Bayesian implementation of a genetic model-free approach to the meta-analysis of genetic association studies

A genetic model-free method for the meta-analysis of genetic association studies is described that estimates the mode of inheritance from the data rather than assuming that it is known. For a bi-allelic polymorphism, with G as risk allele and g as wild-type, the genetic model depends on the ratio of the two log odds ratios, lambda = log OR(Gg)/log OR(GG), where OR(GG) compares GG with gg and OR(Gg) compares Gg with gg. Modelling log OR(GG) as a random effect creates a hierarchical model that can be implemented within a Bayesian framework. In Bayesian modelling, vague prior distributions have to be specified for all unknown parameters when no external information is available. When the data are sparse even supposedly vague prior distributions may have an influence on the posterior estimates. We investigate the impact of different vague prior distributions for the between-study standard deviation of log OR(GG) and for lambda, by considering three published meta-analyses and associated simulations. Our results show that depending on the characteristics of the meta-analysis the results may indeed be sensitive to the choice of vague prior distribution for either parameter. Genetic association studies usually use a case-control design that should be analysed by the corresponding retrospective likelihood. However, under some circumstances the prospective likelihood has been shown to produce identical results and it is usually preferred for its simplicity. In our meta-analyses the two likelihoods give very similar results.