Bayesian mixture modeling of gene-environment and gene-gene interactions

With the advent of rapid and relatively cheap genotyping technologies there is now the opportunity to attempt to identify gene-environment and gene-gene interactions when the number of genes and environmental factors is potentially large. Unfortunately the dimensionality of the parameter space leads to a computational explosion in the number of possible interactions that may be investigated. The full model that includes all interactions and main effects can be unstable, with wide confidence intervals arising from the large number of estimated parameters. We describe a hierarchical mixture model that allows all interactions to be investigated simultaneously, but assumes the effects come from a mixture prior with two components, one that reflects small null effects and the second for epidemiologically significant effects. Effects from the former are effectively set to zero, hence increasing the power for the detection of real signals. The prior framework is very flexible, which allows substantive information to be incorporated into the analysis. We illustrate the methods first using simulation, and then on data from a case-control study of lung cancer in Central and Eastern Europe.