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Bayesian sensitivity analysis for unmeasured confounding in observational studies.

Lawrence C McCandless1, Paul Gustafson, Adrian Levy

  • 1Department of Statistics, University of British Columbia, Vancouver BC, Canada. lawrence@stat.ubc.ca

Statistics in Medicine
|September 26, 2006
PubMed
Summary

Bayesian sensitivity analysis for unmeasured confounding in observational studies can be achieved using prior distributions. Simulations show that credible intervals achieve nominal coverage on average when priors approximate sampling distributions.

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Observational Studies

Background:

  • Unmeasured confounding poses a significant challenge in observational studies, potentially biasing results.
  • Logistic regression models can represent associations between exposure, response, confounders, and unmeasured confounders.

Purpose of the Study:

  • To develop and evaluate a Bayesian sensitivity analysis method for unmeasured confounding.
  • To assess the impact of prior distributions on credible interval coverage in the presence of unmeasured confounding.

Main Methods:

  • A model for unmeasured confounding using logistic regression was formulated.
  • A family of prior distributions was proposed to represent beliefs about unmeasured confounders.
  • Markov chain Monte Carlo (MCMC) simulations were used to sample from the posterior distribution.

Related Experiment Videos

  • Simulation studies investigated coverage probabilities under various prior distributions.

    • Main Results:

    • The model for unmeasured confounding is not identifiable, precluding standard Bayesian asymptotic theory.
    • Credible intervals demonstrated approximately nominal coverage probability on average.
    • Average coverage was achieved when the prior distribution approximated the sampling distribution of model parameters.

    Conclusions:

    • The proposed Bayesian sensitivity analysis method provides a framework for assessing unmeasured confounding.
    • Appropriate selection of prior distributions is crucial for reliable inference in the presence of unmeasured confounding.
    • The method was motivated by a study on beta-blocker therapy for heart failure.