Optimal estimation of generalized causal effects in cluster-randomized trials with multiple outcomes

2026-01-19

AI Summary

This study addresses robust causal inference for the global treatment effect in multi-outcome cluster randomized trials. Within the potential outcomes framework, it proposes the first unified nonparametric approach that flexibly defines causal effects via pairwise contrast functions at both cluster and individual levels. The method integrates weighted clustered U-statistics, efficient influence functions, covariate adjustment, and debiased machine learning to effectively accommodate informative cluster sizes and settings involving prioritized versus non-prioritized outcomes. Under mild regularity conditions, the proposed estimator is consistent, asymptotically normal, and achieves the semiparametric efficiency bound. Its superior performance and practical utility are demonstrated through extensive simulations and an empirical analysis of a chronic pain management trial.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Multiagent Systems: Mechanism Design

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Cluster-randomized trials (CRTs) are widely used to evaluate group-level interventions and increasingly collect multiple outcomes capturing complementary dimensions of benefit and risk. Investigators often seek a single global summary of treatment effect, yet existing methods largely focus on single-outcome estimands or rely on model-based procedures with unclear causal interpretation or limited robustness. We develop a unified potential outcomes framework for generalized treatment effects with multiple outcomes in CRTs, accommodating both non-prioritized and prioritized outcome settings. The proposed cluster-pair and individual-pair causal estimands are defined through flexible pairwise contrast functions and explicitly account for potentially informative cluster sizes. We establish nonparametric estimation via weighted clustered U-statistics and derive efficient influence functions to construct covariate-adjusted estimators that integrate debiased machine learning with U-statistics. The resulting estimators are consistent and asymptotically normal, attain the semiparametric efficiency bounds under mild regularity conditions, and have analytically tractable variance estimators that are proven to be consistent under cross-fitting. Simulations and an application to a CRT for chronic pain management illustrate the practical utility of the proposed methods.

Problem

• cluster-randomized trials
• multiple outcomes
• causal effects
• generalized treatment effects
• optimal estimation

Innovation

• cluster-randomized trials
• multiple outcomes
• causal inference
• U-statistics
• debiasing machine learning