  Genome-wide Association Studies (GWASs) for complex diseases often collect
data on multiple correlated endo-phenotypes. Multivariate analysis of these
correlated phenotypes can improve the power to detect genetic variants.
Multivariate analysis of variance (MANOVA) can perform such association
analysis at a GWAS level, but the behavior of MANOVA under different trait
models has not been carefully investigated. In this paper, we show that MANOVA
is generally very powerful for detecting association but there are situations,
such as when a genetic variant is associated with all the traits, where MANOVA
may not have any detection power. We investigate the behavior of MANOVA, both
theoretically and using simulations, and derive the conditions where MANOVA
loses power. Based on our findings, we propose a unified score-based test
statistic USAT that can perform better than MANOVA in such situations and
nearly as well as MANOVA elsewhere. Our proposed test reports an approximate
asymptotic p-value for association and is computationally very efficient to
implement at a GWAS level. We have studied through extensive simulation the
performance of USAT, MANOVA and other existing approaches and demonstrated the
advantage of using the USAT approach to detect association between a genetic
variant and multivariate phenotypes. We applied USAT to data from three
correlated traits collected on 5,816 Caucasian individuals from the
Atherosclerosis Risk in Communities (ARIC) Study and detected some interesting
associations.
