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

Summary on pooling:

Recommend:

 Identify and pool exchangeable
matched sets

 Carry out stratified analysis or
logistic regression using pooled
strata

 Consider using unconditional
ML estimation (but conditional
ML estimation always unbiased)

VIII. Analysis of Matched
Follow-up Data

Follow-up data:
Unexposed¼referent
Exposed¼index

Unexposed and exposed groups
have same distribution of match-
ing variables.

Exposed Unexposed

White male 30% 30%
White
female

20% 20%

Nonwhite
male

15% 15%

Nonwhite
female

35% 35%

Individual matching
or
Frequency matching (more
convenient, larger sample size)

By “appropriate,” we mean that the odds ratio

from the unconditional ML approach should

be unbiased, and may also yield a narrower

confidence interval around the odds ratio. Con-

ditional ML estimation will always give an

unbiased estimate of the odds ratio, however.

To summarize our discussion of pooling, we

recommend that whenever matching is used,

the investigator should identify and pool

exchangeable matched sets. The analysis can

then be carried out using the reduced number

of strata resulting from pooling using either a

stratified analysis or logistic regression. If the

resulting number of strata is small enough,

then unconditional ML estimation may be

appropriate. Nevertheless, conditional ML esti-

mation will always ensure that estimated odds

ratios are unbiased.

Thus far we have considered only matched

case-control data. We now focus on the analy-

sis of matched cohort data.

In follow-up studies, matching involves the

selection of unexposed subjects (i.e., the refer-

ent group) to have the same or similar distribu-

tion as exposed subjects (i.e., the index group)

on the matching variables.

If, for example, we match on race and sex in a

follow-up study, then the unexposed and

exposed groups should have the same/similar

race by sex (combined) distribution.

As with case-control studies, matching in fol-

low-up studies may involve either individual

matching (e.g.,R-to-1 matching) or frequency

matching. The latter is more typically used

because it is convenient to carry out in practice

and allows for a larger total sample size once a

cohort population has been identified.

EXAMPLE (continued)

Unconditional ML estimation

‘‘appropriate’’ provided

ORunconditionalunbiased

and

CIunconditionalnarrower than

CIconditional

Presentation: VIII. Analysis of Matched Follow-up Data 409