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

Detailed
Outline

I. Overview(page 570)

A. Other approaches for analysis of correlated data:

i. Alternating logistic regressions (ALR)

algorithm

ii. Conditional logistic regression

iii. Generalized linear mixed model (GLMM)

II. Alternating logistic regressions algorithm(pages

571–575)

A. Similar to GEE except that

i. Associations between pairs of responses

are modeled with odds ratios instead of

correlations:

ORijk¼

PðYij¼ 1 ;Yik¼ 1 ÞPðYij¼ 0 ;Yik¼ 0 Þ

PðYij¼ 1 ;Yik¼ 0 ÞPðYij¼ 0 ;Yik¼ 1 Þ

:

ii. Associations between responses may also be

of interest, and not considered nuisance

parameters.

III. Conditional logistic regression(pages 575–579)

A. May be applied in a design where each subject

can be viewed as a stratum (e.g., has an exposed

and an unexposed observation).

B. Subject-specific fixed effects are included in the

model through the use of dummy variables

[Example: Heartburn Relief Study (n¼40)]:

logit PðXÞ¼b 0 þb 1 RXþ~

39

i¼ 1

giVi;

whereVi¼1 for subjectiandVi¼0 otherwise.

C. In the output, there are no parameter estimates

for the intercept or the dummy variables

representing the matched factor, as these

parameters cancel out in the conditional

likelihood.

D. An important distinction between CLR and

GEE is that a matched analysis (CLR) relies on

the within-subject variability in the estimation

of the parameters, whereas a correlated

analysis (GEE) relies on both the within-

subject variability and the between-subject

variability.

IV. The generalized linear mixed model approach

(pages 579–587)

A. A generalization of the linear mixed model.

B. As with the GEE approach, the user can specify

the logit link function and apply a variety of

covariance structures to the model.

Detailed Outline 589