Hierarchical Priors for Bias Parameters in Bayesian Sensitivity Analysis for Unmeasured Confounding

Recent years have witnessed new innovation in Bayesian techniques to adjust for unmeasured
confounding. A challenge with existing methods is that the user is often required to elicit
prior distributions for high dimensional parameters that model competing bias scenarios. This
can render the methods unwieldy. In this paper we propose a novel methodology to adjust
for unmeasured confounding that derives default priors for bias parameters for observational
studies with binary covariates. The confounding e�ects of measured and unmeasured variables
are treated as exchangeable within a Bayesian framework. We model the joint distribution of
covariates using a loglinear model with pairwise interaction terms. Hierarchical priors constrain
the magnitude and direction of bias parameters. An appealing property of the method is that
the conditional distribution of the unmeasured confounder follows a logistic model, giving a
simple equivalence with previously proposed methods. We apply the method in a data example
from pharmacoepidemiology and explore the impact of di�erent priors for bias parameters on
the analysis results.