  In Genome-Wide Association Studies (GWAS) where multiple correlated traits
have been measured on participants, a joint analysis strategy, whereby the
traits are analyzed jointly, can improve statistical power over a single-trait
analysis strategy. There are two questions of interest to be addressed when
conducting a joint GWAS analysis with multiple traits. The first question
examines whether a genetic loci is significantly associated with any of the
traits being tested. The second question focuses on identifying the specific
trait(s) that is associated with the genetic loci. Since existing methods
primarily focus on the first question, this paper seeks to provide a
complementary method that addresses the second question. We propose a novel
method, Variational Inference for Multiple Correlated Outcomes (VIMCO), that
focuses on identifying the specific trait that is associated with the genetic
loci, when performing a joint GWAS analysis of multiple traits, while
accounting for correlation among the multiple traits. We performed extensive
numerical studies and also applied VIMCO to analyze two datasets. The numerical
studies and real data analysis demonstrate that VIMCO improves statistical
power over single-trait analysis strategies when the multiple traits are
correlated and has comparable performance when the traits are not correlated.
