Addressing Positivity Violations in Causal Effect Estimation using Gaussian Process Priors

TL;DR

This paper introduces a Gaussian process-based method for causal effect estimation that accounts for positivity violations by modeling increased uncertainty in regions with limited covariate overlap.

Contribution

It presents a novel Gaussian process approach that handles positivity violations in observational causal inference with minimal assumptions and explicit uncertainty quantification.

Findings

The method effectively captures increased uncertainty in non-overlap regions.

Simulation studies show reduced bias and improved efficiency.

Application to clinical data demonstrates practical utility.

Abstract

In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects, i.e., the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate should be reflected in such situations. With that goal in mind, we construct a Gaussian process model for estimating treatment effects in the presence of practical violations of positivity. Advantages of our method include minimal distributional assumptions, a cohesive model for estimating treatment effects, and more uncertainty associated with areas in the covariate space where there is less overlap. We assess the performance of our approach with respect to bias and efficiency using simulation studies. The method is then applied to a study of critically ill female patients to examine the effect of undergoing right heart catheterization.