Sample size determination for case-control studies and the comparison of stratified and unstratified analyses

Woolson, Bean, and Rojas (1986, Biometrics 42, 927-932) present a simple approximation of sample size for Cochran's (1954, Biometrics 10, 417-451) test for detecting association between exposure and disease. It is useful in the design of case-control studies. We derive a sample size formula for Cochran's statistic with continuity correction which guarantees that the actual Type I error rate of the test does not exceed the nominal level. The corrected sample size is necessarily larger than the uncorrected one given by Woolson et al. and the relative difference between the two sample sizes is considerable. Allocation of equal number of cases and controls within each stratum is asymptotically optimal when the costs per case and control are the same. When any effect of stratification is absent, Cochran's stratified test, although valid, is less efficient than the unstratified one except for the important case of a balanced design.