The vast majority of genome-wide association (GWA) studies analyze a single trait while large-scale multivariate data sets are available. As complex traits are highly polygenic, and pleiotropy seems ubiquitous, it is essential to determine when multivariate association tests (MATs) outperform univariate approaches in terms of power. We discuss the statistical background of 19 MATs and give an overview of their statistical properties. We address the Type I error rates of these MATs and demonstrate which factors can cause bias. Finally, we examine, compare, and discuss the power of these MATs, varying the number of traits, the correlational pattern between the traits, the number of affected traits, and the sign of the genetic effects. Our results demonstrate under which circumstances specific MATs perform most optimal. Through sharing of flexible simulation scripts, we facilitate a standard framework for comparing Type I error rate and power of new MATs to that of existing ones.
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