Conditional Principal Causal Effects via Bayesian Sensitivity Analysis

Thomas M. Menino Convention & Exhibition Center 

Principal stratification provides a principled framework for causal inference with post-treatment intermediate variables, but identification often relies on strong assumptions such as principal ignorability. Existing methods typically focus on marginal effects and provide limited insight into covariate-dependent heterogeneity.

In this talk, we develop a Bayesian sensitivity analysis framework for conditional principal causal effects, defined within latent principal strata and indexed by pre-treatment covariates. Under treatment ignorability and a structured model for potential outcome means, we show that conditional principal causal effects are identifiable up to a small number of interpretable sensitivity parameters that capture violations of principal ignorability and dependence between potential intermediate outcomes. These parameters enter the estimand through an explicit identification formula, enabling transparent sensitivity analysis without imposing monotonicity or exclusion restrictions.

We combine Bayesian nonparametric models for identifiable components with prior distributions on sensitivity parameters to account for both sampling and sensitivity uncertainty.

Principal stratification

Conditional causal effects

Causal effect heterogeneity

Bayesian sensitivity analysis

Bayesian nonparametrics 

Biometrics Section