Functional Regression Models for Gene-Based Longitudinal and Survival Studies

Abstract

Functional regression (FR) models have been applied to gene-based studies to explore the association between genetic variants and univariate traits. However, there are no statistical methods to analyze complex traits from longitudinal and survival studies using the FR models. To fill this gap, I develop stochastic functional regression linear mixed models for longitudinal traits and functional regression mixed effect Cox models for survival traits to test gene-based association. I demonstrate that the models control the type I error correctly for quantitative traits and bivariate survival traits. I evaluate the power of the models by simulation studies and show that they have higher power than alternative methods. I apply the models to identify genes associated with body mass index in Framingham Heart Study and to test for association between the risk of macular degeneration and genes CFH and ARMS2. I show that the proposed models substantially outperform alternative methods. My research extends the application of the FR models to gene-based studies for complex traits and provides competitive methods to analyze longitudinal and survival traits, facilitates gene mapping of complex traits, and disseminates algorithms and software to upgrade public health research and infrastructure.