Varying coefficient model for longitudinal data with informative observation times

2026-01-23

AI Summary

This study addresses the bias arising in existing varying-coefficient models when the dependence between observation times and longitudinal outcomes is ignored. To handle informative observation times, the authors propose a novel approach that models the observation mechanism via a proportional intensity model and, for the first time, integrates inverse intensity weighting with sieve estimation within a weighted least squares framework to obtain closed-form estimates of coefficient functions. Theoretical analysis establishes that the resulting estimator is consistent, achieves the optimal convergence rate, and is asymptotically normal, thereby enabling pointwise confidence interval construction. Simulation studies demonstrate that the proposed method substantially outperforms conventional unweighted approaches under informative observation schemes, and its practical utility is illustrated through an application to neuroimaging data from Alzheimer’s disease patients.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Varying coefficient models are widely used to characterize dynamic associations between longitudinal outcomes and covariates. Existing work on varying coefficient models, however, all assumes that observation times are independent of the longitudinal outcomes, which is often violated in real-world studies with outcome-driven or otherwise informative visit schedules. Such informative observation times can lead to biased estimation and invalid inference using existing methods. In this article, we develop estimation and inference procedures for varying coefficient models that account for informative observation times. We model the observation time process as a general counting process under a proportional intensity model, with time-varying covariates summarizing the observed history. To address potential bias, we incorporate inverse intensity weighting into a sieve estimation framework, yielding closed-form coefficient function estimators via weighted least squares. We establish consistency, convergence rates, and asymptotic normality of the proposed estimators, and construct pointwise confidence intervals for the coefficient functions. Extensive simulation studies demonstrate that the proposed weighted method substantially outperforms the conventional unweighted method when observation times are informative. Finally, we provide an application of our method to the Alzheimer's Disease Neuroimaging Initiative study.

Problem

• varying coefficient model
• longitudinal data
• informative observation times
• biased estimation
• invalid inference

Innovation

• varying coefficient model
• informative observation times
• inverse intensity weighting
• sieve estimation
• longitudinal data