A Gaussian copula joint model for longitudinal and time-to-event data with random effects

Longitudinal and survival sub-models are two building blocks for joint modelling of longitudinal and time-to-event data. Extensive research indicates separate analysis of these two processes could result in biased outputs due to their associations. Conditional independence between measurements of biomarkers and event time process given latent classes or random effects is a conventional approach for characterising the association between the two sub-models while taking the heterogeneity among the population into account. However, this assumption is difficult to validate because of the unobservable latent variables. Thus a Gaussian copula joint model with random effects is proposed to accommodate the scenarios where the conditional independence assumption is questionable. The conventional joint model assuming conditional independence is a special case of the proposed model when the association parameters in the Gaussian copula shrink to zero. Simulation studies and real data application are carried out to evaluate the performance of the proposed model with different correlation structures. In addition, personalised dynamic predictions of survival probabilities are obtained based on the proposed model and comparisons are made to the predictions obtained under the conventional joint model.