We consider the problem of assessing the joint effect of a set of genetic markers on multiple, possibly correlated phenotypes of interest. We develop a kernel machine based multivariate regression framework, where the joint effect of the marker set on each of the phenotypes is modeled using prespecified kernel functions with unknown variance components. Unlike most existing methods that mainly focus on the global association between the marker set and the phenotype set, we develop estimation and testing procedures to study phenotype-specific associations. Specifically, we develop an estimation method based on the penalized likelihood approach to estimate phenotype-specific effects and their corresponding standard errors while accounting for possible correlation among the phenotypes. We develop testing procedures for the association of the marker set with any subset of phenotypes using a score-based variance components testing method. We assess the performance of our proposed methodology via a simulation study and demonstrate the utility of the proposed method using the Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) data.
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