Quantile Regression of Latent Longitudinal Trajectory Features

TL;DR

This paper introduces a flexible trajectory quantile regression framework for longitudinal data, enabling robust analysis of latent trajectory features related to subject characteristics, with theoretical guarantees and practical validation.

Contribution

It develops a novel trajectory quantile regression method that relaxes parametric assumptions, handles measurement errors, and provides asymptotic properties, advancing longitudinal data analysis.

Findings

Method is validated through extensive simulations.

Application uncovers meaningful scientific insights.

Framework demonstrates robustness and practical utility.

Abstract

Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice. In this work, we develop a trajectory quantile regression framework that is designed to robustly and flexibly investigate how latent individual trajectory features are related to observed subject characteristics. The proposed models are built under modeling with usual parametric assumptions lifted or relaxed. We derive our estimation procedure by novelly transforming the problem at hand to quantile regression with perturbed responses and adapting the bias correction technique for handling covariate measurement errors. We establish desirable asymptotic properties of the proposed estimator, including uniform consistency and weak convergence. Extensive simulation studies confirm the validity of the proposed method as well as its robustness. An application to the DURABLE trial uncovers sensible scientific findings and illustrates the practical value of our proposals.