There has been considerable interest in estimating heterogeneous causal effects across individuals or subpopulations. Researchers often assess causal effect heterogeneity based on the subjects' covariates using the conditional average causal effect (CACE). However, substantial heterogeneity may persist even after accounting for the covariates. Existing work on causal effect heterogeneity unexplained by covariates mainly focused on binary treatment and outcome. In this paper, we introduce novel heterogeneity measures, P-CACE and N-CACE, for binary treatment and continuous outcome that represent CACE over the positively and negatively affected subjects, respectively. We also introduce new heterogeneity measures, P-CPICE and N-CPICE, for continuous treatment and continuous outcome by leveraging stochastic interventions, expanding causal questions that researchers can answer. We establish identification and bounding theorems for these new measures. Finally, we show their application to a real-world dataset.

翻译：近年来，估计个体或亚群间异质因果效应的研究引起了广泛关注。研究者通常基于受试者协变量，利用条件平均因果效应（CACE）来评估因果效应异质性。然而，即使在考虑协变量后，显著的异质性可能依然存在。现有关于协变量未解释的因果效应异质性研究主要集中于二元处理与二元结果。本文针对二元处理与连续结果，提出了新的异质性度量指标P-CACE与N-CACE，分别代表正向受影响与负向受影响受试者的CACE。此外，通过利用随机干预，我们针对连续处理与连续结果提出了新的异质性度量指标P-CPICE与N-CPICE，从而扩展了研究者可回答的因果问题范围。我们为这些新度量建立了可识别性定理与边界定理。最后，我们展示了其在真实数据集上的应用。