Alsefri Maha, Sudell Maria, García-Fiñana Marta, Kolamunnage-Dona Ruwanthi
Department of Health Data Science, Institute of Population Health, University of Liverpool, L69 3GL, Liverpool, UK.
Department of Statistics, University of Jeddah, Jeddah, Saudi Arabia.
BMC Med Res Methodol. 2020 Apr 26;20(1):94. doi: 10.1186/s12874-020-00976-2.
In clinical research, there is an increasing interest in joint modelling of longitudinal and time-to-event data, since it reduces bias in parameter estimation and increases the efficiency of statistical inference. Inference and prediction from frequentist approaches of joint models have been extensively reviewed, and due to the recent popularity of data-driven Bayesian approaches, a review on current Bayesian estimation of joint model is useful to draw recommendations for future researches.
We have undertaken a comprehensive review on Bayesian univariate and multivariate joint models. We focused on type of outcomes, model assumptions, association structure, estimation algorithm, dynamic prediction and software implementation.
A total of 89 articles have been identified, consisting of 75 methodological and 14 applied articles. The most common approach to model the longitudinal and time-to-event outcomes jointly included linear mixed effect models with proportional hazards. A random effect association structure was generally used for linking the two sub-models. Markov Chain Monte Carlo (MCMC) algorithms were commonly used (93% articles) to estimate the model parameters. Only six articles were primarily focused on dynamic predictions for longitudinal or event-time outcomes.
Methodologies for a wide variety of data types have been proposed; however the research is limited if the association between the two outcomes changes over time, and there is also lack of methods to determine the association structure in the absence of clinical background knowledge. Joint modelling has been proved to be beneficial in producing more accurate dynamic prediction; however, there is a lack of sufficient tools to validate the prediction.
在临床研究中，对纵向数据和事件发生时间数据进行联合建模的兴趣日益浓厚，因为它可以减少参数估计中的偏差并提高统计推断的效率。关于联合模型的频率主义方法的推断和预测已经得到了广泛的综述，由于数据驱动的贝叶斯方法最近很流行，对当前联合模型的贝叶斯估计进行综述有助于为未来的研究提出建议。
我们对贝叶斯单变量和多变量联合模型进行了全面综述。我们关注结果类型、模型假设、关联结构、估计算法、动态预测和软件实现。
共识别出89篇文章，其中75篇为方法学文章，14篇为应用文章。联合对纵向和事件发生时间结果进行建模的最常见方法包括具有比例风险的线性混合效应模型。通常使用随机效应关联结构来连接两个子模型。马尔可夫链蒙特卡罗（MCMC）算法常用于（93%的文章）估计模型参数。只有六篇文章主要关注纵向或事件时间结果的动态预测。
已经提出了针对多种数据类型的方法；然而，如果两个结果之间的关联随时间变化，研究就会受到限制，而且在缺乏临床背景知识的情况下，也缺乏确定关联结构的方法。联合建模已被证明有助于产生更准确的动态预测；然而，缺乏足够的工具来验证预测。
