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

Matchedþnonmatched variables

+

Use logistic regression

No interaction model:

logit PðXÞ¼aþbVSþ~

i

g 1 iV 1 i

þg 21 OBSþg 22 SMK

4830 totalpairs$ 36 discordantpairs

same results

Need only analyze discordant pairs

Pair-matched case-control studies:

Use only discordant pairs

provided

no other control variables other than

matching variables

When variables not involved in the matching,

such as OBS and SMK, are to be controlled

in addition to the matching variable, we need

to use logistic regression analysis rather than

a stratified analysis based on a McNemar data

layout.

A no-interaction logistic model that would

accomplish such an analysis is shown at the

left. This model takes into account the expo-

sure variable of interest (i.e., VS) as well as

the two variables not matched on (i.e., OBS

and SMK), and also includes terms to distin-

guish the different matched pairs (i.e., theV 1 i

variables).

It turns out (from statistical theory) that the

results from fitting the above model would

be identical regardless of whether all 4,380

matched pairs or just the 36 discordant

matched pairs are input as the data.

In other words, for pair-matched follow-up

studies, even if variables not involved in the

matching are being controlled, a logistic regres-

sion analysis requires only the information on

discordant pairs to obtain correct estimates and

tests.

The above property of pair-matched follow-

up studies does NOT hold for pair-matched

case-control studies. For the latter, discordant

pairs should only be used if there are no other

control variables other than the matching vari-

ables to be considered in the analysis. In other

words, for pair-matched case-control data,

if there are unmatched variables being con-

trolled, the complete dataset must be used to

obtain correct results.

Presentation: VIII. Analysis of Matched Follow-up Data 413