Ignore exchangeability?No!!!Treating such strata separately
is artificial,i.e., exchangeable strata are not
unique
Analysis? Pool exchangeable
matched sets
But should we actually ignore the exchange-
ability of matched sets? We say no, primarily
because to treat exchangeable strata separately
artificially assumes that such strata are unique
from each other when, in fact, they are not. [In
statistical terms, we argue that adding para-
meters (e.g., strata) unnecessarily to a model
results in a loss of precision.]How should the analysis be carried out? The
answer here is to pool exchangeable matched
sets.In our example, pooling would mean that
rather than analyzing 100 distinct strata with
2 persons per strata, the analysis would con-
sider only 2 pooled strata, one pooling 60
matched sets into a smoker’s stratum and the
other pooling the other 40 matched sets into a
nonsmoker’s stratum.More generally, if severalvariables are involved
in the matching, the study data may only contain
a relatively low number of exchangeable matched
sets. In such a situation, the use of a pooled
analysis, even if appropriate, is likely to have a
negligible effect on the estimated odds ratios and
their associated standard errors, when compared
with an unpooled matched analysis.It is, nevertheless, quite possible that the pool-
ing of exchangeable matched sets may greatly
reduce the number of strata to be analyzed. For
example, in the example described earlier, in
which smoking was the only variable being
matched, the number of strata was reduced
from 100 to only 2.When pooling reduces the number of strata
considerably, as in the above example, it may
then be appropriate to use an unconditional
maximum likelihood procedure to fit a logistic
model to the pooled data.EXAMPLE (match on SMK)
Use two pooled strata:
Stratum 1: Smokers (n¼ 60 2)
Stratum 2: Nonsmokers (n¼ 40 2)Matching on several variables
+
May be only a few exchangeable
matched sets
+
Pooling has negligible effect on
odds ratio estimatesHowever, pooling may greatly reduce
the number of strata to be analyzed
(e.g., from 100 to 2 strata)If no. of strata greatly reduced by pooling
+
Unconditional ML may be used
if ‘‘appropriate’’408 11. Analysis of Matched Data Using Logistic Regression