A Likelihood Ratio Test for Genome‐Wide Association under Genetic Heterogeneity

Most existing association tests for genome‐wide association studies (GWASs) fail to account for genetic heterogeneity. Zhou and Pan proposed a binomial‐mixture‐model‐based association test to account for the possible genetic heterogeneity in case‐control studies. The idea is elegant, however, the proposed test requires an expectation‐maximization (EM)‐type iterative algorithm to identify the penalised maximum likelihood estimates and a permutation method to assess p‐values. The intensive computational burden induced by the EM‐algorithm and the permutation becomes prohibitive for direct applications to GWASs. This paper develops a likelihood ratio test (LRT) for GWASs under genetic heterogeneity based on a more general alternative mixture model. In particular, a closed‐form formula for the LRT statistic is derived to avoid the EM‐type iterative numerical evaluation. Moreover, an explicit asymptotic null distribution is also obtained, which avoids using the permutation to obtain p‐values. Thus, the proposed LRT is easy to implement for GWASs. Furthermore, numerical studies demonstrate that the LRT has power advantages over the commonly used Armitage trend test and other existing association tests under genetic heterogeneity. A breast cancer GWAS dataset is used to illustrate the newly proposed LRT.