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

Two tests:

 Score test

 Generalized Wald test

Under H 0 , both test statistics
approximatew^2 with
df¼#of parameters tested.

Chunk test for interaction terms:

Type DF Chi-square P-value

Score 4 3.66 0.4544
Wald 4 3.53 0.4737

Both tests fail to rejectH 0.

Model 2: No interaction model
(GEE)

logit PðD¼ 1 jXÞ

¼b 0 þb 1 ASPIRINþb 2 AGE

þb 3 GENDERþb 4 WEIGHT

þb 5 HEIGHT

Model 2 Output(Exchangeable)

Variable Coefficient

Empirical

Std Err

Wald

p-value

INTERCEPT 0.4713 1.6169 0.7707
ASPIRIN 1.3302 0.1444 0.0001
AGE 0.0086 0.0087 0.3231
GENDER 0.5503 0.2559 0.0315
WEIGHT 0.0007 0.0066 0.9200
HEIGHT 0.0080 0.0105 0.4448

There are two other statistical tests that can be

utilized for GEE models. These are the

generalized Score test and the generalized

Wald test. The test statistic for the Score test

relies on the “score-like” generalized estimat-

ing equations that are solved to produce the

parameter estimates for the GEE model (see

Chap. 14). The test statistic for the generalized

Wald test generalizes the Wald test statistic for

a single parameter by utilizing the variance–

covariance matrix of the parameter estimates.

The test statistics for both the Score test and

the generalized Wald test follow an approxi-

mate chi-square distribution under the null

with the degrees of freedom equal to the num-

ber of parameters that are tested.

The output for the Score test and the

generalized Wald test for the four interaction

terms is shown on the left. The test statistic for

the Score test is 3.66 with the corresponding

p-value at 0.45. The generalized Wald test

yields similar results, as the test statistic is

3.53 with thep-value at 0.47. Both tests indi-

cate that the null hypothesis should not be

rejected and suggest that a model without the

interaction terms may be appropriate.

The no interaction model (Model 2) is pre-

sented at left. The GEE parameter estimates

using the exchangeable correlation structure

are also shown.

Presentation: III. Example 2: Aspirin–Heart Bypass Study 553