Efficient Sampling in Unmatched Case-Control Studies When the Total Number of Cases and Controls Is Fixed

In the case-control design, statistical efficiency is balanced with practical efficiency. In an unmatched case-control study of a binary exposure, in which the expected odds ratio deviates from the null (i.e., no effect) and the sum of the number of cases and controls is fixed, 1:1 sampling of cases and controls may yield suboptimal statistical efficiency. This holds especially for situations where the exposure is rare and for stronger relationships between the exposure and the outcome under study. The equations presented here may provide researchers with a simple and efficient strategy for sampling cases and controls when designing an unmatched case-control study for such a situation.