Meta-analysis of observational studies with unmeasured confounders

Meta-analysis of observational studies is an exciting new area of innovation in statistical science. Unlike randomized controlled trials, which are the gold standard for proving causation, observational studies are prone to biases including confounding. In this article, we describe a novel Bayesian procedure to control for a confounder that is missing across the sequence of studies in a meta-analysis. We motivate the discussion with the example of a meta-analysis of cohort, case-control and cross-sectional studies examining the relationship between oral contraceptives and endometriosis. An important unmeasured confounder is dysmennoreah, which is an indication for oral contraceptive use. To adjust for unmeasured confounding, we combine random effects models with probabilistic sensitivity analysis techniques. Information about the unmeasured confounder is incorporated into the analysis via prior distributions, and we use MCMC to sample from posterior.