Joint models for longitudinal and survival data with measurement errors, missing values, and outliers

近年来，纵向数据和生存数据的联合建模在文献中受到了极大的关注。与通常使用的朴素方法相比，这些联合建模方法可以产生更高效、更少偏差和更稳健的参数估计。混合效应模型通常用于联合模型中，其中纵向模型和生存模型通过共享的随机效应联系在一起。似然法是联合模型估计和推断的标准方法。联合模型的估计和推断的主要挑战是：i)计算可能非常苛刻，因为可能性涉及高维和难以处理的积分。Ii)数据缺失、测量误差和离群值在纵向研究中非常常见，这给计算带来了更大的困难；iii)没有界面友好的软件，这一直是应用统计学家和其他研究人员在实践中使用联合模型的主要障碍。

Joint modelling of longitudinal data and survival data has received great attention in the literature in recent years. Compared with commonly used naive approaches, these joint modelling methods can produce more efficient, less biased, and more robust parameter estimates. Mixed effects models are commonly used in the joint models where the longitudinal model and the survival model are linked through shared random effects. The likelihood method is a standard approach for estimation and inference for joint models. The major challenges for estimation and inference for joint models are: i) computation can be extremely demanding, because the likelihoods involve high-dimensional and intractable integrals. ii) missing data, measurement errors, and outliers are very common in longitudinal studies, and they lead to much greater difficulties in the computation; iii) user-friendly software is unavailable, which has been a major obstacle for applied statisticians and other researchers to use joint model in practise.