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Bayesian sensitivity analysis for unmeasured confounding in observational studies
Author(s) -
McCandless Lawrence C.,
Gustafson Paul,
Levy Adrian
Publication year - 2006
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2711
Subject(s) - confounding , statistics , markov chain monte carlo , bayesian probability , observational study , econometrics , logistic regression , prior probability , sample size determination , sensitivity (control systems) , mathematics , computer science , electronic engineering , engineering
We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large‐sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure. Copyright © 2006 John Wiley & Sons, Ltd.