  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.
