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

VII. Pooling Matching
Strata

To pool or not to pool matched sets?

Case-control study:

 Pair-match on SMK (ever vs.
never)

 100 cases (i.e.,n¼200)

 Smokers – 60 matched pairs
 Nonsmokers – 40 matched
pairs

Matched pair A Matched pair B

Case A – Smoker Case B – Smoker

Control A – Smoker$Control B – Smoker
(interchangeable)

Controls for matched pairs A and B

are interchangeable

+

Matched pairs A and B

areexchangeable

ðdefinitionÞ

Smokers: 60 matched pairs are
exchangeable

Nonsmokers: 40 matched pairs are
exchangeable

Ignoring exchangeability

+

Use stratified analysis with

100 strata, e.g., McNemar’s test

Another issue to be considered in the analysis

of matched data is whether to combine, or

pool, matched sets that have the same values

for all variables being matched on.

Suppose smoking status (SMK), defined as

ever vs. never smoked, is the only matching

variable in a pair-matched case-control study

involving 100 cases. Suppose further that when

the matching is carried out, 60 of the matched

pairs are all smokers and the 40 remaining

matched pairs are all nonsmokers.

Now, let us consider any two of the matched

pairs involving smokers, say pair A and pair B.

Since the only variable being matched on is

smoking, the control in pair A had been eligible

to be chosen as the control for the case in pair

B prior to the matching process. Similarly, the

control smoker in pair B had been eligible to be

the control smoker for the case in pair A.

Even though this did not actually happen after

matching took place, the potential inter-

changeability of these two controls suggests

that pairs A and B should not be treated as

separate strata in a matched analysis. Matched

sets such as pairs A and B are calledexchange-

ablematched sets.

For the entire study involving 100 matched

pairs, the 60 matched pairs all of whom are

smokers are exchangeable and the remaining

40 matched pairs of nonsmokers are separately

exchangeable.

If we ignored exchangeability, the typical anal-

ysis of these data would be a stratified analysis

that treats all 100 matched pairs as 100 sepa-

rate strata. The analysis could then be carried

out using the discordant pairs information in

McNemar’s table, as we described in Sect. III.

Presentation: VII. Pooling Matching Strata 407