Monitoring of individual biomarkers has the potential of explaining the hazard of survival outcomes. In practice, these measurements are intermittently observed and are known to be subject to substantial measurement error. Joint modelling of longitudinal and survival data enables us to associate intermittently measured error-prone biomarkers with risks of survival outcomes and thus plays an important role in the analysis of medical data. Most of the joint models available in the literature have been built on the Gaussian assumption. This makes them sensitive to outliers. In this work, we study a range of robust models to address this issue. Of particular interest is the common occurrence in medical data that outliers can occur with different frequencies over time, for example, in the period when patients adjust to treatment changes. Motivated by the analysis of data gathered from patients with primary biliary cirrhosis, a new model with a time-varying robustness is introduced. Through both the motivating example and a simulation study, this research not only stresses the need to account for longitudinal outliers in the analysis of medical data and in joint modelling research but also highlights the bias and inefficiency from not properly estimating the degrees-of-freedom parameter. This work presents a number of methods in addition to the time-varying robustness, and each method can be fitted using the R package robjm.

中文翻译：

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纵向和生存数据的稳健联合建模：结合时变自由度参数

对个体生物标志物的监测有可能解释生存结果的风险。在实践中，这些测量是间歇性观察的，并且已知会受到很大的测量误差。纵向和生存数据的联合建模使我们能够将间歇性测量的容易出错的生物标志物与生存结果的风险联系起来，从而在医学数据分析中发挥重要作用。文献中可用的大多数联合模型都是建立在高斯假设之上的。这使他们对异常值敏感。在这项工作中，我们研究了一系列稳健的模型来解决这个问题。特别令人感兴趣的是医学数据中经常出现异常值随着时间的推移以不同的频率出现，例如，在患者适应治疗变化的时期。在分析从原发性胆汁性肝硬化患者收集的数据的启发下，引入了一种具有时变稳健性的新模型。通过激励示例和模拟研究，本研究不仅强调了在医学数据分析和联合建模研究中考虑纵向异常值的必要性，而且强调了未正确估计自由度的偏差和低效率范围。除了时变鲁棒性之外，这项工作还提出了许多方法，并且每种方法都可以使用 这项研究不仅强调了在医学数据分析和联合建模研究中考虑纵向异常值的必要性，而且还强调了由于未正确估计自由度参数而导致的偏差和低效率。除了时变鲁棒性之外，这项工作还提出了许多方法，并且每种方法都可以使用 这项研究不仅强调了在医学数据分析和联合建模研究中考虑纵向异常值的必要性，而且还强调了由于未正确估计自由度参数而导致的偏差和低效率。除了时变鲁棒性之外，这项工作还提出了许多方法，并且每种方法都可以使用R包robjm。