The search for the association of rare genetic variants with common diseases is of high interest, yet challenging because of cost considerations. We present an efficient two-stage design that uses diseased cases to first screen for rare variants at stage-1. If too few cases are found to carry any variants, the study stops. Otherwise, the selected variants are screened at stage-2 in a larger set of cases and controls, and the frequency of variants is compared between cases and controls by an exact test that corrects for the stage-1 ascertainment. Simulations show that our new method provides conservative Type-I error rates, similar to the conservative aspect of Fisher's exact test. We show that the probability of stopping at stage-1 increases with a smaller number of cases screened at stage-1, a larger stage-1 continuation threshold, or a smaller carrier probability. Our simulations also show how these factors impact the power at stage-2. To balance stopping early when there are few variant carriers versus continuation to stage-2 when the variants have a reasonable effect size on the phenotype, we provide guidance on designing an optimal study that minimizes the expected sample size when the null hypothesis is true, yet achieves the desired power.
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