Probabilistic Analysis of Balancing Scores for Causal Inference

TL;DR

This paper provides a probabilistic analysis of propensity scores and introduces the outcome score, demonstrating that combining both scores enhances dimensionality reduction in causal inference with discrete covariates.

Contribution

It offers a more general derivation of the prognostic score, called the outcome score, and advocates for using both scores together for better confounder adjustment.

Findings

Outcome score derivation is more general than current literature

Using both propensity and outcome scores improves confounder reduction

Analysis focuses on discrete covariates and outcomes

Abstract

Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic score can be derived simultaneously. However the prognostic score is derived in a limited sense in the current literature whereas our derivation is more general and shows all possibilities of having the score. And we call it outcome score. We argue that application of both the propensity score and the outcome score is the most efficient way for reduction of dimension in the confounding covariates as opposed to current belief that the propensity score alone is the most efficient way.