Bayesian Sensitivity Analysis for Causal Estimation With Time-Varying Unmeasured Confounding

Causal inference relies on the untestable assumption of no unmeasured confounding to ensure the causal parameter of interest is identifiable. Sensitivity analysis quantifies the unmeasured confounding's impact on causal estimates. Among sensitivity analysis methods proposed in the literature, the latent confounder approach is favored for its intuitive interpretation via the use of bias parameters to specify the relationship between the observed and unobserved variables, and the sensitivity function approach directly characterizes the net causal effect of the unmeasured confounding without explicitly introducing latent variables to the causal models. In this paper, we developed and extended these two sensitivity analysis approaches, namely the Bayesian sensitivity analysis with latent confounding variables and the Bayesian sensitivity function approach for the estimation of time-varying treatment effects with longitudinal observational data subjected to time-varying unmeasured confounding. We investigated the performance of these methods in a series of simulation studies and applied them to a multicenter pediatric disease registry to provide practical guidance on their implementation.