similar values for the important confounding variables. The simplest example
of pair-matched data occurs with a single binary exposure (e.g., smoking ver-
sus nonsmoking). The data for outcomes can be represented by a 22 table
(Table 11.7) where ðþ;Þdenotes (exposed, unexposed). For example,n 10
denotes the number of pairs where the case is exposed but the matched con-
trol is unexposed. The most suitable statistical model for making inferences
about the odds ratioyis to use the conditional probability of the number of
exposed cases among the discordant pairs. Givenðn 10 þn 01 Þas fixed,n 10 has
the binomial distributionBðn 10 þn 01 ;pÞ, that is, the binomial distribution with
n¼n 10 þn 01 trials, each with probability of success
p¼OR
1 þOR11.5.2 Analysis
Using the binomial model above with the likelihood function
OR
1 þORn 10
1
1 þORn 01from which one can estimate the odds ratio, the results are
dOROR¼n^10
n 01VarVardðdORORÞ¼n^10 ðn^10 þn^01 Þ
n^301For example, with large samples, a 95% confidence interval for the odds ratio is
given by
dORORGð 1 : 96 Þ½VarVardðORORdÞ^1 =^2The null hypothesis of no risk e¤ect (i.e.,H 0 :OR¼1) can be tested where thez
TABLE 11.7
CaseControl þTotal
þ n 11 n 01 n 11 þn 01
n 10 n 00 n 10 þn 00
Total n 11 þn 10 n 01 þn 00 n
PAIR-MATCHED CASE–CONTROL STUDIES 407