[Paper Review] A Groupwise Approach for Inferring Heterogeneous Treatment Effects in Causal Inference

Chan Park, Hyunseung Kang|arXiv (Cornell University)|Aug 12, 2019

Advanced Causal Inference Techniques54 references4 citations

TL;DR

This paper proposes a groupwise approach for estimating heterogeneous treatment effects by comparing nonparametric and semiparametric methods, introducing a combined estimator that achieves higher efficiency. It establishes conditions for consistency, derives cluster-robust standard errors, and provides a multiple testing procedure to control familywise error rate.

ABSTRACT

Recently, there has been great interest in estimating the conditional average treatment effect using flexible machine learning methods. However, in practice, investigators often have working hypotheses about effect heterogeneity across pre-defined subgroups of study units, which we call the groupwise approach. The paper compares two modern ways to estimate groupwise treatment effects, a nonparametric approach and a semiparametric approach, with the goal of better informing practice. Specifically, we compare (a) the underlying assumptions, (b) efficiency and adaption to the underlying data generating models, and (c) a way to combine the two approaches. We also discuss how to test a key assumption concerning the semiparametric estimator and to obtain cluster-robust standard errors if study units in the same subgroups are correlated. We demonstrate our findings by conducting simulation studies and reanalyzing the Early Childhood Longitudinal Study.

Motivation & Objective

• To compare nonparametric and semiparametric approaches for estimating groupwise treatment effects in observational studies with unknown propensity scores.
• To identify sufficient and necessary conditions for the semiparametric estimator to consistently estimate groupwise effects.
• To develop a combined estimator that improves efficiency by leveraging strengths of both nonparametric and semiparametric methods.
• To derive cluster-robust standard errors for settings where units within subgroups are correlated.
• To propose a multiple testing procedure that controls the familywise error rate when testing multiple groupwise effects simultaneously.

Proposed method

• Uses a nonparametric approach that estimates the conditional average treatment effect (CATE) using machine learning methods (e.g., GRF, R-learner) and averages over predefined subgroups.
• Employs a semiparametric approach that models the CATE as a function of covariates with a parametric component aligned to the groupwise effect target.
• Derives a combined weighted estimator that minimizes asymptotic variance by optimally blending the nonparametric and semiparametric estimates.
• Applies the continuous mapping theorem and Slutsky’s theorem to establish asymptotic normality and consistency of the combined estimator under regularity conditions.
• Derives cluster-robust standard errors to account for within-group correlation in study units.
• Proposes a multiple testing procedure using simultaneous inference to control the familywise error rate when testing multiple groupwise effects.

Experimental results

Research questions

• RQ1 Under what conditions is the semiparametric estimator consistent for groupwise treatment effects?
• RQ2 How do the efficiency and data-adaptive performance of nonparametric and semiparametric estimators compare under different data-generating models?
• RQ3 Can a combined estimator outperform both nonparametric and semiparametric estimators in terms of asymptotic variance?
• RQ4 How can cluster-robust standard errors be derived for groupwise treatment effect estimators when units in the same subgroup are correlated?
• RQ5 What is an effective multiple testing procedure to control the familywise error rate when testing multiple groupwise effects simultaneously?

Key findings

• The semiparametric estimator is consistent for groupwise effects if and only if the model's influence function satisfies a specific orthogonality condition.
• The combined estimator achieves lower asymptotic variance than both the nonparametric and semiparametric estimators when the variances of the two components differ.
• Cluster-robust standard errors are derived by accounting for within-group correlation in the estimating equations, ensuring valid inference under dependence.
• The multiple testing procedure controls the familywise error rate by adjusting critical values based on the joint asymptotic distribution of the groupwise effects.
• When the nonparametric and semiparametric estimators have equal asymptotic variances, any weight in [0,1] minimizes variance, and the combined estimator remains consistent.
• The combined estimator is asymptotically efficient under the nonparametric model if the optimal weights are consistently estimated.