Nonparametric Estimation of Conditional Incremental Effects

TL;DR

This paper introduces nonparametric methods for estimating conditional effects under stochastic interventions that do not require positivity, providing robust estimators and tests for treatment effect heterogeneity, demonstrated on ICU admission data.

Contribution

It proposes a novel nonparametric framework for incremental propensity score effects that relaxes positivity assumptions and offers double robust estimators and heterogeneity tests.

Findings

Developed a projection estimator and a flexible nonparametric estimator.

Both estimators satisfy a form of double robustness.

Applied methods to ICU admission data to analyze mortality effects.

Abstract

Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Most research has focused on estimating the conditional average treatment effect (CATE). However, identification of the CATE requires all subjects have a non-zero probability of receiving treatment, or positivity, which may be unrealistic in practice. Instead, we propose conditional effects based on incremental propensity score interventions, which are stochastic interventions where the odds of treatment are multiplied by some factor. These effects do not require positivity for identification and can be better suited for modeling scenarios in which people cannot be forced into treatment. We develop a projection estimator and a flexible nonparametric estimator that can each estimate all the conditional effects we propose and derive model-agnostic error guarantees showing both estimators satisfy a form of double robustness. Further, we propose a summary of treatment effect heterogeneity and a test for any effect heterogeneity based on the variance of a conditional derivative effect and derive a nonparametric estimator that also satisfies a form of double robustness. Finally, we demonstrate our estimators by analyzing the effect of intensive care unit admission on mortality using a dataset from the (SPOT)light study.