Bayesian sensitivity analysis for unmeasured confounding in observational studies

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 co...

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Bibliographic Details
Published in:Statistics in medicine 2007-05, Vol.26 (11), p.2331-2347
Main Authors: McCandless, Lawrence C., Gustafson, Paul, Levy, Adrian
Format: Article
Language:English
Subjects:
Adrenergic beta-Antagonists - therapeutic use
Aged
Aged, 80 and over
Bayes Theorem
Bayesian analysis
Bias
British Columbia
Cardiac Output, Low - drug therapy
Confounding Factors (Epidemiology)
coverage probability
Drug therapy
Female
Humans
identifiability
Male
Medical statistics
observational studies
Probability
Sensitivity and Specificity
Studies
Treatment Outcome
unmeasured confounding
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Summary: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.
ISSN:0277-6715
1097-0258
DOI:10.1002/sim.2711