• Adiponectin genes;
  • Bayesian inference;
  • generalized linear models;
  • colorectal cancer;
  • genetic interactions;
  • high-dimensional data;
  • logistic regression;
  • probit regression


Complex diseases such as cancers are influenced by interacting networks of genetic and environmental factors. However, a joint analysis of multiple genes and environmental factors is challenging, owing to potentially large numbers of correlated and complex variables. We describe Bayesian generalized linear models for simultaneously analyzing covariates, main effects of numerous loci, gene–gene and gene–environment interactions in population case–control studies. Our Bayesian models use Student-t prior distributions with different shrinkage parameters for different types of effects, allowing reliable estimates of main effects and interactions and hence increasing the power for detection of real signals. We implement a fast and stable algorithm for fitting models by extending available tools for classical generalized linear models to the Bayesian case. We propose a novel method to interpret and visualize models with multiple interactions by computing the average predictive probability. Simulations show that the method has the potential to dissect interacting networks of complex diseases. Application of the method to a large case–control study of adiponectin genes and colorectal cancer risk highlights the previous results and detects new epistatic interactions and sex-specific effects that warrant follow-up in independent studies.