Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate

Standard

Error

Wald

Chi-Square

Pr>

ChiSq

SMK 1 0.7291 0.5613 1.6873 0.1940

SBP 1 0.0456 0.0152 8.9612 0.0028

ECG 1 1.5993 0.8534 3.5117 0.0609

Odds Ratio Estimates

Effect

Point

Estimate

95% Wald

Confidence Limits

SMK 2.073 0.690 6.228

SBP 1.047 1.016 1.078

ECG 4.949 0.929 26.362

The odds ratio estimate for SMK¼1 vs. SMK¼0isexp(0.72906)¼2.073.

Obtaining ROC Curves

Next, we demonstrate how to obtain classification tables and ROC curves using
PROC LOGISTIC with the knee fracture dataset. The knee fracture dataset contains
information on 348 patients of which 45 actually had a knee fracture. The logistic
model contains five dichotomous predictors and is stated below:

logit PðFRACTURE¼ 1 jXÞ¼b 0 þb 1 FLEXþb 2 WEIGHTþb 3 AGECAT

þb 4 HEADþb 5 PATELLAR

The SAS code is presented below. The model statement option, PPROB ¼.00
TO .50 BY .05 CTABLE, requests that a classification table be added to the
default output using cutpoints of predicted probabilities from 0 to 0.50 in increments
of 0.05.

PROC LOGISTIC DATA¼REF .KNEEFR DESCENDING;

MODEL FRACTURE¼FLEX WEIGHT AGECAT HEAD PATELLAR / PPROB¼.00 TO .50 BY

.05 CTABLE;

RUN;

The output follows:

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate

Standard

Error

Wald

Chi-Square Pr>ChiSq

Intercept 1 3.4657 0.4118 70.8372 <.0001

FLEX 1 0.5277 0.3743 1.9877 0.1586

(continued)

614 Appendix: Computer Programs for Logistic Regression