Joint Group-Based Trajectory Modeling for Paired Repeated Measures: An Application to Audiometric Phenotypes and Dietary Associations

2026-07-26

AI Summary

This study addresses a critical limitation in traditional group-based trajectory models when analyzing paired repeated measures: the frequent neglect of hierarchical dependencies, which introduces bias, and the inflation of within-group variability by random effects, obscuring true trajectory patterns. To overcome these issues, the authors propose a novel joint group-based trajectory modeling framework that simultaneously captures both hierarchical dependencies between paired trajectories and heterogeneous latent trajectory patterns—a first in this domain. They develop a dual-path estimation strategy combining two-stage robust estimation with a one-stage EM algorithm to effectively handle estimation challenges posed by rare latent classes. Simulation studies demonstrate that the proposed method substantially corrects bias arising from ignored dependencies. Applied to the CHEARS hearing study, it successfully identifies distinct auditory phenotypes and reveals their significant association with adherence to the DASH diet.

Abstract

The assumption of conditional independence in conventional group-based trajectory modeling (GBTM) is often violated by paired repeated-measures data with heterogeneous trajectory patterns. While random-effects models can accommodate this dependence, they inflate within-group variability and blur distinct phenotypic shapes. We propose a joint GBTM framework that explicitly models hierarchical dependence in paired trajectories while allowing them to follow different latent patterns. We develop a robust two-stage approach to address estimation challenges caused by rare latent groups, and a one-stage EM algorithm that serves as a theoretical baseline under balanced group sizes. Simulations demonstrate that our methods correct the biases caused by ignoring hierarchical dependence. The proposed model was applied to real-world data from the Conservation of Hearing Study (CHEARS) Audiology Assessment Arm (AAA), a subcohort of the Nurses' Health Study II (NHS II), to identify distinct audiometric phenotypes and to investigate the association between the Dietary Approaches to Stop Hypertension (DASH) dietary adherence score and the latent audiometric patterns.

Problem

• group-based trajectory modeling
• paired repeated measures
• hierarchical dependence
• audiometric phenotypes
• conditional independence

Innovation

• joint group-based trajectory modeling
• hierarchical dependence
• paired repeated measures
• latent trajectory patterns
• two-stage estimation