Trivariate mover-stayer counting process models for investigating joint damage in psoriatic arthritis

In psoriatic arthritis, many patients do not develop permanent joint damage even after a prolonged follow-up. This has led several authors to consider the possibility of a subpopulation of stayers (those who do not have the propensity to experience the event of interest), as opposed to assuming the entire population consist of movers (those who have the propensity to experience the event of interest). In addition, it is recognised that the damaged joints process may act very differently across different joint areas, particularly the hands, feet and large joints. From a clinical perspective, interest lies in identifying possible relationships between the damaged joints processes in these joint areas for the movers and estimating the proportion of stayers in these joint areas, if they exist. For this purpose, this paper proposes a novel trivariate mover-stayer model consisting of mover-stayer truncated negative binomial margins, and patient-level dynamic covariates and random effects in the models for the movers and stayers, respectively. The model is then extended to have a two-level mover-stayer structure for its margins so that the nature of the stayer property can be investigated. A particularly attractive feature of the proposed models is that only an optimisation routine is required in their model fitting procedures. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.