Estimating causal effects of functional treatments with modified functional treatment policies

TL;DR

This paper introduces a novel causal inference method for functional treatments, focusing on the modified functional treatment policy (MFTP), which estimates effects of slight treatment modifications using FPCA, with theoretical guarantees and real data application.

Contribution

It proposes a new causal estimand, the MFTP, and develops estimators with theoretical guarantees, addressing challenges of infinite-dimensional functional data analysis.

Findings

Validated estimators through extensive simulations.

Applied MFTP to NHANES accelerometer data.

Estimated causal effects of activity modifications on mortality.

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.