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An assessment of the population variance of the strong ion gap using Monte Carlo simulation.

Deriving the strong ion gap (SIG) is becoming an accepted method for estimating the presence of unmeasured ions in human plasma (1-4). It is calculated from the difference between two methods of measuring the plasma strong ion difference (SID), the apparent strong ion difference ([SID.sub.a]) and the effective strong ion difference ([SID.sub.e]). [SID.sub.a] is calculated from the net charge effect of the measured plasma strong ions, whereas [SID.sub.e] is calculated from the net charge effect of the plasma weak acids with SIG=[SID.sub.a]-[SID.sub.e]. In the absence of unmeasured plasma ions, [SID.sub.a][approximately equal to][SID.sub.e] with SIG[approximately equal to]0.0 mEq/l. Despite its rising popularity, a population variance for SIG has never been established and without such a measure, a reference range cannot be quoted (5). This makes clinical interpretation of SIG virtually impossible. However, with knowledge of the population standard deviations of the parameters that make up the SIG, a 95% confidence interval (CI) for SIG can be indirectly derived using methods of static (Monte Carlo) simulation.

The simulation that follows was undertaken using the assumptions pertaining to current strong ion/weak acid theory. That is, that the three main independent determinants of the acid-base status in any compartment are the SID, weak acid effect and the partial pressure of carbon dioxide (6).

GLOSSARY

[alb] Plasma concentration of albumin (g/l)

[MW.sub.alb] Molecular weight of albumin (66500 Daltons)

[[P.sub.i]] Plasma concentration of inorganic phosphate (mmol/l)

[[A.sup.-]] Total plasma weak acid charge (mEq/l)

PC[O.sub.2] Partial pressure of carbon dioxide (mmHg)

TC[O.sub.2] Total carbon dioxide (mEq/l)

S The solubility coefficient of carbon dioxide in human plasma at 37[degrees]C (0.0307 mmol.l-1.mmHg-1)

SD Standard deviation, where SD equals the positive square root of variance

QHPSS Queensland Health Pathology and Scientific Services. QHPSS is the principal provider of public sector pathology and scientific services in Queensland. All participating laboratories are registered and accredited by the National Association of Testing Authorities (NATA) acting in collaboration with the Royal College of Pathologists of Australasia (RCPA).

All other variables are identified either by name or chemical symbol and are reported in either mEq/l or mmol/l.

MATHEMATICAL AND STATISTICAL METHODOLOGY

In general, the simulation was structured to produce a large sample of 11 primary variables ([[Na.sup.+]], [[K.sup.+]], [[Ca.sup.+2]], [[Mg.sup.+2]], [[Cl.sup.-]], [L-lactate], [alb], [[P.sub.i]], PC[O.sub.2], pH and TC[O.sub.2]) thus enabling the calculation of the dependent variable [HC[[O.sup.-]sub.3] and finally the compound variables SIG, anion gap (AG) and corrected anion gap ([AG.sub.c]).

Equation 1 models the three main independent variables of strong ion theory with [HC[[O.sup.-]sub.3] calculated using the Henderson-Hasselbalch equation (equation 2), [[A.sup.-]] calculated using equation 3 and [SID.sub.a] and [SID.sub.e] calculated using equations 4 and 5 respectively (7,8).

[SID.sub.a]- [HC[[O.sup.-]sub.3]-[[A.sup.-]]=0 (1)

[HC[[O.sup.-]sub.3](mEq/l)=S x PC[O.sub.2] x [10.sup.(pH-6.12)] (2)

[[A.sup.-]](mEq/l)=[alb] x (0.123pH-0.631)+[[P.sub.i]] x (0.309pH-0.469) (3)

[SID.sub.a] (mEq/l) = ([[NA.sup.+]]+[[K.sup.+]]+[[Ca.sup.+2]]+ [[Mg.sup.+2]])-([[CI.sup.-]]+[L-lactate]) (4)

[SID.sub.e] (mEq/l)=[HC[[O.sup.-]sub.3]+[[A.sup.-]] (5)

Using the AUSLAB mean values for the relevant strong ions, weak acids and PC[O.sub.2], a unique value for [[H.sup.+]] was found using the geometric convergence method described by Stewart (see Appendix A) (9). [pH.sub.c] was calculated using equation 6 and this value was used to calibrate the model. SIG and AG were calculated using equations 7 and 8:

[pH.sub.c]= [-log.sub.10]([[H.sup.+]]) (6)

SIG (mEq/l)=[SID.sub.a]-[SID.sub.e] (7)

AG (mEq/l)=[[Na.sup.+]]-([[CI.sup.-]]+[TC[O.sub.2]]) (8)

In equation 8, TC[O.sub.2] represents the total carbon dioxide content of plasma (dissolved C[O.sub.2] plus carbonate and bicarbonate species) and is derived by measuring the rate of change of a sample pH/ PC[O.sub.2] pair. The method is common to large automated analysers and is generally preferred over AUSLAB AUSLAB is the corporate laboratory information system for QHPSS providing a single statewide pathology system for all public facilities in Queensland. AUSLAB provides a standard user interface for all pathology and scientific testing performed within the Queensland Health network and publishes normal population ranges for all measured analytes. These ranges are regularly checked and validated. They are used in this paper to calculate the required standard deviations. the phosphoenolpyruvate/malate dehydrogenase enzymatic method (10-13).

Given that the main current contender for SIG is the albumin and lactate [AG.sub.c], this calculation was also included in the analysis (equation 9) (14).

[AG.sub.c] (mEq/l)=AG+0.25 x (42-[alb])-[L-lactate] (9)

Of interest, it is noted that equation 9 treats albumin as a strong ion (pH invariant charge) though this is contrary to theory. Nevertheless the equation is commonly used.

As a further check, the SIG was also calculated by the method of Staempfli and Constable ([SIG.sub.S&C]) using equation 10 below (15).

[SIG.sub.S&C](mEq/1)=[alb] x (0.378/1 + [10.sup.(7.1--pH))--AG (10)

The simulation was run in three parts. First, the generation of the individual primary variables. These were then used to construct the required samples. Second, the simulator was calibrated. Third, a long run, large sample analysis was conducted.

In order to begin, pairs of (pseudo)random numbers were generated using a linear congruential method (16). Each pair was then used to generate a standard normal variate, n, using the Box-Muller method (17). One normally distributed, primary variable for moiety k, [Z.sub.k], was then constructed using [Z.sub.k] = [[micro].sub.k] + [[sigma].sub.k]n where, for that variable, [[micro].sub.k] is the population mean and [[sigma].sub.k] is the population standard deviation respectively. This process was used to generate each of the primary variables required to eventually calculate one instance of the SIG. This process was repeated until a sample size of 20,000 had been generated.

Because the bulk of the population variance of SIG arises from variation in [[Na.sup.+]] and [[Cl.sup.-]] and the activities of these electrolytes are partially correlated in the general population, special consideration needs to be given to them during the simulation. In order to estimate this correlation, data were collected using 100 healthy reference adults (volunteer blood donors) and dependencies between the measured values for plasma electrolytes, lactate, albumin and phosphate were examined. For these observational data, the local Human research Ethics Committee waived the requirement for ethics approval.

Working thus, three separate samples were created - an independent, dependent and a linked (partially correlated) sample--each as a result of the particular defined relationship between [[Na.sup.+]] and [[Cl.sup.-]].

The simulator was calibrated by comparing the standard deviation of the calculated pH against the population standard deviation for measured pH supplied by AUSLAB.

Every set of variables was checked for normality using the Shapiro-Francia test for samples of size 5 [is less than or equal to]N [is less than or equal to]5000 or the D'Agostino [K.sup.2] test for samples where N >5000 (18,19).

Once the model was checked and calibrated, the final simulation was run using a sample size of 20,000. Even though this figure was selected arbitrarily, it is of sufficient size to reliably generate the required normal variates.

Each run of 20,000 constituted one sample set. Where required, simulation programs were written using C++ and the subsequent results analysed with STATA [TM].

Statistics reported are mean, SD and 95% CI.

RESULTS

The data from the reference volunteer population sample were all normally distributed. The only significant relationship was a partial positive correlation between [[Na.sup.+]] and [[Cl.sup.-]] with r=+0.64 (95% CI +0.51, +0.74). This relationship was further described by the linear regression equation [[CI.sup.-]]=0.64 x [[Na.sup.+]]+15.6 where both coefficients were significant. This correlation coefficient was used to generate the linked sample.

The simulator was loaded with the data from Table 1 and set to generate 3 x 20,000 sample sets - one set for each sodium/chloride correlation (independent: R = 0.00, linked: R = +0.64 and dependent: R = +1.00).

[FIGURE 1 OMITTED]

The primary variables were all normally distributed and Figure 1 illustrates a representative selection of the resulting distributions.

[pH.sub.c] was analysed for each sample within each set and the resulting standard deviations are shown in Table 2. There was no statistical difference between each mean [pH.sub.c] in the sample sets. The validity of the linked model is reinforced by returning a standard deviation for [pH.sub.c] that closely matched the population value for measured pH supplied by AUSLAB.

Simultaneously, the compound variables [SID.sub.a], [SID.sub.e], SIG, AG, [AG.sub.c] and [SIG.sub.S&C] were calculated for each sample within the set using the relevant equations (equations 4, 5, 7, 8, 9 and 10). Each of the compound variables was normally distributed.

The standard deviation results are presented in Table 3. As expected, the standard deviations for the compound variables involving [[Na.sup.+]] and [[Cl.sup.-]] decrease as the respective R value increases.

In each model, the mean SIG was 3.9 mEq/l. The linked model generated a standard deviation for SIG of [approximately equal to]3.29 mEq/l. This resulted in a 95% CI of 3.9 [+ or -] 6.4 mEq/l or a range of -2.5 to 10.3 mEq/l. Figure 2 illustrates this result.

[FIGURE 2 OMITTED]

For the independent and dependent samples, the 95% CIs were calculated as 3.9 [+ or -] 7.6 mEq/l and 3.9 [+ or -] 5.1 mEq/l respectively.

Mean [SIG.sub.S&C] in each sample set was -1.2 mEq/l. When compared to the SIG SD, the [SIG.sub.S&C] SD was larger because the albumin variance was amplified by the exponent [10.sup.(7.1-pH)].

Mean AG was 8.5 mEq/l in each sample set. The standard deviation for the AG in the linked sample was 2.7 mEq/l giving a 95% CI of 3.2 to 13.8 mEq/l. This agreed closely with the reported AUSLAB reference range of 3.0 to 14.0 mEq/l.

Though not used regularly yet in clinical practice, the mean [AG.sub.c] was 7.7 mEq/l with 95% CIs of 0.4 to 15.0 mEq/l, 1.6 to 13.8 mEq/l and 3.0 to 12.4 mEq/l for the independent, linked and dependent sample sets respectively.

DISCUSSION

A simulation based on the strong ion approach to acid-base physiology was conducted to predict the population variance of the calculated variable, SIG. This approach was taken because the calculation of a population estimate for SIG using direct analytical methods of pooled variance is not possible. This difficulty is due to the large variation in the values for mean and standard deviation present in the parameters that constitute SIG. In this context, Monte Carlo methods of simulation are popular because they are robust, efficient and flexible. These methods are particularly suited to problems that either involve an element of 'randomness' or those that are very difficult to solve using other, more direct numerical methods, or both. Using the stochastic methods of Monte Carlo simulation it is possible to reproduce a large enough sample containing all of the statistical vagaries of the real population, calculate the SIG using common algorithms and subject the result to detailed analysis. Thus, a very reliable result can be produced. The simulation can be re-run if the SIG needs to be recalculated for a different population with different parameter means and variances. Once a sample is defined and analysed, the overall clinical utility of a measurement like SIG can be evaluated using clinical studies.

One of the limitations of the strong ion model is the inability to determine an accurate value for the true plasma SID. This affects the calculation and clinical utility of derivatives of strong ion theory, specifically the SIG. In an exhaustive analysis based on analyte values taken from filtrands of human plasma and using techniques of nonlinear regression to solve for multiple variables simultaneously, Staempfli and Constable calculated mean plasma values for both [SID.sub.a] and [SID.sub.e] ranging between 37.1 mEq/l and 46.0 mEq/l with a 95% CI for true SID of 29.0 mEq/l to 45.0 mEq/l (15). Several other authors agree with this range (20-23). The values for [SID.sub.a] (41.5 mEq/l, 95% CI 37.2, 45.8 mEq/l) and [SID.sub.e] (37.7 mEq/l, 95% CI 33.2, 42.2 mEq/l) used in this study lie within the 95% CI quoted by Staempfli et al.

In general, when interpreting any directly measured or calculated variable, two sources of error need to be taken into account. The first and major source is due to natural variation in the population and the second, minor source is due to measurement imprecision. Measurement imprecision is usually only a small fraction of the overall variance and, under normal circumstances, contributes little to the final result presented to the clinician for interpretation (Appendix C). Ultimately, the clinical utility of any measured or calculated variable lies with the ability of the clinician to place that variable either inside or outside its nominal population distribution, where a very wide CI may render the particular variable useless as a diagnostic or prognostic discriminator. To add further complexity, compound variables will always be associated with a population variance inherited from the parameters used in their calculation. For example, if a patient registers a measured serum sodium concentration of 130.0 mmol/l and the reference range is 135.0 to 145.0 mmol/l we may confidently say that he or she is hyponatraemic. However, due to random fluctuations, the parameters used to calculate SIG may disguise the presence of unmeasured ions. Because of this wide intrapopulation variablitiy it is important to ascertain the individual baseline values for the measured components that make up the compound variable in question, otherwise disorders that cause deviations may go unrecognised. For SIG in particular, a patient may harbour a significant activity of unmeasured ions yet have a calculated value that lies within the reference population range. This relative insensitivity is common to all compound variables (e.g. AG, [AG.sub.c] and calculated bicarbonate) and, for SIG, is illustrated in Figure 3.

To date, many studies have been performed to examine the accuracy of several derived parameters including SIG, uncorrected and corrected AG and base excess, as both diagnostic and prognostic indices, with mixed results (14,24-30). Because the uncorrected AG is influenced by the concentration of the plasma weak acids albumin and inorganic phosphate, and because the base excess cannot distinguish between acidaemias due to low [SID.sub.a] or excessive activities of circulating but unmeasured ions, another discriminatory index may be required to aid in the diagnosis of patients where significant and undifferentiated acidaemia is a clinical problem. While it is possible to compensate for some of these influences (e.g. [AG.sub.c]), the SIG integrates these factors into the calculation thus accounting for the effects of the plasma weak acids and the SID. Mathematically, SIG[approximately equal to]AG-[[A.sup.-]] or alternatively, AG[approximately equal to]SIG+[[A.sup.-]]. Thus SIG will report only the unmeasured charged species (both buffer and non-buffer) which are of interest to clinicians and researchers alike. Because of this, SIG may be a better diagnostic and prognostic index and this contention has been borne out by at least one recent publication (31,32). It is interesting to note that, because of the relationship between SIG and AG, any pH-dependent charge variability inherent in the calculation of [[A.sup.-]] will be coupled to the calculation of AG. This apparent variability in the relationship between SIG and AG has been also noted recently33.

While discussing SIG, it may be of some interest to investigate the apparent bias associated with its calculated mean value. The principle of electroneutrality dictates that, in any physiological compartment, the net macroscopic charge equals zero. For any charged species i present in this compartment in concentration [C.sub.i] (mmol/l) and possessing valence [z.sub.i] (eq/mol), this relationship is expressed in equation 11.

[summation] [z.sub.i][C.sub.i] (mEq/l)= 0.0 (11)

Rearranging equation 11 and using absolute valence values, reveals the familiar SIG equation

[summation] (cations)- [summation] (anions)=SIG (mEq/l)=[XA] (12) where [XA] represents the unmeasured ions that are of particular interest to clinicians (8,23). Ideally, in a healthy member of the population [XA]=0.0 mEq/l. However, in this current study SIG=[XA]=3.9 mEq/l, suggesting a net surplus of anions. This unaccounted charge has been variably noted by other authors (1,26). Moviat et al found that the total anionic charge contributed by amino acids, organic acids and uric acid only amounted to approximately 0.60 mEq/l (34). Staempfli and Constable also cite sulphate, D-lactate, nonesterified fatty acids and keto-acids as the likely contributors, noting that "the concentrations of these anions are too low to account for all of the unaccounted charge" (15). In the same paper, they go on to state that "unaccounted protein and phosphate charge are responsible for most of the unmeasured strong anion charge in human plasma".

[FIGURE 3 OMITTED]

In 1993, Fogh-Andersen et al measured the ionic binding of sodium, potassium, calcium and chloride on human albumin across a pH range of 4.0 to 9.0 using both flame-emission photometry and ionselective electrodes (35). On average, they found that at a pH of 7.40, one calcium and seven chloride ions were bound per albumin molecule. At physiological concentrations of albumin ([approximately equal to]0.65 mmol/l) this would result in a net extra surface charge of approximately 0.65 x (-7 x 1+1 x 2)=3.2 mEq/l. Combining this result with the data of Moviat et al virtually accounts for the missing charge. This extra negative charge on albumin is currently unaccounted because the commonly used model of Figge et al (equation 3) is based on native human albumin, stripped of bound ions while contemporary plasma electrolyte measurements use ion selective electrodes. Ion selective electrodes measure unbound (ionised) activities in plasma thus leaving the bound ions unaccounted (36). If this extra ion binding were incorporated into the weak acid equations, [XA] may finally equal zero in the reference population. To be of clinical use, this ion binding would have to be mapped across the physiological range of pH in much greater detail than is currently available.

Finally it is noted that in normally distributed data, the mean and standard deviation are independent. Therefore, adjustment of the mean SIG will not affect its population variance.

In conclusion, a population 95% CI of approximately [+ or -] 6.5 mEq/l will most likely render the calculation of SIG no more or less useful than the calculation of either AG or [AG.sub.c] in the diagnosis, treatment and prognostication of patients with acid-base disturbances. This contention is borne out by the similarities in the standard deviations of the SIG, AG and [AG.sub.c]. Each possesses a relatively large range and share the difficulty of reliably interpreting a value placed outside that range. While the concept of SIG is attractive, its use in clinical practice may be hampered by its wide population CI. Ultimately, it may prove more productive to perfect attempts aimed at directly quantifying the currently unmeasured ions that are of such interest to clinicians (34). For example, the measurement of plasma [beta]-hydroxy butyrate is now becoming much more common and assists in the differential diagnosis of acute metabolic acidaemia in the presence of hyperglycaemia (37-39). Failing this, the use of a parameter that measures system (buffer) capacity such as the Stewart-Figge corrected base excess ([BE.sub.ua]) or a similar parameter derived directly from strong ion theory (e.g. [partial derivative]SID/[partial derivative]pH) may improve both diagnostic and prognostic accuracy (24,40).

Accepted for publication on June 2, 2009.

APPENDICES

Appendix A

A geometric convergence method for calculating pH:

1. Select a pair of positive, non-zero values representing the extremes of the [[H.sup.+]] range. For example, set LO=1.0E-14 and HI=1.0E+00.

2. Calculate [H.sup.+] and [square root of] LO x HI =-log10([[H.sup.+]]).

3. Calculate [SID.sub.a] using equation 4.

4. Calculate [SID.sub.e] using equations 2, 3 and 5.

5. Calculate SIG using equation 7.

6. If SIG <0.0, then set LO=[H.sup.+] whereas if SIG >0.0, set HI=[[H.sup.+]].

7. Repeat steps 2 to 6 until the absolute value of SIG falls below some preset limiting value (e.g. 1.0E-08).

8. The result will be the value for pH at 8. SIG=0.0 mEq/l for that particular apparent SID, concentration of albumin and phosphate and partial pressure of carbon dioxide.

NB: This calculation forces SIG=0.0. If there is a discrepancy between the calculated values of [SID.sub.a] and [SID.sub.e] it will be reflected in a change in the calculated [HC[[O.sup.-]sub.3] and thence pH. For [SID.sub.a] >[SID.sub.e], [HC[[O.sup.-]sub.3] will exceed the reported normal value and the resulting calculated pH will be greater than 7.40.

Appendix B

A method of linking normal distributions to achieve partial correlation (dependence)

Given [Z.sub.Na]=[[micro].sub.Na]+[[sigma].sub.Na][n.sub.1] and [Z.sub.Cl]=[[micro].sub.Cl]+[[sigma].sub.Cl][n.sub.2] where [[micro].sub.ion] and [[sigma].sub.ion] represent the mean and standard deviation of the species respectively and where [n.sub.1]=[N.sub.1](0,1), that is, a normally distributed variable with a mean of zero and a standard deviation of one, then [n.sub.2] may be defined for each of the correlation scenarios as follows:

For complete independence between [Z.sub.Na] and [Z.sub.Cl] (R = 0.00), [n.sub.2]=[N.sub.2](0,1), that is, a second independent normally distributed variable with a mean of zero and a standard deviation of one.

For complete dependence between [Z.sub.Na] and [Z.sub.Cl] (R=+1.00), [n.sub.2]=[n.sub.1].

For partial dependence between [Z.sub.Na] and [Z.sub.Cl] (0.00 <R <+1.00),

[n.sub.2] = R x ([n.sub.1 + [square root of 1/[R.sup.2] - 1 x [N.sub.3] (0,1)]

with R representing the required correlation (R [not equal to] 0) and [N.sub.3] (0,1) a third independent, standard normally distributed variable. By selecting appropriate values for R, +0.64 in this case, the true population correlation coefficient can be closely approximated. Figure 4 illustrates the relationships between [[Na.sup.+]] and [[Cl.sup.-]] used in this study.

NB: This method works equally well for negatively correlated results where (-1.00 <R <0.00).

Appendix C

Quantifying the effect of measurement error

The quoted ranges used by clinicians incorporate both the natural variation in the population and a small amount of measurement imprecision. As an academic exercise it may interesting to quantify the added error due to the measurement imprecision.

[FIGURE 4 OMITTED]

In order to simulate the effect of measurement, each result for each primary variable was altered in accordance with a secondary normal distribution. This secondary distribution was based on the known imprecision associated with the measurement of that particular variable (Table 4).

The measurement results were constructed using [Z.sub.mk]=[Z.sub.k]+[sigma]mkn where [Z.sub.k] is the original simulated value for primary variable k, [sigma]m is the measurement standard deviation associated with that variable k (Table 4) and n is a standard normal variate. The simulation was rerun to generate a sample of 20,000 and the population only standard deviations were calculated using standard techniques of pooled variance.

The combined population + measurement results were approximately 1.5% higher than the population only results. For example, if it were possible to exclude the measurement imprecision, the reported SIG range for the linked model would fall from 3.90 [+ or -] 6.40 mEq/l to 3.90 [+ or -] 6.30 mEq/l. Similar proportionate falls are noted in each compound variable.

In this context, the degree of calculated parameter variance inflation due to the measurement imprecision of modern laboratory analysers is clinically insignificant.

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(40.) Wooten EW. Calculation of physiological acid-base parameters in multicompartment systems with application to human blood. J Appl Physiol 2003; 95:2333-2344.

C. M. ANSTEY *

Department of Critical Care Medicine, Sunshine Coast Hospital, Nambour, Queensland, Australia

* M.B., B.S., B.Sc., M.Sc., F.A.N.Z.C.A., F.J.F.I.C.M., Director.

Address for correspondence: Dr C. M. Anstey, c/- Intensive Care Unit, Department of Critical Care Medicine, PO Box 547, Nambour, Qld 4560.
TABLE 1
Summary of the 10 primary variables used to calculate the SIG.
The 11th variable (TCO2) was generated in order to calculate
AG and [AG.sub.c]

Variable ([Z.sub.k]) Units Mean (95% CI) Calculated SD

[[Na.sup.+]] mEq/l 140.0 (135.0, 145.0) 2.55
[[K.sup.+]] mEq/l 4.00 (3.35, 4.65) 0.33
[[Ca.sup.+2]] mEq/l 2.50 (2.30, 2.70) 0.10
[[Mg.sup.+2]]] mEq/l 0.80 (0.50, 1.10) 0.15
[[Cl.sup.-]] mEq/l 105.0 (100.0, 110.0) 2.55
[L-lactate] mEq/l 0.80 (0.20, 1.40) 0.30
[alb] g/l 42.0 (35.0, 49.0) 3.60
[Pi] mmol/l 1.15 (0.80, 1.50) 0.18
pH - 7.40 (7.35, 7.45) 0.026
PC[O.sub.2] mmHg 40.0 (35.0, 45.0) 2.55
TC[O.sub.2] mEq/l 26.5 (22.0, 31.0) 2.30

Means and 95% CIs for each variable are courtesy of AUSLAB.
SD is calculated from (95% CI upper bound--95% CI lower
bound)/(2.0 x 1.96). Once standard normal variates are generated,
simulated values for each of these 11 primary variables can be
calculated.

TABLE 2
Calculated pH results (pHc) for the initial samples of 20,000

 Independent Dependent
 model Linked model model
 R=0.00 R=+0.64 R=+1.00

pHc mean (SD) 7.466 (0.072) 7.467 (0.027) 7.469 (0.015)

The linked model gives the closest approximation to the reported
population SD for measured pH (0.026). In each case, pHc
was normally distributed. Mean [Ph.sub.c] is elevated for
the reasons outlined in Appendix A.

TABLE 3
Population standard deviation results for the three samples

 Independent Linked Dependent
Compound model model model
variable R=0.00 R=+0.64 R=+1.00

[SID.sub.a] (mEq/l) 3.09 2.24 1.05
[SID.sub.e] (mEq/l) 2.40 2.41 2.40
SIG (mEq/l) 3.89 3.29 2.63
[SIG.sub.S&C] (mEq/l) 4.03 3.42 2.79
AG (mEq/l) 3.69 2.69 2.22
[AG.sub.c] (mEq/l) 3.74 3.10 2.39

The three sodium/chloride models are identified
by their r values. In each case the means were: [SID.sub.a]=41.5
mEq/l, [SID.sub.e]=37.6 mEq/l, SIG=3.9 mEq/l,
[SIG.sub.S&C]=-1.2 mEq/l, AG=8.5 mEq/l and
[AG.sub.c]=7.7 mEq/l. The SD for [AG.sub.c] was
slightly larger than for AG because its calculation
involved more variables. The SD for [SID.sub.e]
remained unchanged between the models because its
calculation does not involve [[Na.sup.+]] or
[[Cl.sup.-]]. 95% CI can be calculated from
(mean [+ or -] 1.96 SD).

TABLE 4
Standard deviations associated with the measurement of the
primary variables

 Measurement Measurement
Variable Units SD Machine methodology

[[Na.sup.+]] * mEq/l 0.500 Radiometer ISE DP
[[K.sup.+]] * mEq/l 0.001 Radiometer ISE DP
[[Ca.sup.+2]] mEq/l 0.008 Radiometer ISE DP
[[Mg.sup.+2]] mmol/l 0.040 Beckman CM
[[Cl.sup.-]] * mEq/l 0.600 Radiometer ISE DP
[lactate] mEq/l 0.050 Radiometer LOM
[alb] g/l 0.870 Beckman BPM
[Pi] mmol/l 0.040 Beckman TEM
PC[O.sub.2] Torr 0.340 Radiometer ISE DP
TC[O.sub.2] mEq/l 0.670 Beckman RCM
pH - 0.002 Radiometer ISE DP

Analysers used were the Beckman[TM] DxC600i and the radiometer[TM]
ABL800 FLEX. Measurement standard deviations were taken
from the May 2009 Queensland Health Uncertainty of
Measurement report. ISE DP=ion selective electrode--direct
potentiometry, CM=Calmagite method, LOM=lactate oxidase
method, BPM=bromocresal purple method, TEM=timed endpoint
method, RCM=pH rate of change method using a C[O.sub.2]
electrode. All samples measured by the Beckman multianalyser
were ultraspun prior to analysis. All measurements were made at
37[degrees]C. It is noted that the standard deviations for those
electrolytes

(*) also measured by indirect potentiometry (Beckman) are not
significantly different from those measured by direct potentiometry
(Radiometer).
COPYRIGHT 2009 Australian Society of Anaesthetists
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Author:Anstey, C.M.
Publication:Anaesthesia and Intensive Care
Article Type:Report
Geographic Code:8AUST
Date:Nov 1, 2009
Words:5993
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