Estimation of sample sizes in case-control studies with multiple controls per case: dichotomous data.

In planning case-control studies with matched sets, the calculation of exact sample sizes is difficult, because this calculation depends on some nuisance parameters that are usually unknown in practice. Using the Pitman efficiency of Miettinen's test relative to McNemar's test, Schlesselman and Stolley (Case-control studies: design, conduct, analysis. Oxford: Oxford University Press, 1982:144-70) derived an approximate sample size formula which requires the assumption that the difference in exposure rates between cases and controls is small. Furthermore, on the basis of an assumption similar to that used in Schlesselman and Stolley's approach, Taylor (Stat Med 1986;5:29-36) proposed another approximation formula. In this paper, an alternative and explicit formula that does not require the exposure difference to be small between case and control groups has been derived. Monte Carlo studies are given for comparing the accuracy of these three procedures. The results indicate that when odds ratios of exposure between cases and controls are small (less than or equal to 4) and there is more than one matched control per case, the formula derived in this paper seems to be the best. When odds ratios are large (greater than or equal to 5), however, Taylor's more conservative estimate is recommended, unless the exposure prevalence in the general population is large (0.9).