Optimal designs for estimating and testing interaction among multiple loci in complex traits by a Gibbs sampler.

A simulation study was conducted to provide a practical guideline for experimental designs with the Bayesian approach using Gibbs sampling (BAGS), a recently developed method for estimating interaction among multiple loci. Various data sets were simulated from combinations of number of loci, within-genotype variance, sample size, and balance of design. Mean square prediction error (MSPE) and empirical statistical power were obtained from estimating and testing the posterior mean estimate of combination genotypic effect. Simultaneous use of both MSPE and power was suggested to find an optimal design because their correlation estimate (-0.8) would not be large enough to ignore either of them. The optimal sample sizes with MSPE >2.0 and power >0.8 with the within-genotype variance of 30 were 135, 675, and >8100 for 2-, 3-, and 4-locus unbalanced data. The BAGS was suggested for interaction effects among limited number (4 or less) of loci in practice. A practical guideline for determining an optimal sample size with a given power or vise versa is provided for BAGS.