# Technical notes.

Components of Score Measuring Severity of Patient Illness at Discharge

A model predicting PASU based on characteristics of patient admission severity, demographic information, events in hospital and patient status at discharge was fitted to construct the severity score measuring severity of patient illness at discharge. A standard stepwise logistic regression model, in which the response was the binary variable PASU, was developed to identify which of these variables were significant predictors (p-value [less than or equal to] 0.05) of PASU. Because the model was being used for estimation not prediction, the full cohort of 39,837 elderly, AMI patients was used in development. We constructed partial residual plots to identify potential problematic areas of model fit but found no striking departures from our assumptions (Landwehr, Pregibon, and Shoemaker, 1984). We tested model discrimination by means of the c statistic.(Hanley and McNeil, 1982). The c statistic for the model was 0.78, which fell above generally accepted value for good accuracy of 0.75.

Table A lists the individual severity variables, mean values, and estimated regression coefficients. Discharge severity for the jth patient at the ith hospital was defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where p indexes the number of covariates, [[delta].sub.p] is the regression coefficient specified in the table, and [X.sup.ijp] is the value of the pth covariate for the jth patient at the ith hospital.

Structure of Hierarchical Logistic Regression Model

A hierarchical logistic regression model was used to model both systematic and random variability in PASU by patients within hospitals. Assume that PASU data are collected on the jth patient (j=1, ..., [n.sub.i] for each hospital i (i=1, ..., 1,500). Let [Y.sub.ij]=1 if the jth patient of the ith hospital used PAS within 30 days of hospital discharge and [Y.sub.ij]=0 otherwise. Therefore, the probability of PASU ([p.sub.ij]) for the jth patient discharged from the ith hospital follows the logistic model:

Stage 1: Within-Hospital Variability

logit([p.sup.ij] | [[alpha].sub.i],[beta])=logit)Pr([Y.sub.ij]=1) | [[alpha].sub.i],[beta]

=[[alpha].sub.i],[beta]+[beta](S[S.sub.ij]-SS)

where S[S.sub.ij] is the discharge severity score for the jth patient of the ith hospital and SS is the average discharge severity score across all patients. The intercept term, [[alpha].sub.i], represents the log-odds of PASU for a patient of average discharge severity treated at the ith hospital, and is assumed to vary across hospitals. [beta] represents the change in the log-odds of PASU per unit change in patient severity and is assumed not to vary across hospitals.

Hospital covariates are incorporated using a regression model on [[alpha].sub.i]:

Stage 2: Between-Hospital Variability

[[alpha].sub.i] | [gamma] ~ N ([[gamma].sub.0][rural.sub.i] +[[gamma].sub.1][nunit.sub.i]+[[gamma].sub.2][gov.sub.i] +[[gamma].sub.3][teach.sub.i]+[[gamma].sub.4][hha.sub.i] +[[gamma].sub.5][fp.sub.i]+[[gamma].sub.6]O[H.sub.i] +[[gamma].sub.7]T[X.sub.i]+[[gamma].sub.8]C[A.sub.i] +[[gamma].sub.9]P[A.sub.i]+[[gamma].sub.10]F[L.sub.i] +[[gamma].sub.11]N[Y.sub.i] +[[gamma].sub.12]M[A.sub.i],[[sigma].sup.2])

where [[alpha].sub.i] assumed to be a function of individual hospital characteristics ([gamma]'s) and random error ([[sigma].sup.2]). Hospital characteristics indicated whether or not a hospital: was rural (rural), had a separate long-term nursing home unit (nunit), was government owned (gov), was a teaching hospital (teach), provided home health services (hha), was for-profit (fp) or was located in a specific State (OH=Ohio, TX=Texas, CA=California, PA=Pennsylvania, FL=Florida, NY=New York, MA=Massachusetts). ([[gamma].sub.6], ..., [[gamma].sub.12]) represent the log-odds of PASU for a patient of average discharge severity treated at an urban, not-for-profit hospital that provides no home health services and has no separate long-term nursing home unit in a particular State. The remaining [gamma]'s represent the change in the log-odds of PASU for a change in the respective hospital indicator variable. [[sigma].sup.2] represents between hospital random variation after adjusting for patient severity and systematic hospital characteristics. In order to complete the specification of the model, non-informative proper prior distributions were assumed for remaining Stage 2 parameters ([gamma], [[sigma].sup.2]). Gibbs sampling was implemented in the BUGS software program (Gilks, Thomas, and Spiegelhalter, 1994) to fit the models.
```Table A

Model Predicting Post-Acute Service Use Following Acute Myocardial
Infarction in Elderly Medicare Beneficiaries: 1994-1995

Coeffi- Odds
Characteristic cient (1) Ratio

Adjusted Age (2) (75) (2) -0.001 1.00
History of Cancer 0.05 1.05
History of Congestive Heart Failure 0.01 1.01
Ventricular Rate Greater Than 100 0.18 1.20
Stress-Induced Cardiac Ischemia 0.19 1.21
Ischemia Not Measured/Missing 0.28 1.33
Mobility (Reference: Independent)
With Assistance -0.10 0.91
Unable to Walk -0.03 0.97
Missing -0.01 0.99
Body Mass Index (kg/[m.sup.2]) 0.002 1.00
BMI Missing/Not Measured 0.10 1.11
Log Mean Arterial Pressure -0.92 0.40
Missing Mean Arterial Pressure -1.64 0.19
Respiration Rate 0.009 1.01
Respiration Rate Missing/Not Measured 0.47 1.60
Albumin (g/L) -0.12 0.89
Albumin Missing/Not Measured -0.47 0.63
Log Blood Urea Nitrogen 0.49 1.63
Missing BUN 0.49 1.64
Creatinine 1.5mg/dl--7.0mg/dl 0.04 1.04
Creatinine Missing/Not Measured -0.09 0.91
Conduction Disturbance on ECG+ 0.08 1.09
Shock on Arrival 0.3 1.36
S3 Gallop Rhythm 0.13 1.13
Congestive Heart Failure on Admission 0.24 1.27
Cardiac Arrest 6 Hours Prior or at Admission 0.10 1.11

Demographic
Female 0.62 1.85
Dually Eligible 0.20 1.22

Events in Hospital
Cardiac Catheterization -0.09 0.91
CABG 1.49 4.46
PTCA -0.08 0.92
Pneumonia 0.47 1.61
Deep Vein Thrombosis 0.53 1.69
Cerebrovascular Accident/Stroke 1.26 3.52
Anoxic Brain Damage 0.94 2.57
Do Not Resuscitate Order 0.24 1.27
Blood Transfusion 0.52 1.68

Status at Discharge
Urinary Incontinence 0.51 1.66
Mobility (Reference: Independent)
With Assistance 0.93 2.54
Unable to Walk 0.72 2.07
Missing 0.26 1.29
Intercept -0.48 --

Mean
Characteristic p-value Value (2)

Adjusted Age (75) 0.0001 0.14 (6.5)
Adjusted Age (2) (75) (2) 0.001 41.8 (43.6)
History of Cancer 0.5 897
History of Congestive Heart Failure 0.83 6,619
Ventricular Rate Greater Than 100 0.0001 10,516
Stress-Induced Cardiac Ischemia 0.003 2,332
Ischemia Not Measured/Missing 0.0001 33,709
Mobility (Reference: Independent)
With Assistance 0.02 4,633
Unable to Walk 0.78 632
Missing 0.92 513
Body Mass Index (kg/[m.sup.2]) 0.55 23.4 (9.6)
BMI Missing/Not Measured 0.19 4,538
Log Mean Arterial Pressure 0.0001 2.0 (0.25)
Missing Mean Arterial Pressure 0.0001 552
Respiration Rate 0.0001 21.4 (6.5)
Respiration Rate Missing/Not Measured 0.0001 491
Albumin (g/L) 0.0001 2.8 (1.7)
Albumin Missing/Not Measured 0.0001 10,746
Log Blood Urea Nitrogen 0.0001 1.26 (0.3)
Missing BUN 0.002 918
Creatinine 1.5mg/dl--7.0mg/dl 0.27 7,909
Creatinine Missing/Not Measured 0.34 1,209
Conduction Disturbance on ECG+ 0.006 7,950
Shock on Arrival 0.002 633
S3 Gallop Rhythm 0.05 1,359
Congestive Heart Failure on Admission 0.0001 15,239
Cardiac Arrest 6 Hours Prior or at Admission 0.27 784

Demographic
Female 0.0001 17,863
Dually Eligible 0.0001 4,258

Events in Hospital
Cardiac Catheterization 0.005 19,961
CABG 0.0001 5,162
PTCA 0.03 8,267
Pneumonia 0.0001 3,056
Deep Vein Thrombosis 0.001 211
Cerebrovascular Accident/Stroke 0.0001 922
Anoxic Brain Damage 0.0001 208
Do Not Resuscitate Order 0.0001 2,530
Blood Transfusion 0.0001 6,788

Status at Discharge
Urinary Incontinence 0.0001 2,238
Mobility (Reference: Independent)
With Assistance 0.0001 7,835
Unable to Walk 0.0001 971
Missing 0.08 254
Intercept 0.13 --

Characteristic Percent

Adjusted Age (2) (75) (2) --
History of Cancer 2.3
History of Congestive Heart Failure 16.6
Ventricular Rate Greater Than 100 26.4
Stress-Induced Cardiac Ischemia 5.9
Ischemia Not Measured/Missing 84.6
Mobility (Reference: Independent)
With Assistance 11.6
Unable to Walk 1.6
Missing 1.3
Body Mass Index (kg/[m.sup.2]) --
BMI Missing/Not Measured 11.4
Log Mean Arterial Pressure --
Missing Mean Arterial Pressure 1.4
Respiration Rate --
Respiration Rate Missing/Not Measured 1.2
Albumin (g/L) --
Albumin Missing/Not Measured 27.0
Log Blood Urea Nitrogen --
Missing BUN 2.3
Creatinine 1.5mg/dl--7.0mg/dl 19.9
Creatinine Missing/Not Measured 3.0
Conduction Disturbance on ECG+ 20.0
Shock on Arrival 1.6
S3 Gallop Rhythm 3.4
Congestive Heart Failure on Admission 38.3
Cardiac Arrest 6 Hours Prior or at Admission 2.00

Demographic
Female 44.8
Dually Eligible 10.7

Events in Hospital
Cardiac Catheterization 50.1
CABG 13.0
PTCA 20.8
Pneumonia 7.7
Deep Vein Thrombosis 0.5
Cerebrovascular Accident/Stroke 2.3
Anoxic Brain Damage 0.5
Do Not Resuscitate Order 6.4
Blood Transfusion 17.0

Status at Discharge
Urinary Incontinence 5.6
Mobility (Reference: Independent)
With Assistance 19.7
Unable to Walk 2.4
Missing 0.6
Intercept --

(1) Coefficients are from logistic regression model where post-acute
service use within 30 days of hospital discharge is the outcome of
interest (c-statistic=0.75).

(2) Mean value reflects mean (standard deviation) for continuous
variables and count for categorical variables.

NOTES: The sample consisted of 39,837 acute myocardial infarction
patients and 14,674 (36.8 percent) used post-acute services within
30 days of hospital discharge. CABG is coronary artery bypass graft
surgery. PTCA is percutaneous transluminal coronary angioplasty.

SOURCE: Bronskill, S.E., Institute for Clinical Evaluative Sciences,
Normand, S.L.T., and McNeil, B.J., Harvard Medical School, 2002.
```
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