Using the posterior distribution of deviance to measure evidence of association for rare susceptibility variants

Aitkin recently proposed an integrated Bayesian/likelihood approach that he claims is general and simple. We have applied this method, which does not rely on informative prior probabilities or large-sample results, to investigate the evidence of association between disease and the 16 variants in the KDR gene provided by Genetic Analysis Workshop 17. Based on the likelihood of logistic regression models and considering noninformative uniform prior probabilities on the coefficients of the explanatory variables, we used a random walk Metropolis algorithm to simulate the distributions of deviance and deviance difference. The distribution of probability values and the distribution of the proportions of positive deviance differences showed different locations, but the direction of the shift depended on the genetic factor. For the variant with the highest minor allele frequency and for any rare variant, standard logistic regression showed a higher power than the novel approach. For the two variants with the strongest effects on Q1 under a type I error rate of 1%, the integrated approach showed a higher power than standard logistic regression. The advantages and limitations of the integrated Bayesian/likelihood approach should be investigated using additional regions and considering alternative regression models and collapsing methods.