Patients with psoriatic arthritis are at risk of developing serious joint damage over the course of their disease. Estimation of the distribution of time to damage has received relatively little attention to date, in part because the times to damage are typically interval-censored, and because statistical methods must account for the association in rates of damage within patients. We consider data from a clinic of patients with psoriatic arthritis, in which patients make periodic clinic visits at which 64 joints are assessed for damage. To model the hazard of joint damage, identify risk factors, and address the correlation in damage rates within patients, proportional hazards regression models are fit for each patient, conditional on multivariate random effect. Specific components of the random effects accommodate association for joints of a particular type, and the correlations between joints of different types are addressed through the covariances of the random effects. The model is fit using a Bayesian approach implemented using an MCMC algorithm. Application to the data from the motivating psoriatic arthritis clinic yields clinical insight into the rates of progression and risk factors.

clustered failure time data, interval censoring, Markov Chain Monte Carlo, multivariate random effect, random effects model.