A joint modelling approach for multistate processes subject to resolution and under intermittent observations.

ABSTRACT

Multistate processes provide a convenient framework when interest lies in characterising the transition intensities between a set of defined states. If, however, there is an unobserved event of interest (not known if and when the event occurs), which when it occurs stops future transitions in the multistate process from occurring, then drawing inference from the joint multistate and event process can be problematic. In health studies, a particular example of this could be resolution, where a resolved patient can no longer experience any further symptoms, and this is explored here for illustration. A multistate model that includes the state space of the original multistate process but partitions the state representing absent symptoms into a latent absorbing resolved state and a temporary transient state of absent symptoms is proposed. The expanded state space explicitly distinguishes between resolved and temporary spells of absent symptoms through disjoint states and allows the uncertainty of not knowing if resolution has occurred to be easily captured when constructing the likelihood; observations of absent symptoms can be considered to be temporary or having resulted from resolution. The proposed methodology is illustrated on a psoriatic arthritis data set where the outcome of interest is a set of intermittently observed disability scores. Estimated probabilities of resolving are also obtained from the model. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.