Multivariate Functional Regression Models for Epistasis Analysis

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's 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. Author Summary Most genetic analyses of complex traits have focused on a single trait association analysis, analyzing each phenotype independently, and additive model in which genetic variation is assumed to contribute independently, additively and cumulatively to the trait. However, multiple phenotypes are correlated. Complex traits are influenced by many genetic and environmental factors and their interactions. Joint gene-gene (GxG) interaction analysis of multiple complementary traits will increase statistical power to identify GxG interactions, 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 GxG interactions in multiple phenotypes remains less developed owing to its potential complexity. Therefore, we propose to develop a multiple functional regression (MFRG) model in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants for simultaneous GxG interaction …