Power of genetic association studies with fixed and random genotype frequencies

When estimating the power of genetic association studies, the allele and genotype frequencies are often assumed to be known, and the numbers of individuals with each genotype are set equal to their expectations under Hardy-Weinberg equilibrium. In fact, both allele and genotype frequencies are unknown and thus random. It has previously been suggested that ignoring uncertainty in these parameters could lead to inflated power expectations. To overcome the problem, one can average power estimates over the distributions of unknown frequencies. We investigate the power-averaging method and find that, despite the intuitive appeal, it may not improve accuracy in practice, while significantly increasing computational time. For a fixed allele frequency, we show that the amount of overestimation diminishes rapidly with sample size and is completely negligible for N > 200. For an unknown frequency, the result of averaging depends on the genetic model, and may not always provide a more conservative estimate of power. We explore the effect of uncertainty in the factors that determine statistical power of association studies and propose a more economical approach to the power analysis.