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).

翻译：联合潜在类别建模在过去二十年中得到了显著发展。在某些情况下，模型通过潜在类别k（即子组数量）进行连接，而在其他情况下，则通过共享随机效应或异质随机协方差矩阵进行连接。我们提出对联合潜在类别模型（JLCM）进行扩展，使得个体属于潜在类别k的概率可以随时间变化。这为分析治疗对患者的影响提供了一种更灵活的方式。例如，患者可能在首次就诊时处于I期，而在第二次就诊时进入II期，这意味着患者之前接受的治疗可能在后续就诊时无效。对于具有这些特定特征的数据集，与基本JLCM相比，允许在不同子组间跳跃的联合潜在类别模型能够提供更多信息，以及更准确的估计和预测结果。采用贝叶斯方法进行估计，并使用DIC准则确定最优类别数量。模拟结果表明，所提出的模型能够产生准确结果，且时变JLCM优于基本JLCM。我们还通过艾滋病数据（Goldman et al., 1996）展示了所提出的JLCM的性能。