A joint latent class model of longitudinal and survival data with a time-varying membership probability

Joint latent class modelling has been developed considerably in the past two decades. In some instances, the models are linked by the latent class k (i.e. the number of subgroups), in others they are joined by shared random effects or a heterogeneous random covariance matrix. We propose an extension to the joint latent class model (JLCM) in which probabilities of subjects being in latent class k can be set to vary with time. This can be a more flexible way to analyse the effect of treatments to patients. For example, a patient may be in period I at the first visit time and may move to period II at the second visit time, implying the treatment the patient had before might be noneffective at the following visit time. For a dataset with these particular features, the joint latent class model which allows jumps among different subgroups can potentially provide more information as well as more accurate estimation and prediction results compared to the basic JLCM. A Bayesian approach is used to do the estimation and a DIC criterion is used to decide the optimal number of classes. Simulation results indicate that the proposed model produces accurate results and the time-varying JLCM outperforms the basic JLCM. We also illustrate the performance of our proposed JLCM on the aids data (Goldman et al., 1996).