Bayesian Causal Effect Estimation with Stan: Parametric and Nonparametric Approaches
Bayesian modeling techniques have been growing in popularity within the causal literature. In this talk, we highlight the unique benefits Bayes brings to the table when estimating causal effects of time-fixed and time-varying treatments. We also highlight how easily these methods can be implemented in Stan – opening up the causal toolkit to a large pool of practicing Bayesian statisticians.
Using synthetic data examples in Stan, we show how informative partial pooling priors can provide shrinkage of conditional average treatment effects when treatment is fixed across the follow-up. In longitudinal settings with time-varying treatment, dynamic Ridge- and Horseshoe-type priors can help us strike a balance between strict frequentist modeling assumptions.
Finally, informative priors can be used to conduct probabilistic sensitivity analysis (PSA) around violations of causal assumptions such as ignorablility. That is, instead of assuming ignorability holds, we can express prior uncertainty about the magnitude and direction of ignorability violations. This prior uncertainty then naturally flows through to posterior inference.
All of these methods for causal estimation and PSA rely on Bayesian bootstrapping and g-computation. The beauty of Bayesian modeling is full posterior inference: once the posterior is sampled, inference about any causal estimand can be done by merely post-processing these draws in different ways. Throughout, we highlight the use of Stan’s generated quantities block for efficient implementation of bootstrapping, g-computation, and post-processing. If time-permits, nonparametric causal effect estimation via Gaussian Processes in Stan will also be discussed.
Arman is a 4th-year Biostatistics PhD candidate at the University of Pennsylvania and Associate Fellow at the Leonard Davis Institute for Health Economics. His research focuses on developing nonparametric Bayesian models for causal inference problems arising in Health Economics, such as joint modeling of survival and marks, time-varying treatments, and heterogenous treatment effect estimation.
He received an MS in biostatistics from Penn and a BA in quantitative economics from Providence College. Before Penn, Arman was a Senior Analyst at Analysis Group's Health Economics and Outcomes Research team in Boston, MA.
Favorite priors include: Enriched Dirichlet Process, Gamma Process, and Zellner.