Gaussian Process Priors for Causal Inference Under Positivity Violations

• Activity Number: 58 - Advanced Bayesian Topics (Part 1)
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yaqian Zhu* and Nandita Mitra and Jason Roy
• Companies: University of Pennsylvania and University of Pennsylvania and Rutgers University
• Keywords: overlap; population average treatment effect; Bayesian nonparametrics; Metropolis within Gibbs; non-small cell lung cancer

Abstract

In observational studies, causal inference relies on several key 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, we should observe both treated and control subjects—the distributions overlap. 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 in simulations and compare with alternative approaches. The method is then applied to a study of non-small cell lung cancer patients to examine the effect of a new chemotherapy regimen.