Generalized propensity score weighting for functional causal inference framework

2026-08-04

AI Summary

This study addresses the challenge of causal effect estimation in observational studies where the treatment is a functional variable—such as a trajectory—rather than a scalar. The authors propose a functional propensity score weighting framework that achieves covariate balance by removing dependencies between time-varying treatments and confounders, thereby enabling identification of marginal causal effects under functional treatments, covariates, and outcomes. A key methodological innovation lies in reformulating weight estimation as a smooth, unconstrained dual optimization problem, which substantially enhances computational scalability and naturally extends to settings with time-varying covariates and longitudinal functional outcomes. Empirical evaluations demonstrate superior performance over existing methods in terms of covariate balance, estimation accuracy, and computational efficiency. The approach is successfully applied to UK Biobank data, revealing the causal effects of BMI trajectories on type 2 diabetes risk and HbA1c trajectories.

Abstract

Estimating causal effects in observational studies requires adjustment for confounding, a task that becomes challenging when the exposure is a function observed over a continuous domain rather than a scalar variable. We develop a functional propensity score weighting framework that achieves covariate balance by removing dependence between time-varying treatments and observed confounders, thereby enabling estimation of marginal causal effects in settings with functional treatments, covariates, and outcomes. We propose a dual formulation of the weight estimation problem that yields a smooth unconstrained optimization and improves computational scalability. The proposed framework extends naturally to settings with time-varying covariates and to longitudinal outcomes via a function-on-function marginal structural model, allowing estimation of causal effect surfaces. The proposed method improves covariate balance, estimation accuracy, and computational efficiency compared to the existing approach and retains these properties when extended to functional covariates and outcomes. We apply the method to data from the UK Biobank to estimate the causal effect of body mass index trajectories on the risk of Type 2 Diabetes and on subsequent glycated hemoglobin trajectories, a functional measure of metabolic status.

Problem

• functional treatment
• causal inference
• confounding adjustment
• observational study
• propensity score weighting

Innovation

• functional propensity score
• causal inference
• weighting
• function-on-function regression
• marginal structural model