Matched Samples in Epidemiologic Studies

The use of matched or paired samples in epidemiologic studies is a subject which has been discussed in general. The conditions under which pairing and subsequent statistical analysis by the marginal x2 test may be expected to produce a more significant result than random sampling and the use of the conventional x2 test have received less attention. Cochran and Cox 1957 in their discussion of the sample size necessary to detect a difference between two proportions state that if the units have been grouped into pairs such that the two members of a pair are highly comparable, there is a reduction in sample size but that the reduction is not great unless the pairing is markedly effective. According to Mantel and Haenszel 1959, it is essential in the matched sample study that there be some appreciable variation in the presence or absence of the factor under study between the strata. If this is not the case, the marginial x2 test is approximately as powerful as the ordinary x2 test for large sample size. Youkeles 1963 has shown that when the pairing has been quite ineffective, the sign test is less sensitive than Fisher's 'exact' test and that ineffective pairing is disadvantageous. It is the purpose here to provide means by which the phrases 'highly comparable', 'appreciable variation', 'quite ineffective' and the like may be quantified and also to discuss the use of the marginal x2 in prospective (cohort) and retrospective (case history) epidemiologic studies. Suppose there is a universe of pairs where a pair is made up of a control and study individual and that the probabilities for the outcomes of the pairs are as follows: Study Group Outcome