Power and sample size for matched case-control studies

The problem of sample size for matched case-control studies is approached without any advance information. In current practice, the probability of exposure theta of matched controls and the correlation coefficient phi between outcomes of a matched pair have to be available as in Dupont (1988, Biometrics 43, 1157-1168); the probability of discordant pairs is required in Schlesselman (1988, Case-Control Studies: Design, Conduct, Analysis) and Parker and Bregman (1986, Biometrics 42, 919-926). The measure of association omega between a case's and the matched control's exposure status and theta are also needed in Fleiss (1988, Proceedings of the XIVth International Biometrics Conference, 29-44). For a test of H-0: psi = 1 against the alternative hypothesis, H-1: psi = psi(0) > 1, sample sizes are determined without requiring any advance information both for pair-matching and for multiple matching using the model of Ejigou and McHugh (1977, Biometrics 33, 552-556; 1981, Biometrika 68, 85-91) and the results in Ejigou (1990, Biometricss 46, 61-69). The weakness of Ury's rule (1975, Biometrics 31, 643-649) is reviewed and alternatives are proposed. As in current procedures, our method enables one to determine power for a given H-1, test size, and sample size. In addition, it also provides a solution to the problem of the number of controls to be matched to each case to achieve a desired level of power. This is also a new feature of our method.