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Simplified Bayesian Sensitivity Analysis for Mismeasured and Unobserved Confounders

Authors

  • P. Gustafson,

    Corresponding author
    1. Department of Statistics, University of British Columbia, Vancouver, British Columbia VRT 1Z2, Canada
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  • L. C. McCandless,

    Corresponding author
    1. Faculty of Health Sciences, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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  • A. R. Levy,

    Corresponding author
    1. Department of Community Health and Epidemiology, Dalhousie University, Halifax, Nova Scotia B3H 1V7, Canada
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  • S. Richardson

    Corresponding author
    1. Centre for Biostatistics and MRC-HPA Centre for Environment and Health, Division of Epidemiology, Public Health and Primary Care, Imperial College, London SW7 2AZ, U.K.
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email:gustaf@stat.ubc.ca

email:mccandless@sfu.ca

email:adrian.levy@dal.ca

email:sylvia.richardson@imperial.ac.uk

Abstract

Summary We examine situations where interest lies in the conditional association between outcome and exposure variables, given potential confounding variables. Concern arises that some potential confounders may not be measured accurately, whereas others may not be measured at all. Some form of sensitivity analysis might be employed, to assess how this limitation in available data impacts inference. A Bayesian approach to sensitivity analysis is straightforward in concept: a prior distribution is formed to encapsulate plausible relationships between unobserved and observed variables, and posterior inference about the conditional exposure–disease relationship then follows. In practice, though, it can be challenging to form such a prior distribution in both a realistic and simple manner. Moreover, it can be difficult to develop an attendant Markov chain Monte Carlo (MCMC) algorithm that will work effectively on a posterior distribution arising from a highly nonidentified model. In this article, a simple prior distribution for acknowledging both poorly measured and unmeasured confounding variables is developed. It requires that only a small number of hyperparameters be set by the user. Moreover, a particular computational approach for posterior inference is developed, because application of MCMC in a standard manner is seen to be ineffective in this problem.

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