Bayesian data fusion: Probabilistic sensitivity analysis for unmeasured confounding using informative priors based on secondary data

Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time‐varying exposures. Building on the Bayesian g‐formula method introduced by Keil et al., we outline a general approach for the estimation of population‐level causal quantities involving dynamic and stochastic treatment regimes, including regimes related to mediation estimands such as natural direct and indirect effects. We further extend this approach to propose a Bayesian data fusion (BDF), an algorithm for performing probabilistic sensitivity analysis when a confounder unmeasured in a primary data set is available in an external data source. When the relevant relationships are causally transportable between the two source populations, BDF corrects confounding bias and supports causal inference and decision‐making within the main study population without sharing of the individual‐level external data set. We present results from a simulation study comparing BDF to two common frequentist correction methods for unmeasured mediator‐outcome confounding bias in the mediation setting. We use these methods to analyze data on the role of stage at cancer diagnosis in contributing to Black–White colorectal cancer survival disparities.