Genome-Wide Likelihood Ratio Tests under Heterogeneity

Abstract

The commonly used statistical methods in medical research generally assume patients arise from one homogeneous population. However, the existence and importance of significant heterogeneity have been widely documented. It is well known that common and complex human diseases usually have heterogeneous disease etiology, which often involves interplay of multiple genetic and environmental factors, leading to latent population substructure. Genome-wide association studies (GWAS) is a useful tool to uncover genetic association with disease of interest, while linkage analysis is a commonly used method to identify statistical association between the inheritance of a human disease and inheritance of marker loci that are in linkage with disease causing loci. We propose a likelihood ratio test for genome-wide linkage analysis under genetic heterogeneity using family data. We derive a closed-form formula for the LRT test statistic and provide explicit asymptotic null distribution. The closed form asymptotic distribution allows easy determination of the asymptotic p-values. Our extensive simulation studies indicate that the proposed test has proper type I error and good power under genetic heterogeneity. In order to simplify application of the proposed method for non-statisticians, we develop an R package gLRTH to implement the proposed LRT for genome-wide linkage analysis as well as Qian and Shao’s LRT for GWAS under heterogeneity. The newly developed open source R package gLRTH is available at CRAN.