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Bayesian group Lasso for nonparametric varying-coefficient models with application to functional genome-wide association studies. (English) Zbl 1397.62260

Summary: 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 \(f\mathrm{GWAS}\). 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 \(f\mathrm{GWAS}\) model, equipped with the Bayesian group Lasso, will provide a useful tool for genetic and developmental analysis of complex traits or diseases.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62G08 Nonparametric regression and quantile regression
62P10 Applications of statistics to biology and medical sciences; meta analysis
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