Bayesian-based Propensity Score Subclassification Estimator

TL;DR

This paper introduces a Bayesian subclassification estimator for causal effect estimation that accounts for uncertainty in the number of strata, enhancing stability and reflecting design phase uncertainties.

Contribution

It proposes a novel Bayesian approach to determine the number of strata in propensity score subclassification, avoiding fixed choices and incorporating uncertainty.

Findings

Improves stability over inverse probability weighting methods.

Accounts for uncertainty in the number of strata.

Maintains flexibility without relying on a likelihood function.

Abstract

Subclassification estimators are one of the methods used to estimate causal effects of interest using the propensity score. This method is more stable compared to other weighting methods, such as inverse probability weighting estimators, in terms of the variance of the estimators. In subclassification estimators, the number of strata is traditionally set at five, and this number is not typically chosen based on data information. Even when the number of strata is selected, the uncertainty from the selection process is often not properly accounted for. In this study, we propose a novel Bayesian-based subclassification estimator that can assess the uncertainty in the number of strata, rather than selecting a single optimal number, using a Bayesian paradigm. To achieve this, we apply a general Bayesian procedure that does not rely on a likelihood function. This procedure allows us to avoid making strong assumptions about the outcome model, maintaining the same flexibility as traditional causal inference methods. With the proposed Bayesian procedure, it is expected that uncertainties from the design phase can be appropriately reflected in the analysis phase, which is sometimes overlooked in non-Bayesian contexts.