.sub.sp](C[O.sub.3])  s-block     4     -0.0435  0.057       0.445

[pK.sub.sp](C[O.sub.3])  transition  6      0.0352  0.006      <.0001

r                        s-block     6       0.436  0.331      0.1878

r                        transition  7      0.7319  0.366      0.0453

[[sigma].sub.p]          s-block     6     -1.9623  5.088      0.6997

[[sigma].sub.p]          transition  6     -5.5388  1.762      0.0017

                                                    MM
                                                estimation

Property                 Group       [R.sup.2]       Slope      SE

AN                       s-block         0.222      0.0059  0.0053

AN                       transition      0.558      0.0065  0.0018

AN/[BETA]IP              s-block          0.19      0.0225   0.022

AN/[BETA]IP              transition      0.461      0.0423  0.0158

AR                       s-block          0.23      0.3469  0.3086

AR                       transition      0.419      0.8748  0.3472

[BETA][E.sup.0]          s-block         0.033     -0.3654   1.093

[BETA][E.sup.0]          transition      0.002      0.0855  0.2036

[BETA]IP                 s-block         0.297     -0.2192  0.1644

[BETA]IP                 transition      9E-04     -0.0025  0.0221

[rho]                    s-block         0.249      0.0001  0.0001

[rho]                    transition      0.682      0.0001       0

MP                       s-block         0.029     -0.0001  0.0004

MP                       transition      0.227     -0.0001  0.0001

[X.sub.m]                s-block         0.345     -1.9266  1.2899

[X.sub.m]                transition      0.281      0.5525  0.3522

X[m.sup.2]r              s-block         0.204      0.8951  0.8875

X[m.sup.2]r              transition      0.622       0.177  0.0506

Z                        s-block         5E-04     -0.0082  0.2641

[Z.sup.2]/r              s-block         0.108     -0.0563  0.0944

[Z.sup.2]/r              transition       0.21     -0.0977   0.065

Z/AR                     s-block         0.091     -0.2793  0.4848

Z/AR                     transition      0.259     -0.7054  0.3069

log([K.sub.OH])          s-block         0.201       0.147   0.153

log([K.sub.OH])          transition      0.239     -0.0236  0.0171

[pK.sub.sp](C[O.sub.3])  s-block         0.219

[pK.sub.sp](C[O.sub.3])  transition      0.411     -0.0056  0.0418

r                        s-block         0.292       0.436   0.331

r                        transition      0.273      0.7319  0.3656

[[sigma].sub.p]          s-block          0.04     -1.9623  5.0877

[[sigma].sub.p]          transition      0.639     -5.5388  1.7617

                                                                S
                                                            estimation

Property                 Group          P-Value  [R.sup.2]       Slope

AN                       s-block         0.2645     0.2118      0.0059

AN                       transition      0.0003     0.5418      0.0065

AN/[BETA]IP              s-block         0.3072     0.1788      0.0225

AN/[BETA]IP              transition      0.0075     0.4528      0.0423

AR                       s-block         0.2609     0.2194      0.3469

AR                       transition      0.0118     0.4404      0.8748

[BETA][E.sup.0]          s-block         0.7381      0.036     -0.3654

[BETA][E.sup.0]          transition      0.6746     0.0101      0.0855

[BETA]IP                 s-block         0.1825     0.2912     -0.2192

[BETA]IP                 transition      0.9085          0     -0.0025

[rho]                    s-block         0.2423     0.2425      0.0001

[rho]                    transition      <.0001     0.5769      0.0001

MP                       s-block         0.7543     0.0301     -0.0001

MP                       transition      0.2317     0.2053     -0.0001

[X.sub.m]                s-block         0.1353      0.334     -1.9266

[X.sub.m]                transition      0.1167     0.2344      0.5525

X[m.sup.2]r              s-block         0.3132     0.2046      0.8951

X[m.sup.2]r              transition      0.0005     0.5342       0.177

Z                        s-block         0.9753     0.0006

[Z.sup.2]/r              s-block         0.5507     0.0956     -0.0563

[Z.sup.2]/r              transition      0.1328     0.2297     -0.0977

Z/AR                     s-block         0.5646     0.0888     -0.2793

Z/AR                     transition      0.0215     0.4036     -0.7054

log([K.sub.OH])          s-block         0.3366     0.1976       0.147

log([K.sub.OH])          transition      0.1663      0.193     -0.0236

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition      0.8935      0.001     -0.0056

r                        s-block         0.1878     0.2833       0.436

r                        transition      0.0453     0.3494      0.7319

[[sigma].sub.p]          s-block         0.6997     0.0432     -1.9623

[[sigma].sub.p]          transition      0.0017     0.5857     -5.5388

Property                 Group          SE     P-Value  [R.sup.2]

AN                       s-block     0.005      0.2645      0.198

AN                       transition  0.002      0.0003      0.731

AN/[BETA]IP              s-block     0.022      0.3072      0.159

AN/[BETA]IP              transition  0.016      0.0075      0.541

AR                       s-block     0.309      0.2609       0.21

AR                       transition  0.347      0.0118      0.469

[BETA][E.sup.0]          s-block     1.093      0.7381      0.021

[BETA][E.sup.0]          transition  0.204      0.6746          0

[BETA]IP                 s-block     0.164      0.1825      0.283

[BETA]IP                 transition  0.022      0.9085          0

[rho]                    s-block     1E-04      0.2423      0.241

[rho]                    transition      0      <.0001      0.715

MP                       s-block     4E-04      0.7543      0.013

MP                       transition  1E-04      0.2317      0.242

[X.sub.m]                s-block      1.29      0.1353      0.341

[X.sub.m]                transition  0.352      0.1167      0.153

X[m.sup.2]r              s-block     0.888      0.3132      0.208

X[m.sup.2]r              transition  0.051      0.0005      0.641

Z                        s-block

[Z.sup.2]/r              s-block     0.094      0.5507      0.093

[Z.sup.2]/r              transition  0.065      0.1328      0.156

Z/AR                     s-block     0.485      0.5646      0.086

Z/AR                     transition  0.307      0.0215      0.425

log([K.sub.OH])          s-block     0.153      0.3366      0.207

log([K.sub.OH])          transition  0.017      0.1663      0.114

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition  0.042      0.8935          0

r                        s-block     0.331      0.1878      0.271

r                        transition  0.366      0.0453      0.311

[[sigma].sub.p]          s-block     5.088      0.6997      0.036

[[sigma].sub.p]          transition  1.762      0.0017      0.679

                                       LTS

Property                 Group         Slope     SE     P-Value

AN                       s-block      0.0059  0.005      0.2645

AN                       transition   0.0059  9E-04      <.0001

AN/[BETA]IP              s-block      0.0225  0.022      0.3072

AN/[BETA]IP              transition   0.0423  0.016      0.0075

AR                       s-block      0.3469  0.309      0.2609

AR                       transition   0.8748  0.347      0.0118

[BETA][E.sup.0]          s-block     -0.3654  1.093      0.7381

[BETA][E.sup.0]          transition  -0.1091  0.138       0.429

[BETA]IP                 s-block     -0.2192  0.164      0.1825

[BETA]IP                 transition   0.0085  0.014      0.5432

[rho]                    s-block      0.0001  1E-04      0.2423

[rho]                    transition   0.0001      0      <.0001

MP                       s-block     -0.0001  4E-04      0.7543

MP                       transition  -0.0002      0      0.0002

[X.sub.m]                s-block     -1.9266   1.29      0.1353

[X.sub.m]                transition   0.5525  0.352      0.1167

X[m.sup.2]r              s-block      0.8951  0.888      0.3132

X[m.sup.2]r              transition    0.177  0.051      0.0005

Z                        s-block     -0.0082  0.264      0.9753

[Z.sup.2]/r              s-block     -0.0563  0.094      0.5507

[Z.sup.2]/r              transition  -0.0977  0.065      0.1328

Z/AR                     s-block     -0.7078  0.342      0.0386

Z/AR                     transition  -0.7054  0.307      0.0215

log([K.sub.OH])          s-block       0.147  0.153      0.3366

log([K.sub.OH])          transition  -0.0236  0.017      0.1663

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition   0.0304  0.023       0.192

r                        s-block       0.436  0.331      0.1878

r                        transition   0.7319  0.366      0.0453

[[sigma].sub.p]          s-block     -8.3749   3.25        0.01

[[sigma].sub.p]          transition  -5.5388  1.762      0.0017

Property                 Group       [R.sup.2]

AN                       s-block         0.248

AN                       transition      0.835

AN/[BETA]IP              s-block         0.166

AN/[BETA]IP              transition      0.608

AR                       s-block         0.236

AR                       transition      0.399

[BETA][E.sup.0]          s-block         0.402

[BETA][E.sup.0]          transition      0.135

[BETA]IP                 s-block         0.431

[BETA]IP                 transition      0.085

[rho]                    s-block         0.403

[rho]                    transition       0.59

MP                       s-block          0.47

MP                       transition       0.57

[X.sub.m]                s-block         0.459

[X.sub.m]                transition      0.037

X[m.sup.2]r              s-block         0.541

X[m.sup.2]r              transition      0.482

Z                        s-block         0.357

[Z.sup.2]/r              s-block          0.49

[Z.sup.2]/r              transition      0.026

Z/AR                     s-block         0.573

Z/AR                     transition      0.371

log([K.sub.OH])          s-block         0.599

log([K.sub.OH])          transition      0.033

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition      0.362

r                        s-block         0.431

r                        transition      0.114

[[sigma].sub.p]          s-block         0.689

[[sigma].sub.p]          transition      0.699

"-" symbol denotes that the simulation did not converge for
the given method-property combination.


Table S9. Comparisons of regression results from the various
robust regression methods for myocardial infarction.

                                            M
                                        estimation

Property                 Group       N       Slope     SE     P-Value

AN                       s-block     5      0.0504  0.015      0.0006

AN                       transition  8     -0.0003  0.004       0.926

AN/[BETA]IP              s-block     5      0.2347  0.054      <.0001

AN/[BETA]IP              transition  8     -0.0007  0.025      0.9763

AR                       s-block     5      1.0143  0.392      0.0096

AR                       transition  8      0.2231  0.588      0.7043

[BETA][E.sup.0]          s-block     5     -0.4954  1.256      0.6932

[BETA][E.sup.0]          transition  8     -0.2292  0.232      0.3231

[BETA]IP                 s-block     5      -0.162  0.041      <.0001

[BETA]IP                 transition  8      0.0095  0.028      0.7362

[rho]                    s-block     5      0.0001  6E-04      0.8964

[rho]                    transition  8           0      0      0.6505

MP                       s-block     5     -0.0009  5E-04      0.0473

MP                       transition  8      0.0001  1E-04      0.4328

[X.sub.m]                s-block     5     -1.3847  1.094      0.2055

[X.sub.m]                transition  8      0.0281  0.354      0.9369

X[m.sup.2]r              s-block     5      0.3577  1.674      0.8308

X[m.sup.2]r              transition  8      0.0111  0.057      0.8448

Z                        s-block     5     -0.6636  0.256      0.0094

[Z.sup.2]/r              s-block     5     -0.1033  8E-04      <.0001

[Z.sup.2]/r              transition  8     -0.0083  0.085      0.9218

Z/AR                     s-block     5     -0.5746  0.023      <.0001

Z/AR                     transition  8      0.0395  0.584      0.9461

log([K.sub.OH])          s-block     5      0.1739  0.013      <.0001

log([K.sub.OH])          transition  8       0.007  0.027      0.7968

[pK.sub.sp](C[O.sub.3])  s-block     3     -0.0969  0.009      <.0001

[pK.sub.sp](C[O.sub.3])  transition  7     -0.0703   0.06      0.2386

r                        s-block     5      1.1697  0.532      0.0277

r                        transition  8      0.1196  0.462      0.7958

[[sigma].sub.p]          s-block     5      -2.098  9.631      0.8276

[[sigma].sub.p]          transition  7      5.0104  0.981      <.0001

                                                    MM
                                                estimation

Property                 Group       [R.sup.2]       Slope      SE

AN                       s-block         0.358       0.039  0.0416

AN                       transition      0.002     -0.0003  0.0035

AN/[BETA]IP              s-block         0.515      0.2012  0.1821

AN/[BETA]IP              transition      3E-04     -0.0007  0.0247

AR                       s-block         0.363      1.0809  0.8016

AR                       transition      0.019      0.2231   0.588

[BETA][E.sup.0]          s-block         0.032     -0.4954  1.2556

[BETA][E.sup.0]          transition      0.128     -0.2292  0.2319

[BETA]IP                 s-block         0.338     -0.1874  0.2686

[BETA]IP                 transition      0.018      0.0095  0.0283

[rho]                    s-block         1E-04      0.0001  0.0006

[rho]                    transition      0.048           0       0

MP                       s-block         0.207     -0.0005  0.0009

MP                       transition      0.097      0.0001  0.0001

[X.sub.m]                s-block         0.174     -1.1776  1.6507

[X.sub.m]                transition      7E-04      0.0281  0.3544

X[m.sup.2]r              s-block         0.006      0.3577  1.6743

X[m.sup.2]r              transition      0.006      0.0111  0.0568

Z                        s-block         0.113     -0.2401   0.579

[Z.sup.2]/r              s-block         0.581     -0.0851  0.1438

[Z.sup.2]/r              transition      9E-04     -0.0083  0.0851

Z/AR                     s-block         0.575     -0.6095  0.8271

Z/AR                     transition      0.004      0.0395  0.5841

log([K.sub.OH])          s-block         0.528      0.2167  0.2459

log([K.sub.OH])          transition      0.011       0.007   0.027

[pK.sub.sp](C[O.sub.3])  s-block         0.945

[pK.sub.sp](C[O.sub.3])  transition      0.169     -0.0703  0.0596

r                        s-block         0.348      1.3175  0.9509

r                        transition       0.01      0.1196   0.462

[[sigma].sub.p]          s-block         0.005      -2.098  9.6306

[[sigma].sub.p]          transition       0.36      1.2891  3.6868

                                                               S
                                                           estimation

Property                 Group       P-Value  [R.sup.2]       Slope

AN                       s-block      0.3487     0.2371       0.039

AN                       transition    0.926     0.0023     -0.0003

AN/[BETA]IP              s-block      0.2692     0.2994      0.2012

AN/[BETA]IP              transition   0.9763     0.0003     -0.0007

AR                       s-block      0.1775     0.3624      1.0809

AR                       transition   0.7043     0.0161      0.2231

[BETA][E.sup.0]          s-block      0.6932     0.0363     -0.4954

[BETA][E.sup.0]          transition   0.3231     0.1214     -0.2292

[BETA]IP                 s-block      0.4854     0.1443     -0.1874

[BETA]IP                 transition   0.7362     0.0172      0.0095

[rho]                    s-block      0.8964     0.0028      0.0001

[rho]                    transition   0.6505     0.0516           0

MP                       s-block      0.5817     0.1014     -0.0005

MP                       transition   0.4328     0.0976      0.0001

[X.sub.m]                s-block      0.4756     0.1475     -1.1776

[X.sub.m]                transition   0.9369     0.0005      0.0281

X[m.sup.2]r              s-block      0.8308     0.0113      0.3577

X[m.sup.2]r              transition   0.8448     0.0054      0.0111

Z                        s-block      0.6784     0.0663     -0.2401

[Z.sup.2]/r              s-block       0.554      0.119     -0.0851

[Z.sup.2]/r              transition   0.9218     0.0007     -0.0083

Z/AR                     s-block      0.4612     0.1637     -0.6095

Z/AR                     transition   0.9461     0.0052      0.0395

log([K.sub.OH])          s-block      0.3783     0.2106      0.2167

log([K.sub.OH])          transition   0.7968     0.0113       0.007

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition   0.2386     0.1676     -0.0703

r                        s-block      0.1659     0.3688      1.3175

r                        transition   0.7958     0.0089      0.1196

[[sigma].sub.p]          s-block      0.8276     0.0097      -2.098

[[sigma].sub.p]          transition   0.7266     0.0549      1.2891

Property                 Group          SE  P-Value  [R.sup.2]

AN                       s-block     0.042   0.3487      0.253

AN                       transition  0.004    0.926          0

AN/[BETA]IP              s-block     0.182   0.2692      0.327

AN/[BETA]IP              transition  0.025   0.9763          0

AR                       s-block     0.802   0.1775       0.38

AR                       transition  0.588   0.7043          0

[BETA][E.sup.0]          s-block     1.256   0.6932          0

[BETA][E.sup.0]          transition  0.232   0.3231      0.092

[BETA]IP                 s-block     0.269   0.4854      0.128

[BETA]IP                 transition  0.028   0.7362          0

[rho]                    s-block     6E-04   0.8964          0

[rho]                    transition      0   0.6505      0.056

MP                       s-block     9E-04   0.5817      0.084

MP                       transition  1E-04   0.4328      0.095

[X.sub.m]                s-block     1.651   0.4756       0.13

[X.sub.m]                transition  0.354   0.9369          0

X[m.sup.2]r              s-block     1.674   0.8308          0

X[m.sup.2]r              transition  0.057   0.8448          0

Z                        s-block     0.579   0.6784      0.048

[Z.sup.2]/r              s-block     0.144    0.554      0.111

[Z.sup.2]/r              transition  0.085   0.9218          0

Z/AR                     s-block     0.827   0.4612      0.159

Z/AR                     transition  0.584   0.9461          0

log([K.sub.OH])          s-block     0.246   0.3783       0.21

log([K.sub.OH])          transition  0.027   0.7968          0

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition   0.06   0.2386      0.122

r                        s-block     0.951   0.1659      0.382

r                        transition  0.462   0.7958          0

[[sigma].sub.p]          s-block     9.631   0.8276          0

[[sigma].sub.p]          transition  3.687   0.7266      0.068

                                       LTS

Property                 Group         Slope     SE     P-Value

AN                       s-block      0.0504  0.015      0.0006

AN                       transition  -0.0003  0.004       0.926

AN/[BETA]IP              s-block      0.2347  0.054      <.0001

AN/[BETA]IP              transition  -0.0007  0.025      0.9763

AR                       s-block      1.0143  0.392      0.0096

AR                       transition   0.2231  0.588      0.7043

[BETA][E.sup.0]          s-block     -0.4954  1.256      0.6932

[BETA][E.sup.0]          transition  -0.2292  0.232      0.3231

[BETA]IP                 s-block     -0.1874  0.269      0.4854

[BETA]IP                 transition   0.0095  0.028      0.7362

[rho]                    s-block     -0.0008  4E-04      0.0304

[rho]                    transition        0      0      0.6505

MP                       s-block     -0.0009  5E-04      0.0473

MP                       transition   0.0001  1E-04      0.4328

[X.sub.m]                s-block     -1.1776  1.651      0.4756

[X.sub.m]                transition   0.0281  0.354      0.9369

X[m.sup.2]r              s-block     -2.2777  1.072      0.0336

X[m.sup.2]r              transition   0.0111  0.057      0.8448

Z                        s-block     -0.6636  0.256      0.0094

[Z.sup.2]/r              s-block     -0.1598  0.066      0.0153

[Z.sup.2]/r              transition  -0.0083  0.085      0.9218

Z/AR                     s-block     -0.8862  0.417      0.0335

Z/AR                     transition   0.0395  0.584      0.9461

log([K.sub.OH])          s-block      0.2684  0.126      0.0337

log([K.sub.OH])          transition    0.007  0.027      0.7968

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition  -0.0703   0.06      0.2386

r                        s-block      1.3175  0.951      0.1659

r                        transition   0.1196  0.462      0.7958

[[sigma].sub.p]          s-block     10.6878  7.334       0.145

[[sigma].sub.p]          transition   1.2891  3.687      0.7266

Property                 Group       [R.sup.2]

AN                       s-block         0.855

AN                       transition      0.103

AN/[BETA]IP              s-block         0.904

AN/[BETA]IP              transition       0.12

AR                       s-block          0.77

AR                       transition      0.113

[BETA][E.sup.0]          s-block         0.196

[BETA][E.sup.0]          transition      0.034

[BETA]IP                 s-block         0.441

[BETA]IP                 transition      0.029

[rho]                    s-block         0.689

[rho]                    transition      0.227

MP                       s-block         0.649

MP                       transition      0.538

[X.sub.m]                s-block         0.423

[X.sub.m]                transition      0.019

X[m.sup.2]r              s-block         0.681

X[m.sup.2]r              transition      0.005

Z                        s-block         0.762

[Z.sup.2]/r              s-block         0.736

[Z.sup.2]/r              transition      0.059

Z/AR                     s-block         0.681

Z/AR                     transition      0.329

log([K.sub.OH])          s-block          0.68

log([K.sub.OH])          transition      0.259

[pK.sub.sp](C[O.sub.3])  s-block

[pK.sub.sp](C[O.sub.3])  transition      0.051

r                        s-block         0.708

r                        transition      0.085

[[sigma].sub.p]          s-block         0.496

[[sigma].sub.p]          transition      0.426

"-" symbol denotes that the simulation did not converge for
the given method-property combination.


Table S10. Comparisons of regression results from the various
robust regression methods for myocardial ischemia.

                                            M
                                        estimation

Property                 Group       N       Slope     SE     P-Value

AN                       s-block     5      0.0584  0.015      0.0001
AN                       transition  9      0.0007  0.002      0.7457
AN/[BETA]IP              s-block     5      0.2757  0.042      <.0001
AN/[BETA]IP              transition  9      0.0055  0.014       0.701
AR                       s-block     5      1.2392  0.561      0.0272
AR                       transition  9      0.0404  0.335      0.9042
[BETA][E.sup.0]          s-block     5      0.0598  1.152      0.9586
[BETA][E.sup.0]          transition  9      -0.119  0.141      0.3984
[BETA]IP                 s-block     5     -0.2487  0.216      0.2491
[BETA]IP                 transition  9     -0.0171  0.012      0.1518
[rho]                    s-block     5           0  6E-04      0.9355
[rho]                    transition  9           0      0      0.4059
MP                       s-block     5     -0.0002  8E-04      0.7878
MP                       transition  9           0  1E-04      0.5437
[X.sub.m]                s-block     5     -1.8231  0.567      0.0013
[X.sub.m]                transition  9      0.1999  0.188      0.2884
X[m.sup.2]r              s-block     5     -0.0503   1.51      0.9734
X[m.sup.2]r              transition  9      0.0257  0.031       0.409
Z                        s-block     5     -0.1504  0.526      0.7748
[Z.sup.2]/r              s-block     5     -0.0852  0.127       0.502
[Z.sup.2]/r              transition  9     -0.0234  0.047      0.6165
Z/AR                     s-block     5     -0.5912  0.728       0.417
Z/AR                     transition  9       0.129  0.337      0.7015
log([K.sub.OH])          s-block     5      0.2224  0.211      0.2918
log([K.sub.OH])          transition  9      0.0145  0.014      0.3012
[pK.sub.sp](C[O.sub.3])  s-block     3     -0.0965  0.087      0.2647
[pK.sub.sp](C[O.sub.3])  transition  8       0.007  0.034      0.8372
r                        s-block     5      1.4671  0.686      0.0324
r                        transition  9      0.1252  0.258      0.6276
[[sigma].sub.p]          s-block     5     -0.9505   8.67      0.9127
[[sigma].sub.p]          transition  8      1.7191    1.8      0.3396

                                                    MM
                                                estimation

Property                 Group       [R.sup.2]       Slope      SE

AN                       s-block         0.571      0.0504  0.0308
AN                       transition      0.015      0.0007   0.002
AN/[BETA]IP              s-block         0.687      0.2525  0.1269
AN/[BETA]IP              transition      0.021      0.0055  0.0143
AR                       s-block           0.6      1.2392   0.561
AR                       transition      0.002      0.0404  0.3353
[BETA][E.sup.0]          s-block         0.003      0.0598   1.152
[BETA][E.sup.0]          transition      0.033      -0.119  0.1409
[BETA]IP                 s-block         0.324     -0.2487  0.2158
[BETA]IP                 transition      0.095     -0.0128  0.0169
[rho]                    s-block         0.001           0  0.0006
[rho]                    transition      0.046           0       0
MP                       s-block         0.026     -0.0002  0.0008
MP                       transition       0.02           0  0.0001
[X.sub.m]                s-block         0.476     -1.6444   1.285
[X.sub.m]                transition      0.052      0.1999  0.1883
X[m.sup.2]r              s-block         0.002     -0.0503  1.5095
X[m.sup.2]r              transition      0.052      0.0257  0.0312
Z                        s-block         0.033     -0.1504  0.5257
[Z.sup.2]/r              s-block         0.153     -0.0852  0.1268
[Z.sup.2]/r              transition      0.028     -0.0234  0.0468
Z/AR                     s-block         0.199     -0.5912  0.7284
Z/AR                     transition      0.014       0.129  0.3365
log([K.sub.OH])          s-block         0.299      0.2224  0.2109
log([K.sub.OH])          transition       0.07      0.0145   0.014
[pK.sub.sp](C[O.sub.3])  s-block         0.539
[pK.sub.sp](C[O.sub.3])  transition      0.001      0.0472  0.0746
r                        s-block         0.587      1.4671  0.6858
r                        transition       0.03      0.1252  0.2581
[[sigma].sub.p]          s-block         0.003     -0.9505  8.6696
[[sigma].sub.p]          transition      0.095      1.7191  1.8002

                                                               S
                                                           estimation

Property                 Group       P-Value  [R.sup.2]       Slope

AN                       s-block      0.1015     0.4751      0.0504
AN                       transition   0.7457      0.007      0.0007
AN/[BETA]IP              s-block      0.0467     0.5663      0.2525
AN/[BETA]IP              transition    0.701       0.01      0.0055
AR                       s-block      0.0272     0.6099      1.2392
AR                       transition   0.9042      0.001      0.0404
[BETA][E.sup.0]          s-block      0.9586      0.003      0.0598
[BETA][E.sup.0]          transition   0.3984      0.033      -0.119
[BETA]IP                 s-block      0.2491     0.3243     -0.2487
[BETA]IP                 transition   0.4489     0.0366     -0.0128
[rho]                    s-block      0.9355     0.0011           0
[rho]                    transition   0.4059     0.0376           0
MP                       s-block      0.7878     0.0273     -0.0002
MP                       transition   0.5437     0.0177           0
[X.sub.m]                s-block      0.2007     0.3716     -1.6444
[X.sub.m]                transition   0.2884     0.0582      0.1999
X[m.sup.2]r              s-block      0.9734     0.0014     -0.0503
X[m.sup.2]r              transition    0.409     0.0401      0.0257
Z                        s-block      0.7748     0.0335     -0.1504
[Z.sup.2]/r              s-block       0.502     0.1521     -0.0852
[Z.sup.2]/r              transition   0.6165     0.0176     -0.0234
Z/AR                     s-block       0.417     0.1986     -0.5912
Z/AR                     transition   0.7015     0.0086       0.129
log([K.sub.OH])          s-block      0.2918     0.2891      0.2224
log([K.sub.OH])          transition   0.3012      0.054      0.0145
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition   0.5274     0.0229       0.007
r                        s-block      0.0324     0.5946      1.4671
r                        transition   0.6276     0.0164      0.1252
[[sigma].sub.p]          s-block      0.9127     0.0024     -0.9505
[[sigma].sub.p]          transition   0.3396     0.0442      1.7191

Property                 Group          SE  P-Value  [R.sup.2]

AN                       s-block     0.031   0.1015      0.508
AN                       transition  0.002   0.7457          0
AN/[BETA]IP              s-block     0.127   0.0467      0.612
AN/[BETA]IP              transition  0.014    0.701          0
AR                       s-block     0.561   0.0272       0.62
AR                       transition  0.335   0.9042          0
[BETA][E.sup.0]          s-block     1.152   0.9586          0
[BETA][E.sup.0]          transition  0.141   0.3984          0
[BETA]IP                 s-block     0.216   0.2491      0.347
[BETA]IP                 transition  0.017   0.4489          0
[rho]                    s-block     6E-04   0.9355          0
[rho]                    transition      0   0.4059          0
MP                       s-block     8E-04   0.7878      0.004
MP                       transition  1E-04   0.5437          0
[X.sub.m]                s-block     1.285   0.2007      0.402
[X.sub.m]                transition  0.188   0.2884          0
X[m.sup.2]r              s-block      1.51   0.9734          0
X[m.sup.2]r              transition  0.031    0.409          0
Z                        s-block     0.526   0.7748      0.016
[Z.sup.2]/r              s-block     0.127    0.502       0.16
[Z.sup.2]/r              transition  0.047   0.6165          0
Z/AR                     s-block     0.728    0.417      0.207
Z/AR                     transition  0.337   0.7015          0
log([K.sub.OH])          s-block     0.211   0.2918      0.308
log([K.sub.OH])          transition  0.014   0.3012          0
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition  0.034   0.8372          0
r                        s-block     0.686   0.0324      0.596
r                        transition  0.258   0.6276          0
[[sigma].sub.p]          s-block      8.67   0.9127          0
[[sigma].sub.p]          transition    1.8   0.3396          0

                                       LTS
Property                 Group         Slope     SE     P-Value

AN                       s-block      0.0584  0.015      0.0001
AN                       transition   0.0007  0.002      0.7457
AN/[BETA]IP              s-block      0.2757  0.042      <.0001
AN/[BETA]IP              transition   0.0055  0.014       0.701
AR                       s-block      2.5855  0.519      <.0001
AR                       transition   0.0404  0.335      0.9042
[BETA][E.sup.0]          s-block      1.5602  0.697      0.0252
[BETA][E.sup.0]          transition   -0.119  0.141      0.3984
[BETA]IP                 s-block     -0.2851  0.108      0.0085
[BETA]IP                 transition  -0.0128  0.017      0.4489
[rho]                    s-block     -0.0008  4E-04      0.0814
[rho]                    transition        0      0      0.4059
MP                       s-block     -0.0002  8E-04      0.7878
MP                       transition        0  1E-04      0.5437
[X.sub.m]                s-block     -1.8231  0.567      0.0013
[X.sub.m]                transition   0.1999  0.188      0.2884
X[m.sup.2]r              s-block     -2.5986  0.262      <.0001
X[m.sup.2]r              transition   0.0257  0.031       0.409
Z                        s-block     -0.1504  0.526      0.7748
[Z.sup.2]/r              s-block     -0.1492  0.068      0.0278
[Z.sup.2]/r              transition  -0.0234  0.047      0.6165
Z/AR                     s-block     -0.5912  0.728       0.417
Z/AR                     transition    0.129  0.337      0.7015
log([K.sub.OH])          s-block      0.2665  0.111      0.0164
log([K.sub.OH])          transition   0.0145  0.014      0.3012
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition  -0.0612  0.024       0.011
r                        s-block      3.2952  0.514      <.0001
r                        transition   0.1252  0.258      0.6276
[[sigma].sub.p]          s-block     10.3909  6.933      0.1339
[[sigma].sub.p]          transition   1.7191    1.8      0.3396

Property                 Group       [R.sup.2]

AN                       s-block          0.84
AN                       transition      0.187
AN/[BETA]IP              s-block         0.941
AN/[BETA]IP              transition      0.244
AR                       s-block         0.873
AR                       transition      0.084
[BETA][E.sup.0]          s-block         0.715
[BETA][E.sup.0]          transition      0.015
[BETA]IP                 s-block         0.776
[BETA]IP                 transition      0.291
[rho]                    s-block         0.603
[rho]                    transition      0.248
MP                       s-block         0.272
MP                       transition      0.004
[X.sub.m]                s-block         0.838
[X.sub.m]                transition      0.214
X[m.sup.2]r              s-block          0.98
X[m.sup.2]r              transition      0.336
Z                        s-block         0.468
[Z.sup.2]/r              s-block         0.708
[Z.sup.2]/r              transition      0.403
Z/AR                     s-block         0.656
Z/AR                     transition      0.009
log([K.sub.OH])          s-block         0.742
log([K.sub.OH])          transition      0.091
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition      0.618
r                        s-block         0.921
r                        transition      0.384
[[sigma].sub.p]          s-block         0.529
[[sigma].sub.p]          transition       0.37

"-" symbol denotes that the simulation did not converge for the
given method-property combination.

Table S11. Comparisons of regression results from the various
robust regression methods for stroke.

                                             M
                                         estimation

Property                 Group        N       Slope     SE     P-Value

AN                       s-block      5      0.0362  0.014      0.0118
AN                       transition  10     -0.0104  0.007      0.1552
AN/[BETA]IP              s-block      5      0.1214  0.092      0.1885
AN/[BETA]IP              transition  10     -0.0672  0.052      0.1927
AR                       s-block      5      0.3086  0.515       0.549
AR                       transition  10     -1.9602  1.058      0.0639
[BETA][E.sup.0]          s-block      5     -0.8545  0.484      0.0773
[BETA][E.sup.0]          transition  10      0.4499  0.523      0.3897
[BETA]IP                 s-block      5      0.0819  0.065      0.2094
[BETA]IP                 transition  10      0.0416  0.043      0.3271
[rho]                    s-block      5      0.0005  2E-04      0.0007
[rho]                    transition  10     -0.0001  1E-04      0.3296
MP                       s-block      5      0.0004  1E-04      0.0011
MP                       transition  10      0.0003  3E-04      0.2347
[X.sub.m]                s-block      5      0.4754  0.419      0.2562
[X.sub.m]                transition  10     -1.1341  0.739      0.1247
X[m.sup.2]r              s-block      5      1.3589  0.451      0.0026
X[m.sup.2]r              transition  10     -0.1863  0.111      0.0946
Z                        s-block      5      0.2601  0.066      <.0001
Z                        transition  10     -0.0466  0.365      0.8985
[Z.sup.2]/r              s-block      5      0.0594  0.023      0.0094
[Z.sup.2]/r              transition  10      0.0447  0.112      0.6901
Z/AR                     s-block      5      0.3351   0.14      0.0169
Z/AR                     transition  10      0.2273  0.363      0.5309
log([K.sub.OH])          s-block      5     -0.1274  0.129      0.3212
log([K.sub.OH])          transition  10     -0.0042   0.05      0.9331
[pK.sub.sp](C[O.sub.3])  s-block      3      -0.114  0.013      <.0001
[pK.sub.sp](C[O.sub.3])  transition   9     -0.2105   0.11      0.0565
r                        s-block      5      0.2701  0.634      0.6703
r                        transition  10     -0.9095  0.858      0.2888
[[sigma].sub.p]          s-block      5     -7.6664  2.744      0.0052
[[sigma].sub.p]          transition   9     -6.8566  6.008      0.2537

                                                    MM
                                                estimation

Property                 Group       [R.sup.2]       Slope      SE

AN                       s-block         0.567      0.0362  0.0144
AN                       transition      0.197     -0.0104  0.0073
AN/[BETA]IP              s-block         0.324      0.1214  0.0923
AN/[BETA]IP              transition      0.183     -0.0672  0.0516
AR                       s-block         0.086      0.3086  0.5151
AR                       transition      0.279     -1.9602  1.0578
[BETA][E.sup.0]          s-block         0.472     -0.8545  0.4837
[BETA][E.sup.0]          transition      0.072      0.4499  0.5231
[BETA]IP                 s-block         0.186      0.1065  0.1427
[BETA]IP                 transition      0.049      0.0237  0.0651
[rho]                    s-block         0.673      0.0005  0.0002
[rho]                    transition      0.086     -0.0001  0.0001
MP                       s-block         0.503      0.0006  0.0004
MP                       transition      0.124      0.0003  0.0003
[X.sub.m]                s-block         0.167      0.5985  0.8933
[X.sub.m]                transition      0.221     -1.1341  0.7386
X[m.sup.2]r              s-block         0.712      1.3589  0.4512
X[m.sup.2]r              transition      0.245     -0.1863  0.1114
Z                        s-block         0.521      0.4177  0.2095
Z                        transition      0.017      -0.272  0.5656
[Z.sup.2]/r              s-block         0.461      0.0923  0.0618
[Z.sup.2]/r              transition      0.017      0.0447  0.1121
Z/AR                     s-block         0.456      0.4743   0.397
Z/AR                     transition          0      0.0094   0.586
log([K.sub.OH])          s-block         0.243     -0.1274  0.1285
log([K.sub.OH])          transition      0.002      0.0015  0.0571
[pK.sub.sp](C[O.sub.3])  s-block         0.947
[pK.sub.sp](C[O.sub.3])  transition      0.169      -0.029  0.1334
r                        s-block         0.043      0.2701  0.6344
r                        transition      0.116     -0.9095  0.8575
[[sigma].sub.p]          s-block         0.543     -7.6664  2.7438
[[sigma].sub.p]          transition      0.029     -1.6205  7.4023

                                                               S
                                                           estimation

Property                 Group       P-Value  [R.sup.2]       Slope
AN                       s-block      0.0118     0.5917      0.0362
AN                       transition   0.1552      0.184     -0.0104
AN/[BETA]IP              s-block      0.1885     0.3166      0.1214
AN/[BETA]IP              transition   0.1927     0.1751     -0.0672
AR                       s-block       0.549     0.0818      0.3086
AR                       transition   0.0639     0.2474     -1.9602
[BETA][E.sup.0]          s-block      0.0773     0.4601     -0.8545
[BETA][E.sup.0]          transition   0.3897     0.0731      0.4499
[BETA]IP                 s-block      0.4556     0.1518      0.1065
[BETA]IP                 transition   0.7159     0.0227      0.0237
[rho]                    s-block      0.0007      0.725      0.0005
[rho]                    transition   0.3296      0.085     -0.0001
MP                       s-block      0.1273     0.4016      0.0006
MP                       transition   0.2347     0.1175      0.0003
[X.sub.m]                s-block      0.5029     0.1283      0.5985
[X.sub.m]                transition   0.1247     0.1915     -1.1341
X[m.sup.2]r              s-block      0.0026     0.7216      1.3589
X[m.sup.2]r              transition   0.0946     0.2353     -0.1863
Z                        s-block      0.0461      0.515      0.4177
Z                        transition   0.6306      0.027      -0.272
[Z.sup.2]/r              s-block      0.1352     0.3893      0.0923
[Z.sup.2]/r              transition   0.6901     0.0117      0.0447
Z/AR                     s-block      0.2322     0.3033      0.4743
Z/AR                     transition   0.9872     0.0002      0.0094
log([K.sub.OH])          s-block      0.3212       0.24     -0.1274
log([K.sub.OH])          transition   0.9792          0      0.0015
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition   0.8277     0.0183      -0.029
r                        s-block      0.6703     0.0376      0.2701
r                        transition   0.2888     0.1091     -0.9095
[[sigma].sub.p]          s-block      0.0052     0.6351     -7.6664
[[sigma].sub.p]          transition   0.8267     0.0113     -1.6205

Property                 Group          SE  P-Value  [R.sup.2]

AN                       s-block     0.014   0.0118       0.66
AN                       transition  0.007   0.1552      0.196
AN/[BETA]IP              s-block     0.092   0.1885      0.286
AN/[BETA]IP              transition  0.052   0.1927      0.204
AR                       s-block     0.515    0.549          0
AR                       transition  1.058   0.0639       0.25
[BETA][E.sup.0]          s-block     0.484   0.0773      0.435
[BETA][E.sup.0]          transition  0.523   0.3897       0.04
[BETA]IP                 s-block     0.143   0.4556      0.117
[BETA]IP                 transition  0.065   0.7159          0
[rho]                    s-block     2E-04   0.0007      0.771
[rho]                    transition  1E-04   0.3296      0.058
MP                       s-block     4E-04   0.1273      0.422
MP                       transition  3E-04   0.2347        0.1
[X.sub.m]                s-block     0.893   0.5029      0.088
[X.sub.m]                transition  0.739   0.1247      0.198
X[m.sup.2]r              s-block     0.451   0.0026      0.715
X[m.sup.2]r              transition  0.111   0.0946      0.266
Z                        s-block      0.21   0.0461      0.549
Z                        transition  0.566   0.6306          0
[Z.sup.2]/r              s-block     0.062   0.1352      0.401
[Z.sup.2]/r              transition  0.112   0.6901          0
Z/AR                     s-block     0.397   0.2322      0.306
Z/AR                     transition  0.586   0.9872          0
log([K.sub.OH])          s-block     0.129   0.3212      0.233
log([K.sub.OH])          transition  0.057   0.9792          0
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition  0.133   0.8277      0.024
r                        s-block     0.634   0.6703          0
r                        transition  0.858   0.2888      0.096
[[sigma].sub.p]          s-block     2.744   0.0052      0.699
[[sigma].sub.p]          transition  7.402   0.8267          0

                                       LTS

Property                 Group         Slope     SE     P-Value

AN                       s-block      0.0381  0.007      <.0001
AN                       transition  -0.0104  0.007      0.1552
AN/[BETA]IP              s-block      0.1214  0.092      0.1885
AN/[BETA]IP              transition  -0.0672  0.052      0.1927
AR                       s-block     -0.2045  0.332      0.5374
AR                       transition  -1.9602  1.058      0.0639
[BETA][E.sup.0]          s-block     -0.8545  0.484      0.0773
[BETA][E.sup.0]          transition  -0.4768  0.378      0.2067
[BETA]IP                 s-block      0.0819  0.065      0.2094
[BETA]IP                 transition   0.0237  0.065      0.7159
[rho]                    s-block      0.0003  1E-04      0.0098
[rho]                    transition  -0.0001  1E-04      0.3296
MP                       s-block      0.0004  1E-04      0.0011
MP                       transition   0.0003  3E-04      0.2347
[X.sub.m]                s-block      0.4754  0.419      0.2562
[X.sub.m]                transition  -1.1341  0.739      0.1247
X[m.sup.2]r              s-block      2.5308  0.083      <.0001
X[m.sup.2]r              transition  -0.1863  0.111      0.0946
Z                        s-block      0.2601  0.066      <.0001
Z                        transition   -0.272  0.566      0.6306
[Z.sup.2]/r              s-block      0.0594  0.023      0.0094
[Z.sup.2]/r              transition   0.0447  0.112      0.6901
Z/AR                     s-block      0.3351   0.14      0.0169
Z/AR                     transition   0.0094  0.586      0.9872
log([K.sub.OH])          s-block      -0.099  0.045      0.0294
log([K.sub.OH])          transition   0.0015  0.057      0.9792
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition  -0.2105   0.11      0.0565
r                        s-block     -0.2842  0.366      0.4369
r                        transition  -0.9095  0.858      0.2888
[[sigma].sub.p]          s-block      -9.635  1.329      <.0001
[[sigma].sub.p]          transition  -1.6205  7.402      0.8267

Property                 Group       [R.sup.2]

AN                       s-block         0.734
AN                       transition       0.16
AN/[BETA]IP              s-block         0.044
AN/[BETA]IP              transition      0.209
AR                       s-block          0.16
AR                       transition      0.285
[BETA][E.sup.0]          s-block         0.185
[BETA][E.sup.0]          transition       0.21
[BETA]IP                 s-block         0.441
[BETA]IP                 transition      0.138
[rho]                    s-block          0.77
[rho]                    transition      0.071
MP                       s-block         0.842
MP                       transition      0.229
[X.sub.m]                s-block         0.392
[X.sub.m]                transition      0.143
X[m.sup.2]r              s-block         0.992
X[m.sup.2]r              transition      0.322
Z                        s-block         0.885
Z                        transition      0.003
[Z.sup.2]/r              s-block         0.771
[Z.sup.2]/r              transition      0.032
Z/AR                     s-block         0.741
Z/AR                     transition      0.061
log([K.sub.OH])          s-block         0.703
log([K.sub.OH])          transition      0.007
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition      0.548
r                        s-block         0.232
r                        transition      0.096
[[sigma].sub.p]          s-block         0.826
[[sigma].sub.p]          transition      0.085

"-" symbol denotes that the simulation did not converge for the
given method-property combination.

Table S12. Comparisons of regression results from the various
robust regression methods for thrombosis.

                                             M
                                         estimation

Property                 Group        N       Slope     SE  P-Value

AN                       s-block      5      0.0533  0.037   0.1481
AN                       transition  10     -0.0006  0.006   0.9181
AN/[BETA]IP              s-block      5      0.2012  0.186   0.2785
AN/[BETA]IP              transition  10     -0.0004  0.043   0.9924
AR                       s-block      5      0.4295   0.34   0.2058
AR                       transition  10     -0.2463  0.958   0.7971
[BETA][E.sup.0]          s-block      5      0.2067  1.301   0.8737
[BETA][E.sup.0]          transition  10     -0.0081  0.416   0.9845
[BETA]IP                 s-block      5     -0.1347  0.087   0.1213
[BETA]IP                 transition  10     -0.0416  0.048   0.3831
[rho]                    s-block      5     -0.0002  3E-04   0.5436
[rho]                    transition  10           0  1E-04    0.403
MP                       s-block      5      0.0008  8E-04    0.302
MP                       transition  10           0  2E-04   0.9312
[X.sub.m]                s-block      5     -0.8471  0.519   0.1029
[X.sub.m]                transition  10     -0.2727  0.632   0.6662
X[m.sup.2]r              s-block      5     -0.0163  1.711   0.9924
X[m.sup.2]r              transition  10      -0.038  0.098    0.697
Z                        s-block      5      0.3923   0.56   0.4834
Z                        transition  10     -0.2048  0.431   0.6343
[Z.sup.2]/r              s-block      5      0.0302  0.153   0.8435
[Z.sup.2]/r              transition  10     -0.0457  0.085   0.5894
Z/AR                     s-block      5       0.175  0.906   0.8468
Z/AR                     transition  10     -0.2306  0.438   0.5988
log([K.sub.OH])          s-block      5      0.1485  0.073   0.0431
log([K.sub.OH])          transition  10      0.0364  0.042   0.3807
[pK.sub.sp](C[O.sub.3])  s-block      3     -0.1205  0.181   0.5065
[pK.sub.sp](C[O.sub.3])  transition   9     -0.0631  0.097   0.5152
r                        s-block      5      0.5346  0.388   0.1682
r                        transition  10      0.1399  0.695   0.8404
[[sigma].sub.p]          s-block      5      2.2646  4.531   0.6172
[[sigma].sub.p]          transition   9    -10.2186  3.012   0.0007

                                                    MM
                                                estimation

Property                 Group       [R.sup.2]       Slope      SE

AN                       s-block         0.387      0.0533  0.0368
AN                       transition      1E-04     -0.0006  0.0063
AN/[BETA]IP              s-block         0.224      0.2012  0.1857
AN/[BETA]IP              transition      0.002     -0.0004  0.0432
AR                       s-block         0.263      0.6533  0.9587
AR                       transition      0.001     -0.2463  0.9582
[BETA][E.sup.0]          s-block         0.014      0.2067  1.3005
[BETA][E.sup.0]          transition      2E-04     -0.0081   0.416
[BETA]IP                 s-block         0.238     -0.0971  0.2883
[BETA]IP                 transition      0.097     -0.0416  0.0477
[rho]                    s-block          0.02      0.0004  0.0006
[rho]                    transition      0.095           0  0.0001
MP                       s-block          0.15      0.0008  0.0008
MP                       transition      2E-04           0  0.0002
[X.sub.m]                s-block         0.239     -0.9183   1.731
[X.sub.m]                transition      0.019     -0.2727  0.6321
X[m.sup.2]r              s-block         0.006     -0.0163  1.7108
X[m.sup.2]r              transition      0.013      -0.038  0.0976
Z                        s-block             0      0.3923  0.5597
Z                        transition      0.034     -0.2048  0.4305
[Z.sup.2]/r              s-block         8E-04      0.0302  0.1532
[Z.sup.2]/r              transition      0.062     -0.0457  0.0846
Z/AR                     s-block         0.002       0.175  0.9059
Z/AR                     transition      0.064     -0.2306  0.4384
log([K.sub.OH])          s-block         0.275       0.003  0.2798
log([K.sub.OH])          transition      0.082      0.0364  0.0415
[pK.sub.sp](C[O.sub.3])  s-block         0.298
[pK.sub.sp](C[O.sub.3])  transition      0.045     -0.0631   0.097
r                        s-block         0.316      0.6495  1.1766
r                        transition      0.022      0.1399   0.695
[[sigma].sub.p]          s-block          0.02     -5.2262  9.3696
[[sigma].sub.p]          transition      0.246     -5.6593  5.2736

                                                               S
                                                         estimation

Property                 Group       P-Value  [R.sup.2]       Slope
AN                       s-block      0.1481     0.3524      0.0533
AN                       transition   0.9181      0.001     -0.0006
AN/[BETA]IP              s-block      0.2785     0.2364      0.2012
AN/[BETA]IP              transition   0.9924     0.0043     -0.0004
AR                       s-block      0.4956      0.123      0.6533
AR                       transition   0.7971     0.0001     -0.2463
[BETA][E.sup.0]          s-block      0.8737     0.0086      0.2067
[BETA][E.sup.0]          transition   0.9845     0.0008     -0.0081
[BETA]IP                 s-block      0.7362     0.0464     -0.0971
[BETA]IP                 transition   0.3831     0.0967     -0.0416
[rho]                    s-block      0.5663     0.0844      0.0004
[rho]                    transition   0.5862     0.0635           0
MP                       s-block       0.302     0.2368      0.0008
MP                       transition   0.9312     0.0019           0
[X.sub.m]                s-block      0.5958     0.0899     -0.9183
[X.sub.m]                transition   0.6662     0.0154     -0.2727
X[m.sup.2]r              s-block      0.9924     0.0009     -0.0163
X[m.sup.2]r              transition    0.697      0.009      -0.038
Z                        s-block      0.4834     0.1144      0.3923
Z                        transition   0.6343     0.0396     -0.2048
[Z.sup.2]/r              s-block      0.8435     0.0032      0.0302
[Z.sup.2]/r              transition   0.5894     0.0604     -0.0457
Z/AR                     s-block      0.8468     0.0027       0.175
Z/AR                     transition   0.5988     0.0462     -0.2306
log([K.sub.OH])          s-block      0.9914      0.004       0.003
log([K.sub.OH])          transition   0.3807     0.0739      0.0364
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition   0.5152     0.0472     -0.0631
r                        s-block       0.581     0.0914      0.6495
r                        transition   0.8404      0.022      0.1399
[[sigma].sub.p]          s-block       0.577     0.0805     -5.2262
[[sigma].sub.p]          transition   0.2832     0.2899    -10.2186

Property                 Group          SE  P-Value  [R.sup.2]

AN                       s-block     0.037   0.1481       0.28
AN                       transition  0.006   0.9181          0
AN/[BETA]IP              s-block     0.186   0.2785      0.163
AN/[BETA]IP              transition  0.043   0.9924          0
AR                       s-block     0.959   0.4956      0.049
AR                       transition  0.958   0.7971          0
[BETA][E.sup.0]          s-block     1.301   0.8737          0
[BETA][E.sup.0]          transition  0.416   0.9845          0
[BETA]IP                 s-block     0.288   0.7362          0
[BETA]IP                 transition  0.048   0.3831      0.096
[rho]                    s-block     6E-04   0.5663          0
[rho]                    transition  1E-04   0.5862      0.076
MP                       s-block     8E-04    0.302      0.122
MP                       transition  2E-04   0.9312          0
[X.sub.m]                s-block     1.731   0.5958      0.017
[X.sub.m]                transition  0.632   0.6662          0
X[m.sup.2]r              s-block     1.711   0.9924          0
X[m.sup.2]r              transition  0.098    0.697          0
Z                        s-block      0.56   0.4834          0
Z                        transition  0.431   0.6343      0.246
[Z.sup.2]/r              s-block     0.153   0.8435          0
[Z.sup.2]/r              transition  0.085   0.5894      0.067
Z/AR                     s-block     0.906   0.8468          0
Z/AR                     transition  0.438   0.5988      0.132
log([K.sub.OH])          s-block      0.28   0.9914          0
log([K.sub.OH])          transition  0.042   0.3807      0.055
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition  0.097   0.5152          0
r                        s-block     1.177    0.581      0.014
r                        transition  0.695   0.8404      0.021
[[sigma].sub.p]          s-block      9.37    0.577          0
[[sigma].sub.p]          transition  3.012   0.0007      0.447

                                       LTS

Property                 Group          Slope     SE     P-Value

AN                       s-block       0.0136  0.024      0.5658
AN                       transition   -0.0006  0.006      0.9181
AN/[BETA]IP              s-block       0.0766  0.089      0.3872
AN/[BETA]IP              transition   -0.0004  0.043      0.9924
AR                       s-block       0.4295   0.34      0.2058
AR                       transition    2.2079  0.544      <.0001
[BETA][E.sup.0]          s-block       0.2254  0.549      0.6815
[BETA][E.sup.0]          transition   -0.0081  0.416      0.9845
[BETA]IP                 s-block      -0.1347  0.087      0.1213
[BETA]IP                 transition   -0.0416  0.048      0.3831
[rho]                    s-block       0.0014  2E-04      <.0001
[rho]                    transition         0  1E-04      0.5862
MP                       s-block      -0.0007  4E-04      0.0734
MP                       transition         0  2E-04      0.9312
[X.sub.m]                s-block      -0.8471  0.519      0.1029
[X.sub.m]                transition   -0.2727  0.632      0.6662
X[m.sup.2]r              s-block      -0.4083  0.699      0.5591
X[m.sup.2]r              transition    0.2045  0.145       0.157
Z                        s-block      -0.3294   0.24      0.1698
Z                        transition   -0.2048  0.431      0.6343
[Z.sup.2]/r              s-block      -0.0773  0.049      0.1121
[Z.sup.2]/r              transition   -0.0457  0.085      0.5894
Z/AR                     s-block      -0.4815   0.27      0.0741
Z/AR                     transition   -2.5961  0.572      <.0001
log([K.sub.OH])          s-block       0.1485  0.073      0.0431
log([K.sub.OH])          transition    0.0364  0.042      0.3807
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition   -0.1861  0.088      0.0338
r                        s-block       0.5346  0.388      0.1682
r                        transition    0.1399  0.695      0.8404
[[sigma].sub.p]          s-block     -19.6662  3.708      <.0001
[[sigma].sub.p]          transition  -10.2186  3.012      0.0007

Property                 Group       [R.sup.2]

AN                       s-block         0.142
AN                       transition       0.33
AN/[BETA]IP              s-block         0.272
AN/[BETA]IP              transition      0.423
AR                       s-block         0.445
AR                       transition      0.662
[BETA][E.sup.0]          s-block         0.078
[BETA][E.sup.0]          transition      0.148
[BETA]IP                 s-block         0.546
[BETA]IP                 transition      0.122
[rho]                    s-block         0.843
[rho]                    transition      0.254
MP                       s-block         0.616
MP                       transition      0.088
[X.sub.m]                s-block         0.571
[X.sub.m]                transition      0.001
X[m.sup.2]r              s-block         0.146
X[m.sup.2]r              transition      0.288
Z                        s-block         0.485
Z                        transition      0.248
[Z.sup.2]/r              s-block         0.558
[Z.sup.2]/r              transition      0.191
Z/AR                     s-block         0.615
Z/AR                     transition      0.653
log([K.sub.OH])          s-block         0.672
log([K.sub.OH])          transition      0.021
[pK.sub.sp](C[O.sub.3])  s-block
[pK.sub.sp](C[O.sub.3])  transition      0.273
r                        s-block         0.487
r                        transition      0.415
[[sigma].sub.p]          s-block         0.598
[[sigma].sub.p]          transition      0.676

"- " symbol denotes that the simulation did not converge
for the given method-property combination.

Table S13. Average results from 1000 Monte Carlo simulations of
the LTS regression. Percent error denotes the relative error
between the LTS slope from the data model fit compared with the
LTS slope from the Monte Carlo simulation for cardiac arrhythmia.

Property                 Group         Slope     SE (a)   Simulated
                                                            Slope
                                                          Variance
                                                             (a)

AN                       s-block      5.82E-03  4.64E-03   4.27E-05
AN                       transition   5.81E-03  1.18E-03   3.99E-06
AN/[BETA]IP              s-block      2.33E-02  2.01E-02   7.07E-04
AN/[BETA]IP              transition   4.40E-02  1.60E-02   5.02E-04
AR                       s-block      3.55E-01  2.74E-01   1.62E-01
AR                       transition   8.89E-01  3.63E-01   2.31E-01
[BETA][E.sup.0]          s-block     -3.61E-01  1.09E+00   2.61E+00
[BETA][E.sup.0]          transition  -1.03E-01  1.46E-01   3.58E-02
[rho]                    s-block      1.38E-04  1.05E-04   3.11E-08
[rho]                    transition   6.25E-05  1.77E-05   1.12E-09
[BETA]IP                 s-block     -2.19E-01  1.79E-01   7.56E-02
[BETA]IP                 transition   8.63E-03  1.74E-02   6.04E-04
log([K.sub.OH])          s-block      1.51E-01  1.41E-01   4.02E-02
log([K.sub.OH])          transition  -2.49E-02  1.82E-02   5.46E-04
MP                       s-block     -1.37E-04  3.86E-04   2.87E-07
MP                       transition  -1.80E-04  5.54E-05   5.04E-09
[pK.sub.sp](C[O.sub.3])  transition   3.11E-02  2.68E-02   1.91E-03
r                        s-block      4.69E-01  3.69E-01   2.91E-01
r                        transition   7.18E-01  3.98E-01   2.53E-01
[[sigma].sub.p]          s-block     -8.40E+00  3.13E+00   2.17E+01
[[sigma].sub.p]          transition  -5.49E+00  1.61E+00   5.66E+00
[X.sub.m]                s-block     -1.99E+00  1.14E+00   2.72E+00
[X.sub.m]                transition   5.21E-01  3.75E-01   2.51E-01
X[m.sup.2]r              s-block      8.95E-01  8.46E-01   1.90E+00
X[m.sup.2]r              transition   1.80E-01  5.20E-02   7.05E-03
Z                        s-block     -1.29E-02  2.91E-01   1.47E-01
Z/AR                     s-block     -6.89E-01  3.65E-01   3.11E-01
Z/AR                     transition  -7.02E-01  3.19E-01   1.77E-01
[Z.sup.2]/r              s-block     -5.22E-02  9.49E-02   1.79E-02
[Z.sup.2]/r              transition  -9.05E-02  6.88E-02   9.61E-03

Property                 Group        Percent
                                       Error

AN                       s-block      6.57E-01
AN                       transition   8.23E-01
AN/[BETA]IP              s-block     -3.75E+00
AN/[BETA]IP              transition  -4.07E+00
AR                       s-block     -2.20E+00
AR                       transition  -1.64E+00
[BETA][E.sup.0]          s-block      1.34E+00
[BETA][E.sup.0]          transition   5.88E+00
[rho]                    s-block     -8.23E+00
[rho]                    transition   3.14E-01
[BETA]IP                 s-block     -1.70E-02
[BETA]IP                 transition  -1.49E+00
log([K.sub.OH])          s-block     -2.42E+00
log([K.sub.OH])          transition  -5.35E+00
MP                       s-block     -1.76E+01
MP                       transition   4.61E-01
[pK.sub.sp](C[O.sub.3])  transition  -2.59E+00
r                        s-block     -7.47E+00
r                        transition   1.89E+00
[[sigma].sub.p]          s-block     -2.43E-01
[[sigma].sub.p]          transition   8.13E-01
[X.sub.m]                s-block     -3.13E+00
[X.sub.m]                transition   5.78E+00
X[m.sup.2]r              s-block     -4.52E-02
X[m.sup.2]r              transition  -1.46E+00
Z                        s-block     -5.74E+01
Z/AR                     s-block      2.61E+00
Z/AR                     transition   5.11E-01
[Z.sup.2]/r              s-block      7.27E+00
[Z.sup.2]/r              transition   7.34E+00

(a) Square root of the mean of the sum of the squares of SE
for each fo the 1000 simulations; (b) Variance of the 1000
simulated slopes

Table S14. Average results from 1000 Monte Carlo simulations
of the LTS regression. Percent error denotes the relative error
between the LTS slope from the data model fit compared with the
LTS slope from the Monte Carlo simulation for myocardial infarction.

Property                 Group         Slope     SE (a)   Simulated
                                                            Slope
                                                          Variance
                                                             (a)

AN                       s-block      5.03E-02  1.61E-02   9.28E-04
AN                       transition  -6.00E-04  3.66E-03   3.50E-05
AN/[BETA]IP              s-block      2.36E-01  6.01E-02   1.24E-02
AN/[BETA]IP              transition  -1.54E-03  2.53E-02   1.69E-03
AR                       s-block      1.03E+00  4.61E-01   6.74E-01
AR                       transition   1.86E-01  5.61E-01   7.00E-01
[BETA][E.sup.0]          s-block     -4.31E-01  1.24E+00   5.70E+00
[BETA][E.sup.0]          transition  -2.16E-01  2.54E-01   1.34E-01
[rho]                    s-block     -8.55E-04  3.27E-04   3.13E-07
[rho]                    transition  -1.49E-05  4.34E-05   6.99E-09
[BETA]IP                 s-block     -2.04E-01  2.40E-01   2.15E-01
[BETA]IP                 transition   1.24E-02  3.59E-02   7.23E-03
log([K.sub.OH])          s-block      2.73E-01  1.40E-01   6.72E-02
log([K.sub.OH])          transition   5.19E-03  3.00E-02   2.78E-03
MP                       s-block     -9.26E-04  4.99E-04   7.45E-07
MP                       transition   1.00E-04  9.81E-05   2.05E-08
[pK.sub.sp](C[O.sub.3])  transition  -7.41E-02  5.93E-02   5.92E-03
r                        s-block      1.38E+00  8.24E-01   2.53E+00
r                        transition   1.36E-01  4.52E-01   5.18E-01
[[sigma].sub.p]          s-block      1.11E+01  6.41E+00   1.21E+02
[[sigma].sub.p]          transition   1.11E+00  3.77E+00   2.60E+01
[X.sub.m]                s-block     -1.20E+00  1.54E+00   9.93E+00
[X.sub.m]                transition   2.09E-02  3.55E-01   3.41E-01
X[m.sup.2]r              s-block     -2.29E+00  9.26E-01   2.78E+00
X[m.sup.2]r              transition   1.50E-02  6.85E-02   2.10E-02
Z                        s-block     -6.49E-01  2.70E-01   1.52E-01
Z/AR                     s-block     -8.89E-01  4.71E-01   6.68E-01
Z/AR                     transition  -2.27E-02  5.69E-01   7.78E-01
[Z.sup.2]/r              s-block     -1.60E-01  7.43E-02   1.77E-02
[Z.sup.2]/r              transition  -8.48E-03  8.21E-02   1.57E-02

Property                 Group        Percent
                                       Error

AN                       s-block      1.29E-01
AN                       transition  -8.30E+01
AN/[BETA]IP              s-block     -7.14E-01
AN/[BETA]IP              transition  -1.10E+02
AR                       s-block     -1.97E+00
AR                       transition   1.68E+01
[BETA][E.sup.0]          s-block      1.30E+01
[BETA][E.sup.0]          transition   5.94E+00
[rho]                    s-block     -1.10E+00
[rho]                    transition   1.59E+01
[BETA]IP                 s-block     -8.73E+00
[BETA]IP                 transition  -3.03E+01
log([K.sub.OH])          s-block     -1.88E+00
log([K.sub.OH])          transition   2.54E+01
MP                       s-block     -2.20E+00
MP                       transition   4.99E+00
[pK.sub.sp](C[O.sub.3])  transition  -5.45E+00
r                        s-block     -4.46E+00
r                        transition  -1.37E+01
[[sigma].sub.p]          s-block     -3.74E+00
[[sigma].sub.p]          transition   1.40E+01
[X.sub.m]                s-block     -2.00E+00
[X.sub.m]                transition   2.54E+01
X[m.sup.2]r              s-block     -4.94E-01
X[m.sup.2]r              transition  -3.53E+01
Z                        s-block      2.14E+00
Z/AR                     s-block     -3.44E-01
Z/AR                     transition   1.58E+02
[Z.sup.2]/r              s-block     -6.00E-02
[Z.sup.2]/r              transition  -1.55E+00

(a) Square root of the mean of the sum of the squares of SE
for each fo the 1000 simulations; (b) Variance of the 1000
simulated slopes

Table S15. Average results from 1000 Monte Carlo simulations
of the LTS regression. Percent error denotes the relative error
between the LTS slope from the data model fit compared with the
LTS slope from the Monte Carlo simulation for myocardial ischemia.

Property                 Group         Slope     SE (a)   Simulated
                                                            Slope
                                                          Variance
                                                             (a)

AN                       s-block      5.91E-02  1.70E-02   8.95E-04
AN                       transition   5.55E-04  2.48E-03   1.84E-05
AN/[BETA]IP              s-block      2.76E-01  4.56E-02   7.16E-03
AN/[BETA]IP              transition   7.08E-03  1.70E-02   6.57E-04
AR                       s-block      2.56E+00  3.34E-01   3.57E-01
AR                       transition   1.12E-02  3.95E-01   2.98E-01
[BETA][E.sup.0]          s-block      1.57E+00  6.09E-01   1.52E+00
[BETA][E.sup.0]          transition  -1.12E-01  1.61E-01   4.72E-02
[rho]                    s-block     -7.41E-04  3.55E-04   4.13E-07
[rho]                    transition   1.87E-05  2.71E-05   1.93E-09
[BETA]IP                 s-block     -2.88E-01  1.30E-01   6.67E-02
[BETA]IP                 transition  -1.20E-02  2.04E-02   1.27E-03
log([K.sub.OH])          s-block      2.69E-01  1.27E-01   5.09E-02
log([K.sub.OH])          transition   1.37E-02  1.73E-02   7.40E-04
MP                       s-block     -2.91E-04  6.91E-04   1.26E-06
MP                       transition   4.15E-05  8.95E-05   1.42E-08
[pK.sub.sp](C[O.sub.3])  transition  -6.28E-02  2.46E-02   1.34E-03
r                        s-block      3.30E+00  3.22E-01   3.43E-01
r                        transition   1.17E-01  3.19E-01   2.02E-01
[[sigma].sub.p]          s-block      9.85E+00  5.94E+00   1.02E+02
[[sigma].sub.p]          transition   1.61E+00  2.15E+00   1.43E+01
[X.sub.m]                s-block     -1.77E+00  7.22E-01   2.05E+00
[X.sub.m]                transition   1.99E-01  2.27E-01   1.20E-01
X[m.sup.2]r              s-block     -2.59E+00  2.15E-01   1.84E-01
X[m.sup.2]r              transition   2.60E-02  4.38E-02   6.36E-03
Z                        s-block     -1.60E-01  4.87E-01   5.18E-01
Z/AR                     s-block     -5.51E-01  6.29E-01   1.23E+00
Z/AR                     transition   1.47E-01  3.92E-01   3.29E-01
[Z.sup.2]/r              s-block     -1.48E-01  7.66E-02   1.71E-02
[Z.sup.2]/r              transition  -2.37E-02  5.69E-02   5.47E-03

Property                 Group        Percent
                                       Error

AN                       s-block     -1.13E+00
AN                       transition   1.54E+01
AN/[BETA]IP              s-block     -1.15E-01
AN/[BETA]IP              transition  -2.89E+01
AR                       s-block      1.11E+00
AR                       transition   7.23E+01
[BETA][E.sup.0]          s-block     -5.74E-01
[BETA][E.sup.0]          transition   6.00E+00
[rho]                    s-block      1.52E+00
[rho]                    transition  -3.41E+00
[BETA]IP                 s-block     -1.16E+00
[BETA]IP                 transition   6.04E+00
log([K.sub.OH])          s-block     -8.39E-01
log([K.sub.OH])          transition   5.76E+00
MP                       s-block     -3.32E+01
MP                       transition   8.40E+00
[pK.sub.sp](C[O.sub.3])  transition  -2.54E+00
r                        s-block     -9.39E-02
r                        transition   6.27E+00
[[sigma].sub.p]          s-block      5.23E+00
[[sigma].sub.p]          transition   6.21E+00
[X.sub.m]                s-block      2.81E+00
[X.sub.m]                transition   5.61E-01
X[m.sup.2]r              s-block      3.08E-01
X[m.sup.2]r              transition  -1.08E+00
Z                        s-block     -6.63E+00
Z/AR                     s-block      6.83E+00
Z/AR                     transition  -1.41E+01
[Z.sup.2]/r              s-block      7.16E-01
[Z.sup.2]/r              transition  -1.02E+00

(a) Square root of the mean of the sum of the squares of SE
for each fo the 1000 simulations; (b) Variance of the 1000
simulated slopes

Table S16. Average results from 1000 Monte Carlo simulations of
the LTS regression. Percent error denotes the relative error
between the LTS slope from the data model fit compared with the
LTS slope from the Monte Carlo simulation for stroke.

Property                 Group         Slope     SE (a)   Simulated
                                                            Slope
                                                          Variance
                                                             (a)

AN                       s-block      3.85E-02  8.44E-03   2.33E-04
AN                       transition  -1.10E-02  7.54E-03   1.14E-04
AN/[BETA]IP              s-block      1.21E-01  8.06E-02   1.93E-02
AN/[BETA]IP              transition  -6.93E-02  4.85E-02   4.32E-03
AR                       s-block     -1.98E-01  3.13E-01   3.22E-01
AR                       transition  -2.06E+00  1.09E+00   1.84E+00
[BETA][E.sup.0]          s-block     -8.86E-01  5.18E-01   9.48E-01
[BETA][E.sup.0]          transition  -4.56E-01  4.43E-01   2.88E-01
[rho]                    s-block      3.31E-04  1.03E-04   3.21E-08
[rho]                    transition  -8.35E-05  9.04E-05   1.64E-08
[BETA]IP                 s-block      7.56E-02  7.73E-02   2.47E-02
[BETA]IP                 transition   2.16E-02  7.15E-02   1.45E-02
log([K.sub.OH])          s-block     -9.89E-02  5.24E-02   8.75E-03
log([K.sub.OH])          transition   2.59E-03  5.79E-02   6.97E-03
MP                       s-block      3.82E-04  1.25E-04   4.91E-08
MP                       transition   3.52E-04  2.86E-04   1.24E-07
[pK.sub.sp](C[O.sub.3])  transition  -2.20E-01  1.12E-01   2.42E-02
r                        s-block     -2.91E-01  3.66E-01   4.84E-01
r                        transition  -9.07E-01  8.43E-01   1.26E+00
[[sigma].sub.p]          s-block     -9.59E+00  1.34E+00   5.20E+00
[[sigma].sub.p]          transition  -1.37E+00  7.51E+00   1.02E+02
[X.sub.m]                s-block      4.55E-01  5.17E-01   1.20E+00
[X.sub.m]                transition  -1.12E+00  7.13E-01   1.02E+00
X[m.sup.2]r              s-block      2.53E+00  5.38E-02   1.06E-02
X[m.sup.2]r              transition  -1.88E-01  1.09E-01   2.62E-02
Z                        s-block      2.59E-01  7.03E-02   9.85E-03
Z                        transition  -2.50E-01  5.77E-01   3.80E-01
Z/AR                     s-block      3.38E-01  1.58E-01   7.50E-02
Z/AR                     transition  -1.02E-02  7.12E-01   1.33E+00
[Z.sup.2]/r              s-block      6.10E-02  2.56E-02   1.81E-03
[Z.sup.2]/r              transition   4.56E-02  1.16E-01   3.06E-02

Property                 Group        Percent
                                       Error

AN                       s-block     -1.18E+00
AN                       transition  -5.57E+00
AN/[BETA]IP              s-block      1.57E-01
AN/[BETA]IP              transition  -3.06E+00
AR                       s-block      3.08E+00
AR                       transition  -5.23E+00
[BETA][E.sup.0]          s-block     -3.74E+00
[BETA][E.sup.0]          transition   4.33E+00
[rho]                    s-block     -2.15E+00
[rho]                    transition   2.32E+00
[BETA]IP                 s-block      7.80E+00
[BETA]IP                 transition   8.72E+00
log([K.sub.OH])          s-block      6.53E-02
log([K.sub.OH])          transition  -7.42E+01
MP                       s-block     -2.41E+00
MP                       transition  -2.06E+00
[pK.sub.sp](C[O.sub.3])  transition  -4.66E+00
r                        s-block     -2.24E+00
r                        transition   2.84E-01
[[sigma].sub.p]          s-block      4.74E-01
[[sigma].sub.p]          transition   1.56E+01
[X.sub.m]                s-block      4.21E+00
[X.sub.m]                transition   1.14E+00
X[m.sup.2]r              s-block      2.06E-01
X[m.sup.2]r              transition  -7.66E-01
Z                        s-block      3.26E-01
Z                        transition   7.91E+00
Z/AR                     s-block     -8.80E-01
Z/AR                     transition   2.09E+02
[Z.sup.2]/r              s-block     -2.66E+00
[Z.sup.2]/r              transition  -2.12E+00

(a) Square root of the mean of the sum of the squares of SE
for each fo the 1000 simulations; (b) Variance of the 1000
simulated slopes

Table S17. Average results from 1000 Monte Carlo simulations
of the LTS regression. Percent error denotes the relative
error between the LTS slope from the data model fit compared
with the LTS slope from the Monte Carlo simulation for thrombosis.

Property                 Group         Slope     SE (a)   Simulated
                                                            Slope
                                                          Variance
                                                             (a)

AN                       s-block      1.35E-02  2.26E-02   1.53E-03
AN                       transition  -6.38E-04  5.48E-03   6.45E-05
AN/[BETA]IP              s-block      7.37E-02  9.07E-02   2.69E-02
AN/[BETA]IP              transition   2.00E-03  3.64E-02   2.27E-03
AR                       s-block      4.39E-01  3.92E-01   4.71E-01
AR                       transition   2.24E+00  5.66E-01   4.82E-01
[BETA][E.sup.0]          s-block      2.24E-01  6.42E-01   1.47E+00
[BETA][E.sup.0]          transition   3.02E-03  4.25E-01   2.89E-01
P                        s-block      1.35E-03  1.32E-04   5.03E-08
[rho]                    transition   3.54E-05  7.23E-05   1.07E-08
[rho]                    s-block     -1.41E-01  1.05E-01   4.73E-02
[BETA]IP                 transition  -3.92E-02  4.71E-02   5.09E-03
[BETA]IP                 s-block      1.51E-01  8.09E-02   2.25E-02
log([K.sub.OH])          transition   3.50E-02  4.28E-02   3.43E-03
MP                       s-block     -7.05E-04  2.92E-04   2.34E-07
MP                       transition   2.02E-05  2.42E-04   9.16E-08
[pK.sub.sp](C[O.sub.3])  transition  -1.84E-01  1.08E-01   2.49E-02
r                        s-block      5.07E-01  4.54E-01   6.34E-01
r                        transition   1.65E-01  5.69E-01   5.41E-01
[[sigma].sub.p]          s-block     -1.98E+01  2.98E+00   2.97E+01
[[sigma].sub.p]          transition  -1.05E+01  3.39E+00   2.13E+01
[X.sub.m]                s-block     -8.56E-01  6.63E-01   2.04E+00
[X.sub.m]                transition  -3.02E-01  6.46E-01   9.21E-01
X[m.sup.2]r              s-block     -4.22E-01  8.16E-01   2.41E+00
X[m.sup.2]r              transition   2.04E-01  9.91E-02   2.46E-02
Z                        s-block     -3.19E-01  2.17E-01   9.16E-02
Z                        transition  -1.99E-01  4.41E-01   2.39E-01
Z/AR                     s-block     -4.99E-01  2.87E-01   2.54E-01
Z/AR                     transition  -2.60E+00  2.95E-01   2.48E-01
[Z.sup.2]/r              s-block     -7.69E-02  5.19E-02   8.80E-03
[Z.sup.2]/r              transition  -4.39E-02  8.93E-02   1.78E-02

Property                 Group        Percent
                                       Error

AN                       s-block      9.22E-01
AN                       transition   7.49E-01
AN/[BETA]IP              s-block      3.80E+00
AN/[BETA]IP              transition   5.82E+02
AR                       s-block     -2.23E+00
AR                       transition  -1.61E+00
[BETA][E.sup.0]          s-block      7.89E-01
[BETA][E.sup.0]          transition   1.37E+02
P                        s-block      1.90E-01
[rho]                    transition   6.08E+00
[rho]                    s-block     -4.31E+00
[BETA]IP                 transition   5.82E+00
[BETA]IP                 s-block     -1.52E+00
log([K.sub.OH])          transition   3.81E+00
MP                       s-block     -3.50E+00
MP                       transition   2.05E+00
[pK.sub.sp](C[O.sub.3])  transition   9.19E-01
r                        s-block      5.24E+00
r                        transition  -1.78E+01
[[sigma].sub.p]          s-block     -6.95E-01
[[sigma].sub.p]          transition  -2.75E+00
[X.sub.m]                s-block     -1.02E+00
[X.sub.m]                transition  -1.06E+01
X[m.sup.2]r              s-block     -3.38E+00
X[m.sup.2]r              transition   1.06E-01
Z                        s-block      3.12E+00
Z                        transition   2.73E+00
Z/AR                     s-block     -3.61E+00
Z/AR                     transition  -7.69E-02
[Z.sup.2]/r              s-block      4.67E-01
[Z.sup.2]/r              transition   3.89E+00

(a) Square root of the mean of the sum of the squares of SE
for each fo the 1000 simulations; (b) Variance of the 1000
simulated slopes


Qingyu Meng, (1) Jennifer Richmond-Bryant, (2) Shou-En Lu, (1) Barbara Buckley, (2) William J. Welsh, (3) Eric A. Whitsel, (4), (5) Adel Hanna, (6) Karin B. Yeatts,5 Joshua Warren, (7) Amy H. Herring, (7) and Aijun Xiu (6)

(1) School of Public Health, University of Medicine and Dentistry of New Jersey, Piscataway, New Jersey, USA; (2) National Center for Environmental Assessment, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, USA; (3) Robert Wood Johnson Medical School, University of Medicine and Dentistry of New Jersey, Piscataway, New Jersey, USA; (4) Department of Medicine, (5) Department of Epidemiology, (6) Institute for the Environment, and (7) Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
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Title Annotation:Research
Author:Meng, Qingyu; Richmond-Bryant, Jennifer; Lu, Shou-En; Buckley, Barbara; Welsh, William J.; Whitsel,
Publication:Environmental Health Perspectives
Article Type:Report
Geographic Code:1USA
Date:May 1, 2013
Words:27127
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