Based on the proposed time-varying JLCM (Miao and Charalambous, 2022), the heterogeneous random covariance matrix can also be considered, and a regression submodel for the variance-covariance matrix of the multivariate latent random effects can be added to the joint latent class model. A general joint latent class model with heterogeneous random-effects modelling is a natural extension of the time-varying JLCM, which consists of the linear and the log link functions to model the covariance matrices as the variance-covariance regression submodel based on the modified Cholesky decomposition, longitudinal submodel, survival submodel as well as the membership probability. It can help to get more information from the random covariance matrix through the regression submodel and get unbiased estimates for all parameters by modelling the variance-covariance matrix. By adding the regression model, the homogeneous random effects assumption can be tested and the issue of high-dimensional heterogeneous random effects can be easily solved. The Bayesian approach will be used to estimate the data. DIC value is the criterion for deciding the optimal k value. We illustrate our general JLCM on a real data set of AIDS study and we are interested in the prospective accuracy of our proposed JLCM as well as doing the dynamic predictions for time-to-death in the joint model using the longitudinal CD4 cell count measurements.

翻译：基于所提出的时变联合潜类别模型（Miao与Charalambous，2022），可进一步考虑异质性随机协方差矩阵，并在联合潜类别模型中增加针对多元潜随机效应方差-协方差矩阵的回归子模型。具有异质性随机效应建模的通用联合潜类别模型是时变联合潜类别模型的自然扩展，其包含基于修正Cholesky分解的方差-协方差回归子模型（采用线性与对数连接函数建模协方差矩阵）、纵向子模型、生存子模型以及类别隶属概率。通过回归子模型可从随机协方差矩阵中获取更多信息，且通过对方差-协方差矩阵建模可获得所有参数的无偏估计。通过引入该回归模型，可检验随机效应同质性假设，并能有效处理高维异质性随机效应问题。本研究将采用贝叶斯方法进行数据估计，以DIC值作为确定最优k值的判据。我们通过艾滋病研究的真实数据集验证所提出的通用联合潜类别模型，重点关注该模型的前瞻性预测准确性，并基于纵向CD4细胞计数测量数据对联合模型中的死亡时间进行动态预测。