Quasi-Monte Carlo (QMC) methods using quasi-random sequences, as opposed to pseudo-random samples, are proposed for use in the joint modelling of time-to-event and multivariate longitudinal data. The QMC integration framework extends the Monte Carlo Expectation Maximisation approaches that are commonly adopted, namely using ordinary and antithetic variates. The motivation of QMC integration is to increase the convergence speed by using nodes that are scattered more uniformly. Through simulation, estimates and computational times are compared and this is followed with an application to a clinical dataset. There is a distinct speed advantage in using QMC methods for small sample sizes and QMC is comparable to the antithetic MC method for moderate sample sizes. The new method is available in an updated version of the R package joineRML.

中文翻译：

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对事件时间和多变量纵向数据的联合模型进行更快的蒙特卡罗估计

使用准随机序列而不是伪随机样本的准蒙特卡罗 (QMC) 方法被提议用于时间到事件和多变量纵向数据的联合建模。QMC 集成框架扩展了常用的蒙特卡罗期望最大化方法，即使用普通变量和对立变量。QMC 集成的动机是通过使用分散更均匀的节点来提高收敛速度。通过模拟，比较估计和计算时间，然后应用到临床数据集。对于小样本量使用 QMC 方法有明显的速度优势，并且 QMC 与中等样本量的对立 MC 方法相当。新方法在 R 包 joineRML 的更新版本中可用。