Choosing the number of controls in a matched case‐control study, some sample size, power and efficiency considerations

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Abstract
This paper investigates the efficiency of using multiple controls in a case‐control study, when there is a single binary exposure variable. Specifically, we consider the asymptotic power of the Cochran1 test statistic against non‐local alternatives of interest. When it is desirable to take multiple controls per case, we show that the marginal return rapidly diminishes as the number of controls per case increases. The effect is as strong, if not stronger, for non‐local alternatives as it is for local alternatives. Hence, it is rarely worth choosing more than three controls per case. We also provide a table of sample sizes necessary to achieve 80 per cent power for some odds ratios not equal to one. We extend the results to a special case when there are two binary exposure variables.