Modeling repeated self-reported outcome data: a continuous-time longitudinal Item Response Theory model

TL;DR

This paper introduces a continuous-time longitudinal IRT model that handles varying observation times across individuals, enabling detailed analysis of latent health constructs over time.

Contribution

It combines IRT with mixed models to model latent processes in continuous time, accommodating irregular measurement occasions and providing an R package implementation.

Findings

Applied to renal disease data to track depression trajectories.

Demonstrated ability to detect measurement invariance issues.

Enabled assessment of differential item functioning over time.

Abstract

Item Response Theory (IRT) models have received growing interest in health science for analyzing latent constructs such as depression, anxiety, quality of life, or cognitive functioning from the information provided by each individual's items responses. However, in the presence of repeated item measures, IRT methods usually assume that the measurement occasions are made at the exact same time for all patients. In this paper, we show how the IRT methodology can be combined with the mixed model theory to provide a longitudinal IRT model which exploits the information of a measurement scale provided at the item level while simultaneously handling observation times that may vary across individuals and items. The latent construct is a latent process defined in continuous time that is linked to the observed item responses through a measurement model at each individual- and occasion-specific observation time; we focus here on a Graded Response Model for binary and ordinal items. The Maximum Likelihood Estimation procedure of the model is available in the R package lcmm. The proposed approach is contextualized in a clinical example in end-stage renal disease, the PREDIALA study. The objective is to study the trajectories of depressive symptomatology (as measured by 7 items of the Hospital Anxiety and Depression scale) according to the time from registration on the renal transplant waiting list and the renal replacement therapy. We also illustrate how the method can be used to assess Differential Item Functioning and lack of measurement invariance over time.