Entropy-based joint analysis for two-stage genome-wide association studies

Genome-wide association studies (GWAS) are being conducted to identify common genetic variants that predispose to human diseases to unravel the genetic etiology of complex human diseases now. Because of genotyping cost constraints, it often follows a two-stage design, in which a large number of markers are identified in a proportion of the available samples in stage 1, and then the markers identified in stage 1 are examined in all the samples in stage 2. In this paper, we introduce a nonlinear entropy-based statistic for joint analysis for two-stage genome-wide association studies. Type I error rates and power of the entropy-based statistic for association tests are validated using simulation studies in single-locus test. The power of entropy-based joint analysis is investigated by simulations. And the results suggest that entropy-based joint analysis is always more powerful than linear joint analysis that uses a linear function of risk allele frequencies in cases and controls when detecting rare genetic variants; the powers of these two joint analyses are comparable when detecting common genetic variants. Furthermore, when the false discovery rate is controlled, entropy-based joint analysis is more powerful and needs fewer samples than linear joint analysis that uses a linear function of risk allele frequencies in cases and controls. So, we recommend we should use entropy-based strategy for two-stage genome-wide association studies to detect the rare and common genetic variants with moderate to large genetic effect underlying a complex disease.