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

üCase-control

üCross-sectional

Breslow and Day (1981)
Prentice and Pike (1979)

Robust conditions

Case-control studies

Robust conditions

Cross-sectional studies

E

E

D

D

Case control:

Follow-up:

Treat case control like follow-up

LIMITATION

case-control and
cross-sectional studies:

individual risk

üOR

The answer isyes: logistic regression can be

applied to study designs other than follow-up.

Two papers, one byBreslowandDayin 1981

and the other byPrenticeandPikein 1979 have

identified certain “robust” conditions under

which the logistic model can be used with

case-control data. “Robust” means that the

conditions required, which are quite complex

mathematically and equally as complex to ver-

ify empirically, apply to a large number of data

situations that actually occur.

The reasoning provided in these papers carries

over tocross-sectional studiesalso, though this

has not been explicitly demonstrated in the

literature.

In terms ofcase-controlstudies, it has been

shown that even though cases and controls

are selected first, after which previous expo-

sure status is determined, the analysis may

proceed as if the selection process were the

other way around, as in a follow-up study.

In other words, even with a case-control design,

one can pretend, when doing the analysis, that

the dependent variable is disease outcome and

the independent variables are exposure status

plus any covariates of interest. When using a

logistic model with a case-control design, you

can treat the data as if it came from a follow-up

study and still get avalidanswer.

Although logistic modeling is applicable to case-

control and cross-sectional studies, there is one

important limitation in the analysis of such

studies. Whereas in follow-up studies, as we

demonstrated earlier, a fitted logistic model

can be used to predict the risk for an individual

with specified independent variables, this model

cannot be used to predict individual risk for

case-control or cross-sectional studies. In fact,

only estimates ofodds ratioscanbeobtainedfor

case-control and cross-sectional studies.

12 1. Introduction to Logistic Regression