  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).
