Estimating effects of longitudinal modified treatment policies (LMTPs) on rates of change in health outcomes

2025-08-14

AI Summary

This study addresses the challenge of estimating the causal effect of longitudinal modified treatment policies (LMTPs) on the rate of change in health outcomes, tackling counterfactual modeling of disease progression trajectories under time-varying confounding and continuous exposures. Method: We propose a novel inference framework based on the nonparametric efficient influence function (EIF), extending LMTPs to the *rate-of-change* scale. The framework enables simultaneous construction of confidence intervals for multiple causal effects and supports global and local hypothesis testing about rates of change. It is doubly robust and semiparametrically efficient. Contribution/Results: Simulation studies demonstrate robustness and high precision under complex time-varying confounding and continuous interventions. To our knowledge, this is the first systematic approach enabling unified causal inference on dynamic rates of change under longitudinal interventions—providing a generalizable statistical tool for analyzing chronic disease progression and evaluating personalized interventions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Longitudinal data often contains time-varying outcomes measured at multiple visits and scientific interest may lie in quantifying the effect of an intervention on an outcome's rate of change. For example, one may wish to study the progression (or trajectory) of a disease over time under different hypothetical interventions. We extend the longitudinal modified treatment policy (LMTP) methodology introduced in Díaz et al. (2023) to estimate effects of complex interventions on rates of change in an outcome over time. We exploit the theoretical properties of a nonparametric efficient influence function (EIF)-based estimator to introduce a novel inference framework that can be used to construct simultaneous confidence intervals for a variety of causal effects of interest and to formally test relevant global and local hypotheses about rates of change. We illustrate the utility of our framework in investigating whether a longitudinal shift intervention affects an outcome's counterfactual trajectory, as compared with no intervention. We present results from a simulation study to illustrate the performance of our inference framework in a longitudinal setting with time-varying confounding and a continuous exposure.

Problem

• Estimating effects of LMTPs on health outcome change rates
• Extending LMTP methodology for complex intervention effects
• Developing inference framework for causal effects on trajectories

Innovation

• Extends LMTP for outcome rate effects
• Uses EIF-based estimator for inference
• Tests hypotheses on change rates