A Causal Framework for Evaluating Jointly Longitudinal Outcomes and Surrogate Markers: A State-Space Approach

2026-04-14

AI Summary

This study addresses the challenge of evaluating the extent to which dynamic surrogate markers explain the treatment effect on a primary outcome in longitudinal settings. Building upon the potential outcomes framework, it proposes the first causal evaluation method specifically designed for longitudinal surrogate markers. The approach employs a state-space model combined with Kalman filtering and smoothing to efficiently estimate the time-varying proportion of treatment effect explained by the surrogate. To enhance inferential robustness, the method integrates a nonparametric bootstrap strategy and a test for temporal homogeneity of surrogate efficacy. Simulation studies and an application to a diabetes clinical trial demonstrate that the proposed method performs well even with limited sample sizes, offering a reliable and interpretable causal quantification tool for assessing the validity of longitudinal surrogate markers.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Surrogate markers offer the potential to reduce the burden of data collection by replacing costly or invasive primary outcomes with more accessible measurements, provided that they can faithfully indicate the effectiveness of a treatment. However, appropriate evaluation of a surrogate is particularly complex in longitudinal studies, where both outcomes and surrogates can evolve dynamically over time and interest lies not only in the treatment effect at one time, but rather treatment effects that may vary along the entire trajectory. In this paper, we develop a statistical framework for surrogate evaluation when both the surrogate and primary outcome are measured over time. Specifically, within the potential outcomes framework, we propose a formal causal definition of the proportion of the treatment effect on the longitudinal primary outcome that is explained by the treatment effect on the longitudinal surrogate. For estimation, we leverage state-space models, together with the Kalman filter and smoother, enabling efficient estimation of treatment effects under realistic conditions of temporal evolution and patient-level variability. We introduce a nonparametric bootstrap strategy for state-space models, a temporal homogeneity test, and demonstrate the finite-sample performance of our proposed methods via a simulation study and application to a diabetes clinical trial.

Problem

• surrogate markers
• longitudinal outcomes
• causal inference
• treatment effect
• state-space models

Innovation

• causal surrogate evaluation
• state-space model
• longitudinal outcomes
• Kalman filter
• nonparametric bootstrap