  To date, most genetic analyses of phenotypes have focused on analyzing single
traits or, analyzing each phenotype independently. However, joint epistasis
analysis of multiple complementary traits will increase statistical power, and
hold the key to understanding the complicated genetic structure of the complex
diseases. Despite their importance in uncovering the genetic structure of
complex traits, the statistical methods for identifying epistasis in multiple
phenotypes remains fundamentally unexplored. To fill this gap, we formulate a
test for interaction between two gens in multiple quantitative trait analysis
as a multiple functional regression (MFRG) in which the genotype functions
(genetic variant profiles) are defined as a function of the genomic position of
the genetic variants. We use large scale simulations to calculate its type I
error rates for testing interaction between two genes with multiple phenotypes
and to compare its power with multivariate pair-wise interaction analysis and
single trait interaction analysis by a single variate functional regression
model. To further evaluate its performance, the MFRG for epistasis analysis is
applied to five phenotypes and exome sequence data from the NHLBI Exome
Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 136 pairs
of genes that formed a genetic interaction network showed significant evidence
of epistasis influencing five traits. The results demonstrate that the joint
interaction analysis of multiple phenotypes has much higher power to detect
interaction than the interaction analysis of single trait and may open a new
direction to fully uncovering the genetic structure of multiple phenotypes.
