Computationally and statistically efficient estimation of time-smoothed counterfactual curves

2025-09-30

AI Summary

Existing methods for estimating time-smooth counterfactual curves in longitudinal causal inference suffer from low accuracy under high missingness rates and strong confounding. Method: We propose a multiply robust, time-adaptive estimation framework that integrates multiply robust estimation with time-series smoothing techniques within the generalized g-formula. It accommodates continuous, multivalued, and binary time-varying treatments and is compatible with non-monotone missingness and censoring mechanisms. By embedding flexible nonparametric machine learning models, it substantially improves statistical efficiency and stability for repeatedly measured outcomes. Contribution/Results: Theoretical analysis and simulation studies demonstrate superior performance over state-of-the-art methods under high missingness and strong confounding. An empirical application to estimating the long-term effect of union membership on wages validates both methodological effectiveness and practical utility.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• 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

Abstract

Longitudinal causal inference is concerned with defining, identifying, and estimating the effect of a time-varying intervention on a time-varying outcome that is indexed by a follow-up time. In an observational study, Robins's generalized g-formula can identify causal effects induced by a broad class of time-varying interventions. Various methods for estimating the generalized g-formula have been posed for different outcome types, such as a failure event indicator by a specified time (e.g. mortality by 5 year follow-up), as well as continuous or dichotomous/multi-valued outcomes measures at a specified time (e.g. blood pressure in mm/hg or an indicator of high blood pressure at 5-year follow-up). Multiply-robust, data-adaptive estimators leverage flexible nonparametric estimation algorithms while allowing for statistical inference. However, extant methods do not accommodate time-smoothing when multiple outcomes are measured over time, which can lead to substantial loss of precision. We propose a novel multiply-robust estimator of the generalized g-formula that accommodates time-smoothing over numerous available outcome measures. Our approach accommodates any intervention that can be described as a Longitudinal Modified Treatment Policy, a flexible class suitable for binary, multi-valued, and continuous longitudinal treatments. Our method produces an estimate of the effect curve: the causal effect of the intervention on the outcome at each measurement time, taking into account censoring and non-monotonic outcome missingness patterns. In simulations we find that the proposed algorithm outperforms extant multiply-robust approaches for effect curve estimation in scenarios with high degrees of outcome missingness and when there is strong confounding. We apply the method to study longitudinal effects of union membership on wages.

Problem

• Estimating time-smoothed counterfactual curves with multiple outcomes over time
• Addressing precision loss in longitudinal causal inference with missing data
• Developing robust estimators for time-varying intervention effects under confounding

Innovation

• Novel multiply-robust estimator for generalized g-formula
• Incorporates time-smoothing across multiple outcome measures
• Handles censoring and non-monotonic missingness patterns