Propensity score regression for causal inference with treatment heterogeneity

Abstract

Understanding how treatment effects vary on individual characteristics is critical in the contexts of personalized medicine, personalized advertising and policy design. When the characteristics are of practical interest are only a subset of full covariate, non-parametric estimation is often desirable; but few methods are available due to the computational difficult. Existing nonparametric methods such as the inverse probability weighting methods have limitations that hinder their use in many practical settings where the values of propensity scores are close to 0 or 1. We propose the propensity score regression (PSR) that allows the non-parametric estimation of the heterogeneous treatment effects in a wide context. PSR includes two non-parametric regressions in turn, where it first regresses on the propensity scores together with the characteristics of interest, to obtain an intermediate estimate; and then, regress the intermediate estimates on the characteristics of interest only. By including propensity scores as regressors in the non-parametric manner, PSR is capable of substantially easing the computational difficulty while remain (locally) insensitive to any value of propensity scores. We present several appealing properties of PSR, including the consistency and asymptotical normality, and in particular the existence of an explicit variance estimator, from which the analytical behaviour of PSR and its precision can be assessed. Simulation studies indicate that PSR outperform existing methods in varying settings with extreme values of propensity scores. We apply our method to the national 2009 flu survey (NHFS) data to investigate the effects of seasonal influenza vaccination and having paid sick leave across different age groups.

Doubly Robust Collaborative Targeted Learning for Debiased Recommendations

“…There are five desired properties for evaluating debiasing methods, including doubly robust, robust to small propensities [38], boundedness [16,34,39], without extrapolation [16,31], and low variance. Robust to small propensities.…”

“…There are five different perspectives to evaluate a debiasing method, including robust to small propensities [38], without extrapolation [16,31], doubly robust [36], low variance [31] and boundedness [16,34]. Failing to meet any of them may lead to sub-optimal performance [16,34].…”

Stabilized Doubly Robust Learning for Recommendation on Data Missing Not at Random

“…The proposed method builds on the stabilized average caual effect estimation approaches in causal inference. [16,37] summarized the limitations of doubly robust methods, including unstable to small propensities [36], unboundedness [30], and large variance [29]. These issues inspired a series of stabilized causal effect estimation methods in statistics [10,2,30,16].…”