Assessing Unmeasured Confounding in Observational Research via Bayesian Semiparametric Modeling

It is challenging to infer a causal relationship with observational data. Untestable assumptions of ignorability or exchangeability are often utilized to facilitate causal effect estimation, which opens the door to arguments for and against the validity of a causal conclusion. In their 1959 seminal paper, Cornfield and colleagues provided sophisticated statistical reasoning for causal inference with observational data and made a key technical contribution to sensitivity analysis. Cornfield's idea paved the way for the development of modern tools for assessment of causality if ignorability assumptions fail. Compared with classical/frequentist approaches, Bayesian methods for sensitivity analysis are less fully developed. In this commentary, we first introduce a Bayesian semiparametric model for causal inference, then present a sensitivity analysis strategy for the Gaussian process model. Our method is easily interpretable and avoids restrictive parametric outcome assumptions. It can also be applied to both population-level and conditional causal effects.