Primary Submission Category: Heterogeneous Treatment Effects
Quantifying Treatment Effect Heterogeneity via the CATE Distribution Function
Authors: Nolan Cole, Marco Carone, Lars van der Laan,
Presenting Author: Nolan Cole*
Understanding how treatment effects are distributed across a population is essential for moving beyond mean summaries toward a richer characterization of treatment effect heterogeneity. The conditional average treatment effect (CATE) function is a fundamental object for studying such heterogeneity. Visualizing the distribution of CATE values in the target population (i.e., the CATE distribution) can reveal meaningful patterns of heterogeneity beyond the single metrics commonly used for this purpose. However, in a nonparametric model, the corresponding distribution function is an irregular parameter, precluding standard root-n inference.
In this work, we leverage the monotonicity of the distribution function to develop principled estimators that enable valid statistical inference. Specifically, we construct a Grenander-type estimator of the CATE distribution function and establish its large-sample properties, including consistency, double robustness, and cube-root convergence of its estimation error to a Chernoff limit distribution, which enables the construction of asymptotically valid confidence intervals. Simulation studies demonstrate that the proposed procedure has favorable finite-sample performance and can be readily used to obtain valid inference for quantiles of the CATE distribution.