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。 在这个建议中，我们计划在未来5年内进行以下研究：(1)提出和评估各种联合模型的计算效率更高的近似方法，例如基于一阶和高阶拉普拉斯近似和泰勒近似的方法，在有和没有缺失数据和测量误差的情况下；(2)对联合模型的各种推断方法进行深入的比较，包括蒙特卡洛EM方法、数值积分方法、两步方法及其修改、Bootstrap方法和近似方法，使用经验和理论方法；(3)研究近似估计的渐近性能；(4)同时处理联合模型中的缺失数据、测量误差和离群值；(5)开发用户友好的软件。鉴于联合建模方法的重要性和普及性，由于上述问题一直是该领域的主要问题，因此拟议的研究有望对这一重要领域做出重大贡献。

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. In this proposal, we plan the following research for the next 5 years: (1) propose and evaluate computationally more efficient approximate methods for various joint models, such as those based on first and higher order Laplace approximations and Taylor approximations, with and without missing data and measurement errors; (2) make thorough comparisons of various inference methods for joint models, including Monte Carlo EM methods, numerical integration methods, two-step methods and their modifications, bootstrap methods, and approximate methods, using empirical and theoretical methods; (3) study the asymptotic performances of the approximate estimates; (4) address missing data, measurement errors, and outliers in joint models simultaneously; (5) develop user-friendly software. Given the importance and popularity of joint modelling methods, the proposed research is expected to make a significant contribution to this important field since the above problems have been major issues in this field.