  Although genome-wide association studies (GWAS) have proven powerful for
comprehending the genetic architecture of complex traits, they are challenged
by a high dimension of single-nucleotide polymorphisms (SNPs) as predictors,
the presence of complex environmental factors, and longitudinal or functional
natures of many complex traits or diseases. To address these challenges, we
propose a high-dimensional varying-coefficient model for incorporating
functional aspects of phenotypic traits into GWAS to formulate a so-called
functional GWAS or fGWAS. The Bayesian group lasso and the associated MCMC
algorithms are developed to identify significant SNPs and estimate how they
affect longitudinal traits through time-varying genetic actions. The model is
generalized to analyze the genetic control of complex traits using
subject-specific sparse longitudinal data. The statistical properties of the
new model are investigated through simulation studies. We use the new model to
analyze a real GWAS data set from the Framingham Heart Study, leading to the
identification of several significant SNPs associated with age-specific changes
of body mass index. The fGWAS model, equipped with the Bayesian group lasso,
will provide a useful tool for genetic and developmental analysis of complex
traits or diseases.
