Empirical Statistical Power for Testing Multilocus Genotypic Effects under Unbalanced Designs Using a Gibbs Sampler

  • Lee, Chae-Young (Department of Bioinformatics and Life Science, Soongsil University)
  • Received : 2012.03.08
  • Accepted : 2012.05.05
  • Published : 2012.11.01


Epistasis that may explain a large portion of the phenotypic variation for complex economic traits of animals has been ignored in many genetic association studies. A Baysian method was introduced to draw inferences about multilocus genotypic effects based on their marginal posterior distributions by a Gibbs sampler. A simulation study was conducted to provide statistical powers under various unbalanced designs by using this method. Data were simulated by combined designs of number of loci, within genotype variance, and sample size in unbalanced designs with or without null combined genotype cells. Mean empirical statistical power was estimated for testing posterior mean estimate of combined genotype effect. A practical example for obtaining empirical statistical power estimates with a given sample size was provided under unbalanced designs. The empirical statistical powers would be useful for determining an optimal design when interactive associations of multiple loci with complex phenotypes were examined.


Supported by : National Research Foundation of Korea (NRF)


  1. Chen, X. and H. Ishwaran. 2012. Random forests for genomic data analysis. Genomics
  2. Culverhouse, R., T. Klein and W. Shannon. 2004. Detecting epistatic interactions contributing to quantitative traits. Genet. Epidemiol. 27:141-152.
  3. Frankel, W. N. and N. J. Schork. 1996. Who's afraid of epistasis? Nat. Genet. 14:371-373.
  4. He, X., W. Qian, Z. Wang, Y. Li and J. Zhang. 2010. Prevalent positive epistasis in Escherichia coli and Saccharomyces cerevisiae metabolic networks. Nat. Genet. 42:272-276.
  5. Lee, C. and Y. Kim. 2008. Optimal designs for estimating and testing interaction among multiple loci in complex traits by a Gibbs sampler. Genomics 92:446-451.
  6. Lee, C. and J. Park. 2007. Estimation of epistasis among finite polygenic loci for complex traits with a mixed model using Gibbs sampling. J. Biomed. Inform. 40:500-506.
  7. Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery. 1992. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge, UK.
  8. Wang, H, K. P. Smith, E. Combs, T. Blake, R. D. Horsley and G. J. Muehlbauer. 2012. Effect of population size and unbalanced data sets on QTL detection using genome-wide association mapping in barley breeding germplasm. Theor. Appl. Genet. 124:111-124.