Optimal Sample Size for Testing Multilocus Genotypic Effects by a Bayesian Method Using a Gibbs Sampler

The potential epistasis that may explain a large portion of the phenotypic variation for complex traits has been ignored in many genetic association studies. A Baysian method using a Gibbs sampler was introduced to draw inferences about multilocus genotypic effects based on their marginal posterior distributions by a Gibbs sampler. This method would be applied to studies for interaction effects among limited number of loci although theoretically they are applicable to all the possible interaction of millions of single nucleotide variants resulted from genomewide association study. A simulation study was conducted to provide an optimal sample size for experimental designs with this method. Data were simulated with more than 42,240 data sets produced by combined designs of number of loci (2, 3, 4, and 5 loci), within genotype variance (10 ~ 40, 16 levels), and sample size (5 ~ 100, 20 levels) in unbalanced designs with various portions of null genotypic cells (0 ~ 50%, 11 levels). Mean empirical statistical power was estimated for each data set in testing the posterior mean estimate of combination genotypic effect. Additionally, mean square prediction error was obtained from estimating the posterior mean estimate. The optimal sample sizes were provided with the prediction error > 2.0 and the statistical power >0.8 under various designs. The Baysian method using a Gibbs sampler was suggested for testing and estimating epistatic effects among limited number (2~4) of loci. Practical guidelines for determining the optimal sample size with a specific power are provided when population geneticists apply the Baysian method to their genetic association studies.