Optimum allocation of samples in strata‐matching case‐control studies when cost per sample differs from stratum to stratum

We investigate the allocation of samples over strata in case-control studies with consideration of sampling costs. We consider two situations, typical of strata-matched case-control studies. Subject to a fixed total cost we derived optimum allocations that maximize the asymptotic efficiency of Cochran's test, that is, minimize the variance of the maximum likelihood estimator of the common odds ratio when the common odds ratio is one. Our results show that the standard design with equal numbers of cases and controls in each stratum is inefficient when costs per control differ greatly from stratum to stratum. We show that the optimum design suggested in this paper is robust for values of the odds ratio common in epidemiologic studies.