Semiparametric Allelic Tests for Mapping Multiple Phenotypes: Binomial Regression and Mahalanobis Distance

Binary phenotypes commonly arise due to multiple underlying quantitative precursors and genetic variants may impact multiple traits in a pleiotropic manner. Hence, simultaneously analyzing such correlated traits may be more powerful than analyzing individual traits. Various genotype‐level methods, e.g., MultiPhen (O'Reilly et al. [ 2012 ]), have been developed to identify genetic factors underlying a multivariate phenotype. For univariate phenotypes, the usefulness and applicability of allele‐level tests have been investigated. The test of allele frequency difference among cases and controls is commonly used for mapping case‐control association. However, allelic methods for multivariate association mapping have not been studied much. In this article, we explore two allelic tests of multivariate association: one using a Binomial regression model based on inverted regression of genotype on phenotype (Binomial regression‐based Association of Multivariate Phenotypes [BAMP]), and the other employing the Mahalanobis distance between two sample means of the multivariate phenotype vector for two alleles at a single‐nucleotide polymorphism (Distance‐based Association of Multivariate Phenotypes [DAMP]). These methods can incorporate both discrete and continuous phenotypes. Some theoretical properties for BAMP are studied. Using simulations, the power of the methods for detecting multivariate association is compared with the genotype‐level test MultiPhen's. The allelic tests yield marginally higher power than MultiPhen for multivariate phenotypes. For one/two binary traits under recessive mode of inheritance, allelic tests are found to be substantially more powerful. All three tests are applied to two different real data and the results offer some support for the simulation study. We propose a hybrid approach for testing multivariate association that implements MultiPhen when Hardy‐Weinberg Equilibrium (HWE) is violated and BAMP otherwise, because the allelic approaches assume HWE.