A grid-search algorithm for optimal allocation of sample size in two-stage association studies

Multiple testing occurs commonly in genome-wide association studies with dense SNPs map. With numerous SNPs, not only the genotyping cost and time increase dramatically, many family wise error rate (FWER) controlling methods may fail for being too conservative and of less power when detecting SNPs associated with disease is of interest. Recently, several powerful two-stage strategies for multiple testing have received great attention. In this paper, we propose a grid-search algorithm for an optimal design of sample size allocation for these two-stage procedures. Two types of constraints are considered, one is the fixed overall cost and the other is the limited sample size. With the proposed optimal allocation of sample size, bearable false-positive results and larger power can be achieved to meet the limitations. The simulations indicate, as a general rule, allocating at least 80% of the total cost in stage one provides maximum power, as opposed to other methods. If per-genotyping cost in stage two differs from that in stage one, downward proportion of the total cost in earlier stage maintains good power. For limited total sample size, evaluating all the markers on 55% of the subjects in the first stage provides the maximum power while the cost reduction is approximately 43%.