Inferences for joint modelling of repeated ordinal scores and time to event data

In clinical trials and other follow-up studies, it is natural that a response variable is repeatedly measured during follow-up and the occurrence of some key event is also monitored. There has been a considerable study on the joint modelling these measures together with information on covariates. But most of the studies are related to continuous outcomes. In many situations instead of observing continuous outcomes, repeated ordinal outcomes are recorded over time. The joint modelling of such serial outcomes and the time to event data then becomes a bit complicated. In this article we have attempted to analyse such models through a latent variable model. In view of the longitudinal variation on the ordinal outcome measure, it is desirable to account for the dependence between ordered categorical responses and survival time for different causes due to unobserved factors. A flexible Monte Carlo EM (MCEM) method based on exact likelihood is proposed that can simultaneously handle the longitudinal ordinal data and also the censored time to event data. A computationally more efficient MCEM method based on approximation of the likelihood is also proposed. The method is applied to a number of ordinal scores and survival data from trials of a treatment for children suffering from Duchenne Muscular Dystrophy. Finally, a simulation study is conducted to examine the finite sample properties of the proposed estimators in the joint model under two different methods.