Estimating causal effects of functional treatments with modified functional treatment policies

2026-02-09

AI Summary

This study addresses the limitations of existing methods for causal inference with high-dimensional continuous functional treatments, which rely on strong positivity assumptions and offer limited interpretability. The authors propose a novel causal estimator—Modified Functional Treatment Policy (MFTP)—that, for the first time, identifies and estimates individual potential outcomes under infinitesimally perturbed treatment trajectories under weak regularity conditions. By defining population averages over an infinite-dimensional intervention space via functional principal component analysis (FPCA), the approach integrates outcome regression, inverse probability weighting, and doubly robust estimation to overcome the constraints of conventional functional average dose-response functions. Simulations confirm the method’s validity, and its application to NHANES accelerometer data successfully quantifies the causal effects of modest reductions in nighttime interruptions and low-activity duration on all-cause mortality, substantially enhancing both interpretability and practical applicability.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Security and Privacy: Large-scale security measurements
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Functional data are increasingly prevalent in biomedical research. While functional data analysis has been established for decades, causal inference with functional treatments remains largely unexplored. Existing methods typically focus on estimating the causal average dose response functional (ADRF), which requires strong positivity assumptions and offers limited interpretability. In this work, we target a new causal estimand, the modified functional treatment policy (MFTP), which focuses on estimating the average potential outcome when each individual slightly modifies their treatment trajectory from the observed one. A major challenge for this new estimand is the need to define an average over an infinite-dimensional object with no density. By proposing a novel definition of the population average over a functional variable using a functional principal component analysis (FPCA) decomposition, we establish the causal identifiability of the MFTP estimand. We further derive outcome regression, inverse probability weighting, and doubly robust estimators for the MFTP, and provide theoretical guarantees under mild regularity conditions. The proposed estimators are validated through extensive simulation studies. Applying our MFTP framework to the National Health and Nutrition Examination Survey (NHANES) accelerometer data, we estimate the causal effects of reducing disruptive nighttime activity and low-activity duration on all-cause mortality.

Problem

• functional treatment
• causal inference
• modified functional treatment policy
• average potential outcome
• infinite-dimensional treatment

Innovation

• functional treatment
• causal inference
• modified functional treatment policy
• functional principal component analysis
• doubly robust estimation