Outcome-Adjusted Balance Measure for Generalized Propensity Score Model Selection

TL;DR

This paper introduces an outcome-adjusted balance measure for selecting generalized propensity score models, improving the estimation of treatment effects in observational studies with multiple treatments by focusing on outcome-related covariates.

Contribution

It proposes a novel balance measure that effectively identifies the optimal GPS model by leveraging covariate-outcome relationships, ensuring consistent and efficient treatment effect estimation.

Findings

The measure consistently selects the optimal GPS model under certain assumptions.

Simulation studies show improved finite sample performance over existing methods.

Application to Tutoring data demonstrates practical utility.

Abstract

In this article, we propose the outcome-adjusted balance measure to perform model selection for the generalized propensity score (GPS), which serves as an essential component in estimation of the pairwise average treatment effects (ATEs) in observational studies with more than two treatment levels. The primary goal of the balance measure is to identify the GPS model specification such that the resulting ATE estimator is consistent and efficient. Following recent empirical and theoretical evidence, we establish that the optimal GPS model should only include covariates related to the outcomes. Given a collection of candidate GPS models, the outcome-adjusted balance measure imputes all baseline covariates by matching on each candidate model, and selects the model that minimizes a weighted sum of absolute mean differences between the imputed and original values of the covariates. The weights are defined to leverage the covariate-outcome relationship, so that GPS models without optimal variable selection are penalized. Under appropriate assumptions, we show that the outcome-adjusted balance measure consistently selects the optimal GPS model, so that the resulting GPS matching estimator is asymptotically normal and efficient. We compare its finite sample performance with existing measures in a simulation study. We illustrate an application of the proposed methodology in the analysis of the Tutoring data.