A variance components factor model for genetic association studies: a Bayesian analysis

Studies of gene-trait associations for complex diseases often involve multiple traits that may vary by genotype groups or patterns. Such traits are usually manifestations of lower-dimensional latent factors or disease syndromes. We illustrate the use of a variance components factor (VCF) model to model the association between multiple traits and genotype groups as well as any other existing patient-level covariates. This model characterizes the correlations between traits as underlying latent factors that can be used in clinical decision-making. We apply it within the Bayesian framework and provide a straightforward implementation using the WinBUGS software. The VCF model is illustrated with simulated data and an example that comprises changes in plasma lipid measurements of patients who were treated with statins to lower low-density lipoprotein cholesterol, and polymorphisms from the apolipoprotein-E gene. The simulation shows that this model clearly characterizes existing multiple trait manifestations across genotype groups where individuals' group assignments are fully observed or can be deduced from the observed data. It also allows one to investigate covariate by genotype group interactions that may explain the variability in the traits. The flexibility to characterize such multiple trait manifestations makes the VCF model more desirable than the univariate variance components model, which is applied to each trait separately. The Bayesian framework offers a flexible approach that allows one to incorporate prior information.