Estimation of heterogeneous principal effects under principal ignorability

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.

Figures (21)

• Figure 1: Root mean squared error (RMSE, log scale) of $\tau^{10}(X)$ estimators across sample sizes (1,000–16,000). Results compare the T-learner, subset, EIF, and one-step estimators.
• Figure 2: Boxplots display the distribution of RMSE for four estimators (EIF, One-step, Subset, and Tlearner) estimated by GAM model across three sample sizes ($n=1000$, $n=2000$, $n=4000$)
• Figure 3: Estimated complier-specific treatment effects, ordered by the point estimates, with 95% confidence intervals computed by grf. The top subpanel displays unit-level estimates for all compliers with corresponding confidence intervals, while the bottom subpanel highlights individuals whose effects are statistically distinguishable from zero (i.e., whose confidence intervals exclude 0). Red points denote estimated beneficial effects ($\tau^{10}(x)<0$), whereas blue points indicate increased readmission risk ($\tau^{10}(x)>0$).
• Figure 4: Plot of simulated subset data of simple example and estimated functions of outcome models
• Figure 5: Estimated CPCE and the true CPCE in the simple example

Theorems & Definitions (21)

• Theorem 2.1
• Theorem 3.1
• Theorem 3.2
• Definition 1: EIF quantities
• Theorem 3.3
• Theorem 3.4
• Theorem 3.5
• Theorem 3.6
• Definition 2: Stability; kennedy2023towards
• Theorem 4.1: Stability of linear smoothers; kennedy2023towards