A family-based robust multivariate association test using maximum statistic

For characterizing the genetic mechanisms of complex diseases familial data with multiple correlated quantitative traits are usually collected in genetic studies. To analyze such data, various multivariate tests have been proposed to investigate the association between the underlying disease genes and the multiple traits. Although these multivariate association tests may have better power performance than the univariate association tests, they suffer from loss of testing power when the genetic models of the putative genes are misspecified. To address the problem, in this paper we aim to develop a family-based robust multivariate association test. We will first establish the optimal multivariate score tests for the recessive, additive, and dominant genetic models. Based on these optimal tests, a maximum-type robust multivariate association test is then obtained. Simulations are conducted to compare the power of our method with that of other existing multivariate methods. The results show that the robust multivariate test does manifest the robustness in power over all plausible genetic models. A practical data set is applied to demonstrate the applicability of our approach. The results suggest that the robust multivariate test is more powerful than the robust univariate test when dealing with multiple quantitative traits.