Quantile regression for longitudinal data: unobserved heterogeneity and informative missingness

TL;DR

This paper develops a comprehensive quantile regression model for longitudinal data that accounts for unobserved heterogeneity, informative missingness, and both time-varying and time-constant effects, demonstrated through simulations and real data.

Contribution

It introduces a novel joint model incorporating time-varying and constant random effects and addresses dropout via a pattern mixture approach in quantile regression.

Findings

Model effectively captures heterogeneity in longitudinal responses.

Handles informative missingness due to dropout.

Performs well in simulations and real data applications.

Abstract

Linear quantile regression models aim at providing a detailed and robust picture of the (conditional) response distribution as function of a set of observed covariates. Longitudinal data represent an interesting field of application of such models; due to their peculiar features, they represent a substantial challenge, in that the standard, cross-sectional, model representation needs to be extended for dealing with such kind of data. In fact, repeated observations from the same statistical unit poses a problem of dependence; in a conditional perspective, this dependence could be ascribed to sources of unobserved, individual-specific, heterogeneity. Along these lines, quantile regression models have recently been extended to the analysis of longitudinal, continuous, responses, by modelling dependence via time-constant or time-varying random effects. In this manuscript, we introduce a general quantile regression model for longitudinal, continuous, responses where time-varying and time-constant random parameters are jointly taken into account. A further feature of longitudinal designs is the presence of partially incomplete sequences, due to some individuals leaving the study before its designed end. The missing data process may produce a selection of units which can be informative with respect to the parameters of the longitudinal data model. To deal with the case of irretrievable drop-out, we introduce a pattern mixture version of the linear quantile hidden Markov model, where we account for time-varying heterogeneity and for changes in the fixed effect vector due to differential propensities to stay in the study. The proposed models are illustrated using a well known benchmark dataset on longitudinal dynamics of CD4 cells and by means of a large scale simulation study, entailing different quantiles and both complete and partially complete (ie subject to drop-out) individual sequences.