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Assessing sensitivity to unmeasured confounding in observational studies : a bayesian approach

Systematic error due to possible unmeasured confounding may weaken the validity of findings from observational studies investigating the effects of exposures on disease. Because study subjects are assigned to exposure levels in a non-random way, hidden differences between exposure groups may bias effect estimates in a way which is difficult to predict. A solution is to conduct a Bayesian sensitivity analysis (BSA) which incorporates uncertainty about unmeasured confounding into the analysis as prior distributions on bias parameters. Markov chain Monte Carlo techniques can then be used to summarize the posterior distribution of the exposure effect given the data and prior belief's about unmeasured confounding. We consider B S A in the context of logistic regression models for a binary exposure, binary outcome, binary unmeasured confounder and covariate vector. Because the resulting model is not identifiable, standard theory governing the large sample behaviour of posterior distributions cannot be applied, complicating an evaluation of the performance of B S A . However, using two simulation studies, we demonstrate that if the prior distribution for the analysis of datasets from a sequence of observational studies approximates the distribution from which study parameters arise, then the coverage probabilities of B S A 95% credible intervals will be approximately 95% when averaged over many studies. Moreover, we demonstrate that B S A credible intervals tends to yield greater coverages probabilities of the true exposure effect compared to methods which ignore unmeasured confouding. As an example, we investigate the effect of possible unmeasured confouding on risk of elevated triglyceride levels among HIV infected persons treated with protease inhibitors.