Simplified Bayesian Sensitivity Analysis for Mismeasured and Unobserved Confounders
Article first published online: 11 JAN 2010
© 2010, The International Biometric Society
Volume 66, Issue 4, pages 1129–1137, December 2010
How to Cite
Gustafson, P., McCandless, L. C., Levy, A. R. and Richardson, S. (2010), Simplified Bayesian Sensitivity Analysis for Mismeasured and Unobserved Confounders. Biometrics, 66: 1129–1137. doi: 10.1111/j.1541-0420.2009.01377.x
- Issue published online: 11 JAN 2010
- Article first published online: 11 JAN 2010
- Received February 2009. Revised August 2009. Accepted October 2009.
- Bayesian inference;
- Measurement error;
- Sensitivity analysis;
- Unobserved confounder
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.