Robust Estimating Method for Propensity Score Models and its Application to Some Causal Estimands: A review and proposal

TL;DR

This paper reviews existing propensity score estimation methods, proposes a robust two-step strategy, and evaluates their performance in estimating causal effects through simulations, highlighting boosted CART and CBPS as effective approaches.

Contribution

The paper introduces a novel robust two-step propensity score estimation method and compares it with existing techniques through simulation studies.

Findings

Boosted CART and CBPS with higher-order balancing perform well.

These methods yield small variance and bias in estimating ATE and ATO.

Boosted CART and CBPS are versatile for various causal estimands.

Abstract

In observational study, the propensity score has the central role to estimate causal effects. Since the propensity score is usually unknown, estimating by appropriate procedures is an indispensable step. A point to note that a causal effect estimator might have some bias if a propensity score model was misspecified; valid model construction is important. To overcome the problem, a variety of interesting methods has been proposed. In this paper, we review four methods: using ordinary logistic regression approach; CBPS proposed by Imai and Ratkovic; boosted CART proposed by McCaffrey and colleagues; a semiparametric strategy proposed by Liu and colleagues. Also, we propose the novel robust two step strategy: estimating each candidate model in the first step and integrating them in the second step. We confirm the performance of these methods through simulation examples by estimating the ATE and ATO proposed by Li and colleagues. From the results of the simulation examples, the boosted CART and CBPS with higher-order balancing condition have good properties; both the estimate of the ATE and ATO has the small variance and the absolute value of bias. The boosted CART and CBPS are useful for a variety of estimands and estimating procedures.