Zhang Zili, Charalambous Christiana, Foster Peter
Department of Mathematics, University of Manchester, Manchester, UK.
J Appl Stat. 2022 Jun 2;50(13):2739-2759. doi: 10.1080/02664763.2022.2081965. eCollection 2023.
Joint modelling of longitudinal and time-to-event data is usually described by a joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of the two processes can be derived straightforwardly by assuming conditional independence given the random effects. Alternative approaches to induce interdependency into sub-models have also been considered in the literature and one such approach is using copulas to introduce non-linear correlation between the marginal distributions of the longitudinal and time-to-event processes. The multivariate Gaussian copula joint model has been proposed in the literature to fit joint data by applying a Monte Carlo expectation-maximisation algorithm. In this paper, we propose an exact likelihood estimation approach to replace the more computationally expensive Monte Carlo expectation-maximisation algorithm and we consider results based on using both the multivariate Gaussian and copula functions. We also provide a straightforward way to compute dynamic predictions of survival probabilities, showing that our proposed model is comparable in prediction performance to the shared random effects joint model.
纵向数据和事件发生时间数据的联合建模通常由一个联合模型来描述，该模型使用共享或相关的潜在效应来捕捉两个过程之间的关联。在此框架下，通过假设给定随机效应时的条件独立性，可以直接推导出两个过程的联合分布。文献中也考虑了将相依性引入子模型的替代方法，其中一种方法是使用copula函数在纵向过程和事件发生时间过程的边缘分布之间引入非线性相关性。文献中提出了多元高斯copula联合模型，通过应用蒙特卡罗期望最大化算法来拟合联合数据。在本文中，我们提出了一种精确似然估计方法来替代计算成本更高的蒙特卡罗期望最大化算法，并考虑基于使用多元高斯和copula函数的结果。我们还提供了一种直接的方法来计算生存概率的动态预测，表明我们提出的模型在预测性能上与共享随机效应联合模型相当。
