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

CLR approach )
responses assumed independent

Subject-specific gi allows for conditioning by
subject

fixed effect

Responses can be independent if
conditioned by subject

When using the CLR approach for modeling

P(X), the responses from a specific subject are

assumed to be independent. This may seem

surprising since throughout this chapter we

have viewed two or more responses on the

same subject as likely to be correlated. Never-

theless, when dummy variables are used for

each subject, each subject has his/her own

subject-specific fixed effect included in the

model. The addition of these subject-specific

fixed effects can account for correlation that

may exist between responses from the same

subject in a GEE model. In other words,

responses can be independent ifconditioned

by subject. However, this is not always the

case. For example, if the actual underlying

correlation structure is autoregressive, condi-

tioning by subject would not account for the

within-subject autocorrelation.

Returning to the Heartburn Relief Study data,

the output obtained from running the condi-

tional logistic regression is presented on the left.

With a conditional logistic regression, parame-

ter estimates are not obtained for the intercept

or the dummy variables representing the

matched factor (i.e., subject). These para-

meters cancel out in the expression for the

conditional likelihood. However, this is not a

problem because the parameter of interest is

the coefficient of the treatment variable (RX).

The odds ratio estimate for the effect of

treatment for relieving heartburn is exp

(0.4055)¼1.50, with a 95% confidence interval

of (0.534, 4.214).

EXAMPLE (continued)

Model 1:conditional logistic

regression

Variable Coefficient

Std.

error

Wald

P-value

RX 0.4055 0.5271 0.4417

Nob 0 orgiestimates in CLR model

(cancel out in conditional

likelihood)

Odds ratio and 95% CI

dOR¼expð 0 : 4055 Þ¼ 1 : 50

95 %CI¼ð 0 : 534 ; 4 : 214 Þ

576 16. Other Approaches for Analysis of Correlated Data