Some new models and methods for complex longitudinal and survival data

纵向研究在实践中得到了广泛应用。它们使研究人员能够调查关键变量的值如何随时间变化，以及这些变化是否与感兴趣的事件(如感染疾病)有关。例如，研究人员可能有兴趣研究CD_4细胞计数的下降是否可能与艾滋病毒感染的风险有关，或者不同国家的新冠肺炎日计数的增加是否可能与死亡风险的增加有关。这里，随着时间的推移重复测量CD_4或新冠肺炎每日计数是纵向数据，而感染时间或死亡时间是生存数据。复杂的纵向数据和生存数据的统计分析可能极具挑战性，因为i)关键变量的纵向轨迹可能因个人而异，这些变化可能因个人而异并随时间变化；ii)数据中可能存在离群值、测量误差、审查和缺失值，从而现有的统计方法可能不可靠；iii)两阶段研究可能是必要的，其中第二阶段可能涉及不等概率抽样和更频繁的重复测量；以及iv)与复杂模型的统计推断相关的计算可能非常具有挑战性。尽管在纵向数据和生存数据的分析方面已经有了广泛的研究，但由于许多新的纵向研究和数据集的复杂性，仍有许多问题有待解决，并出现了新的具有挑战性的问题。这些提出的新模型和方法有望在艾滋病毒/艾滋病研究和新冠肺炎研究等许多领域做出重大贡献，因为它们可能会产生基于现有模型和方法可能无法获得的新发现。例如，拟议的新方法可能使我们能够比现有方法更好地评估抗艾滋病毒治疗。所提出的新模型和方法是相当普遍的，因为它们可以用来分析各种各样的纵向数据或聚集数据，因此它们有望在许多领域产生重要影响。

Longitudinal studies are widely used in practice. They allow researchers to investigate how the values of key variables change over time and if these changes may be associated with events of interest such as infection of a disease. For example, researchers may be interested in studying if the declines in CD4 counts may be associated with the risk of HIV infection, or if the increases of Covid-19 daily counts in different countries may be associated with increases in the risk of death. Here, the repeated measurements of CD4 or Covid-19 daily counts over time are longitudinal data, while the time-to-infection or time-to-death are survival data. Statistical analyses of complex longitudinal data and survival data can be highly challenging, since i) longitudinal trajectories of key variables may vary substantially across individuals and these variations may be individual-specific and change over time; ii) there may be outliers, measurement errors, censoring, and missing values in the data so that existing statistical methods may be unreliable; iii) two-phase studies may be necessary where the second phase may involve unequal probability sampling and more frequent repeated measurements; and iv) computations associated with statistical inference for complex models can be highly challenging. Although there has been extensive research in the analyses of longitudinal data and survival data, many issues remain to be addressed and new challenging issues emerge, due to the complexities of many new longitudinal studies and datasets.         We propose to develop some innovative statistical models and methods to address some of the foregoing issues. These proposed new models and methods are expected to make significant contributions in many fields, such as HIV/AIDS research and Covid-19 research, because they may lead to new findings which may be unavailable based on existing models and methods. For example, the proposed new methods may allow us to better evaluate anti-HIV treatments than existing ones. The proposed new models and methods are quite general in the sense that they can be used to analyse a wide variety of longitudinal data or clustered data, and thus they are expected to make important impacts in many fields.