Estimating PATE under positivity violations: SBART+SPL for high-dimensional covariates

Lennard Maßmann

Keywords: Bayesian causal inference, regression trees, overlap, extrapolation

TL;DR: We introduce SBART+SPL, a SoftBART-based extension of BART+SPL that improves precision and coverage in PATE estimation under positivity violations in high-dimensional settings while preserving the original target population.

Abstract:

The positivity assumption is a fundamental requirement for causal inference in the potential out-
comes framework, ensuring that all individuals have a positive probability of receiving each treat-
ment option. However, real-world datasets often violate this assumption in regions of
weak overlap where one treatment group is underrepresented or entirely absent for certain com-
binations of confounding variables. Traditional approaches, such as trimming and weighting, ad-
dress these violations but typically modify the target population and potentially introducing bias. The
Bayesian Additive Regression Trees with Spline Models (BART+SPL) has been proposed as a
solution to this issue. This approach combines Bayesian Additive Regression Trees (BART) for
imputation in regions of overlap with spline models (SPL) to extrapolate into regions of weak
overlap, thereby preserving the initial target population. While delivering precise results when
considering low-dimensional covariates, performance of BART+SPL is compromised under high-
dimensional covariates. To address this limitation, we propose SBART+SPL, an extension of the
BART+SPL framework that integrates SoftBART into the estimation procedure. SoftBART gener-
alizes BART by implementing smooth decision rules and sparsity-inducing splitting probabilities.
A simulation study demonstrates that SBART+SPL yields better precision and improved cover-
age compared to BART+SPL when estimating population average treatment effects (PATE) in the
presence of high-dimensional covariates and violations of the positivity assumption. The applica-
bility of SBART+SPL is illustrated by re-analyzing an empirical study that evaluates the impact of
exposure to natural gas compressor stations on cancer mortality rates across U.S. counties.

Submission Number: 39