Calibrated and Conformal Propensity Scores for Causal Effect Estimation

TL;DR

This paper emphasizes the importance of calibrating propensity scores for unbiased causal effect estimation and introduces recalibration techniques that improve accuracy and efficiency in various observational data analyses.

Contribution

It proposes simple recalibration methods for propensity scores, proving calibration's necessity for unbiased estimates and demonstrating improved causal inference in diverse applications.

Findings

Calibration improves bias and variance in causal estimates.

Calibrated scores reduce extreme weights, stabilizing estimates.

Enhanced efficiency in genome-wide association studies.

Abstract

Propensity scores are commonly used to estimate treatment effects from observational data. We argue that the probabilistic output of a learned propensity score model should be calibrated -- i.e., a predictive treatment probability of 90% should correspond to 90% of individuals being assigned the treatment group -- and we propose simple recalibration techniques to ensure this property. We prove that calibration is a necessary condition for unbiased treatment effect estimation when using popular inverse propensity weighted and doubly robust estimators. We derive error bounds on causal effect estimates that directly relate to the quality of uncertainties provided by the probabilistic propensity score model and show that calibration strictly improves this error bound while also avoiding extreme propensity weights. We demonstrate improved causal effect estimation with calibrated propensity scores in several tasks including high-dimensional image covariates and genome-wide association studies (GWASs). Calibrated propensity scores improve the speed of GWAS analysis by more than two-fold by enabling the use of simpler models that are faster to train.