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.

翻译：本研究探讨了在二元处理和二元中介变量情境下，异质性主因果效应的估计与推断问题。主因果效应是指根据中介变量的潜在取值所定义子组内的效应，其中包含依从者效应。我们提出了一个在主可忽略性假设下估计异质性主因果效应并构建逐点置信区间的框架。本文发展了几种估计量，并刻画了其稳健性特征：一种估计量具有双重稳健性，而另外两种则达到了介于双重与三重稳健性之间的中间稳健性；相比之下，主因果效应仅能以三重稳健的方式进行估计。我们在非参数光滑性条件下建立了大样本理论，并分析了各种方法的偏差来源，从而为超越光滑设定（包括高维情形）下的性能提供了深入见解。本文通过估计异质性依从者效应，以卡姆登联盟热点随机试验为例对所提方法进行了说明。