Stochastic functional linear models for gene-based association analysis of quantitative traits in longitudinal studies

Longitudinally measured phenotypes are important for exploring genetic and environmental factors that affect complex traits over time. Genetic analysis of multiple measures in longitudinal studies provides a valuable opportunity to understand genetic architecture and biological variations of complex diseases. In this paper, stochastic functional linear models are developed for temporal association analysis at gene levels to analyze sequence data and longitudinally measured quantitative traits. Functional data analysis techniques are utilized to reduce high dimensionality of sequence data and draw useful information. A variance-covariance structure is constructed to model the measurement variation and correlations of the traits based on the theory of stochastic processes. Spline models are used to estimate the time-dependent trajectory mean function. By intensive simulation studies, it is shown that the proposed stochastic models control type I errors well, and have higher power levels than those of the perturbation tests. In addition, the proposed methods are robust when the correlation function is mis-specified. We test and refine the models and related software using real data sets of Framingham Heart Study.