  Bayesian causal inference offers a principled approach to policy evaluation
of proposed interventions on mediators or time-varying exposures. We outline a
general approach to the estimation of causal quantities for settings with
time-varying confounding, such as exposure-induced mediator-outcome
confounders. We further extend this approach to propose two Bayesian data
fusion (BDF) methods for unmeasured confounding. Using informative priors on
quantities relating to the confounding bias parameters, our methods incorporate
data from an external source where the confounder is measured in order to make
inferences about causal estimands in the main study population. We present
results from a simulation study comparing our data fusion methods to two common
frequentist correction methods for unmeasured confounding bias in the mediation
setting. We also demonstrate our method with an investigation of the role of
stage at cancer diagnosis in contributing to Black-White colorectal cancer
survival disparities.
