Bayesian synthesis of epidemiological evidence with different combinations of exposure groups: application to a gene-gene-environment interaction

Meta-analysis to investigate the joint effect of multiple factors in the aetiology of a disease is of increasing importance in epidemiology. This task is often challenging in practice, because studies typically concentrate on studying the effect of only one exposure, sometimes may report the interaction between two exposures, but rarely address more complex interactions that involve more than two exposures. In this paper, we develop a meta-analysis framework that combines estimates from studies of multiple exposures. A key development is an approach to combining results from studies that report information on any subset or combination of the full set of exposures. The model requires assumptions to be made about the prevalence of the specific exposures. We discuss several possible model specifications and prior distributions, including information internal and external to the meta-analysis data set, and using fixed-effect and random-effects meta-analysis assumptions. The methodology is implemented in an original meta-analysis of studies relating the risk of bladder cancer to two N-acetyltransferase genes, NAT1 and NAT2, and smoking status.