Joint modelling of longitudinal ordinal and multi-state data

Abstract

Joint modeling of longitudinal and survival data is increasingly used in biomedical studies. However, existing joint models are not applicable to model the longitudinal ordinal responses with non-ignorable missing values caused by the occurrence of events in a multi-state process. In this article, we introduce a joint model for longitudinal ordinal measurements and multi-state data. Our proposed joint model consists of two sub-models: a proportional odds sub-model for longitudinal ordinal measurements and a multi-state sub-model with transition-specific proportional hazards for times of transitions between different health states, both linked by shared random effects. The model parameters were estimated employing the maximum likelihood method for a piecewise constant baseline hazard function. The proposed joint model is evaluated in a simulation study and, as an illustration, it is fitted to real data from people with human immunodeficiency virus.