Genetic studies of complex diseases often collect multiple phenotypes relevant to the disorders. As these phenotypes can be correlated and share common genetic mechanisms, jointly analyzing these traits may bring more power to detect genes influencing individual or multiple phenotypes. Given the advancement brought by the multivariate phenotype approaches and the multimarker kernel machine regression, we construct a multivariate regression based on kernel machine to facilitate the joint evaluation of multimarker effects on multiple phenotypes. The kernel machine serves as a powerful dimension-reduction tool to capture complex effects among markers. The multivariate framework incorporates the potentially correlated multidimensional phenotypic information and accommodates common or different environmental covariates for each trait. We derive the multivariate kernel machine test based on a score-like statistic, and conduct simulations to evaluate the validity and efficacy of the method. We also study the performance of the commonly adapted strategies for kernel machine analysis on multiple phenotypes, including the multiple univariate kernel machine tests with original phenotypes or with their principal components. Our results suggest that none of these approaches has the uniformly best power, and the optimal test depends on the magnitude of the phenotype correlation and the effect patterns. However, the multivariate test retains to be a reasonable approach when the multiple phenotypes have none or mild correlations, and gives the best power once the correlation becomes stronger or when there exist genes that affect more than one phenotype. We illustrate the utility of the multivariate kernel machine method through the Clinical Antipsychotic Trails of Intervention Effectiveness antibody study.
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