Estimation of heterogeneous principal effects under principal ignorability

TL;DR

This paper develops methods for estimating and making inferences about subgroup causal effects in studies with binary treatments and intermediates, under the principal ignorability assumption, with robustness properties analyzed.

Contribution

It introduces a framework for estimating heterogeneous principal causal effects with multiple estimators exhibiting various robustness properties, including doubly and triply robust methods.

Findings

One estimator is doubly robust.

Two estimators have intermediate robustness.

Application to Camden Coalition trial illustrates methods.

Abstract

We study estimation and inference for heterogeneous principal causal effects with binary treatments and binary intermediate variables. Principal causal effects are subgroup effects within strata defined by potential values of an intermediate variable, including effects among compliers. We propose a framework for estimating and forming pointwise confidence intervals for heterogeneous principal causal effects under the principal ignorability assumption. Several estimators are developed, and their robustness properties are characterized: one estimator is doubly robust, whereas the other two attain intermediate robustness between double and triple robustness; in contrast, principal causal effects can be estimated in a triply robust manner only. We establish large-sample theory under nonparametric smoothness conditions and analyze the bias contributions of each approach, providing insight into performance beyond the smooth setting, including in high-dimensional regimes. Camden Coalition hotspotting randomized trial are used to illustrate the methods by estimating heterogeneous complier effects.