Measures for Assessing Causal Effect Heterogeneity Unexplained by Covariates

2026-02-09

AI Summary

Existing methods struggle to effectively quantify residual heterogeneity in causal effects after adjusting for covariates, particularly lacking suitable metrics in settings with continuous treatments or continuous outcomes. This work proposes, for the first time, P/N-CACE for binary treatments with continuous outcomes and P/N-CPICE for continuous treatments with continuous outcomes, both designed to characterize causal effect heterogeneity unexplained by observed covariates. Building upon the conditional average causal effect (CACE) framework and stochastic intervention strategies, we establish formal identification theorems and develop corresponding bounding analysis theory. Empirical applications on real-world data demonstrate the effectiveness and practical utility of the proposed measures in uncovering residual heterogeneity, substantially expanding the scope of answerable questions in causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• causal effect heterogeneity
• unexplained heterogeneity
• continuous outcome
• binary treatment
• stochastic interventions

Innovation

• Causal Effect Heterogeneity
• Stochastic Interventions
• Conditional Average Causal Effect
• Unexplained Heterogeneity
• Continuous Treatment