Abstract
The behavior of a gene can be dynamic; thus, if longitudinal data are available, it is important that we study the dynamic effects of genes on a trait over time. The effect of a haplotype can be expressed by time-varying coefficients. In this paper, we use the natural cubic B-spline to express these coefficients that capture the trends of the effects of haplotypes, some of which may be rare, over time; that is, at different ages. More specifically, to capture disease-associated common and rare haplotypes and environmental factors for data from unrelated individuals, we developed a method of time-varying coefficients that uses the logistic Bayesian LASSO methodology and B-spline by setting proper prior distributions. Haplotype and environmental effect coefficients are obtained by using Markov chain Monte Carlo methods. We applied the method to analyze the MAP4 gene on chromosome 3 and have identified several haplotypes that are associated with hypertension with varying effect sizes in the range of 55 to 85 years of age.