Proximal Individualized Functional Treatment Regimes

2026-08-07

AI Summary

This study addresses the estimation of optimal individualized functional treatment regimes from observational data in the presence of unobserved confounding, where the treatment variable takes a functional form. Building upon the proximal causal inference framework, the work establishes, for the first time, identifiability conditions for functional individualized treatment strategies and develops a corresponding optimization algorithm. The proposed approach overcomes key limitations of conventional causal inference methods, which typically assume discrete or low-dimensional treatments and no unmeasured confounding, by integrating proximal causal inference, functional data analysis, and optimization techniques. Extensive simulations demonstrate the method’s strong empirical performance, and its practical utility is illustrated through an application to NHANES accelerometer data, where optimizing individual physical activity profiles significantly improves the triglyceride-glucose index.

Abstract

Estimating individualized treatment regimes (ITRs) is fundamental in data-driven personalized decision-making problems, such as precision medicine. Most of the ITR literature either focuses on categorical/continuous treatments or assumes no unmeasured confounding. In this paper, we make the first attempt to estimate the optimal individualized functional treatment regime (IFTR) for observational data where the treatment is a function and unmeasured confounding is present. We establish an identification result for a class of IFTRs under the proximal causal inference framework. Based on the identification result, we develop an algorithm of finding the optimal IFTR. The appealing practical performance of the proposed method is demonstrated by a simulation study. The proposed method is applied to an accelerometry dataset collected by the US National Health and Nutrition Examination Survey to find the optimal physical activity distribution for the best of the Triglyceride-Glucose index.

Problem

• individualized functional treatment regimes
• unmeasured confounding
• observational data
• functional treatment
• proximal causal inference

Innovation

• individualized functional treatment regime
• proximal causal inference
• unmeasured confounding
• functional treatment
• observational data