Functional Regression Models for Gene-Based Association Analysis of Complex Traits

Abstract

Gene-based association studies can identify gene regions that contain multiple genetic risk variants with small and moderate effects for complex traits. In my research, I develop functional ordinal logistic regression (FOLR) models, bivariate functional ordinal linear regression (BFOLR) models, and stochastic bivariate functional linear models (SBFLMs) to perform gene-based association analysis for univariate ordinal traits, bivariate traits, and bivariate quantitative traits in longitudinal studies, respectively. The technique of functional data analysis is used to reduce the high dimensionality of sequence data and derive useful genetic information. The idea of functional models is to view genotype data as stochastic functions of physical positions, with the genetic effects treated as functions of physical positions. The FOLR models can analyze univariate ordinal traits. The BFOLR models take the correlation of two ordinal traits into account by considering latent regression models. Two link functions are used to model the error terms: a probit link function from a bivariate normal distribution and a logit link function from a bivariate logistic distribution with t-copula. In the SBFLMs, a variance-covariance structure is constructed to describe (1) variation accounting for the correlation between the two traits and (2) variation accounting for the correlation within multiple measurements of a trait on the same subject. Likelihood ratio test statistics are developed for these models to test the association between genes and phenotypes. Extensive simulation studies demonstrate the superior performance of FOLR models, BFOLR models, and SBFLMs compared to existing methods. FOLR and BFOLR models are applied to the Age-Related Eye Disease Study (AREDS) dataset to detect the genes associated with age-related macular degeneration (AMD). SBFLMs are applied to the Multi-Ethnic Study of Atherosclerosis (MESA) dataset to identify the genes associated with blood pressure in longitudinal studies.