New challenges and methods for the analysis of longitudinal and survival data

纵向研究在实践中得到了广泛的应用，特别是在与健康相关的研究中。在纵向研究中，我们在一段时间内反复收集一组变量的数据，我们经常对变量的值如何随时间变化感兴趣。此外，我们还可能观察到某些感兴趣的事件，如辍学和疾病感染。在许多研究中，纵向轨迹和事件发生的时间是相关联的，因此一些纵向变量可能被用作感兴趣事件的潜在标记。例如，在艾滋病毒/艾滋病研究中*，CD4和病毒载量数据通常是随时间收集的*，它们的纵向轨迹可能与患艾滋病或死亡的时间有关。在肺癌研究中，浸润前病变的历史和进展可能与肺癌的发生有关。在这些研究中，重要的是在早期阶段发现疾病，因此一个主要目标是确定进展为艾滋病或癌症的标志物或风险预测因素。为了对这些数据进行统计分析，需要纵向数据和生存数据的联合模型，以获得无偏的结果。**近年来，文献对纵向和生存数据的联合模型进行了广泛的研究。然而，由于许多纵向研究中纵向和生存数据的复杂性，统计分析在实践中不断出现新的挑战。在这些情况下，现有的统计模型和方法不能使用或不可取。例如，(i)*感兴趣的变量可以是离散型、连续型或其他混合型；（ii）纵向数据可能被删减，例如，病毒载量可能低于艾滋病*研究中的检测极限，或者可能是半连续的；（iii）纵向数据可能包含测量误差、缺失数据和异常值；*(iv)模型参数可能受到生物学规律的约束；(v)既可能存在空间依赖性，也可能存在纵向依赖性；并且(vi)*统计推断中的计算可能相当具有挑战性。因此，需要开发新的或更好的统计模型和方法来解决这些问题。在本提案中，我们以当前的几个HIV/AIDS数据集和癌症数据集为动力，提出开发一系列新的联合模型和方法来解决上述问题。这些新模型和方法一旦开发出来，可能会对艾滋病和癌症研究产生重要影响，因为它们可能会带来基于现有模型和方法无法获得的新见解和新发现。＊＊＊

Longitudinal studies are widely used in practice, especially in health related research. In a longitudinal *study, we collect data on a set of variables repeatedly over time, *and we are often interested in how the values of the variables change over time. *In addition, we may also observe certain events of interest, *such as dropouts and infection of a disease.*In many studies, the longitudinal trajectories and the times to *the events are associated, so some longitudinal variables may be used as *potential markers for the events of interest. For example, *in HIV/AIDS studies, CD4 and viral load data are usually collected over time, *and their longitudinal trajectories may be associated with times to AIDS or deaths. *In lung cancer studies, the histories and progressions of pre-invasive lesions may be associated *with occurrences of lung cancer. In these studies, it is important to detect the disease in early *stages, so a major goal is to identify markers or risk predictors for progression *to AIDS or cancer. For statistical analyses of these data, *joint models of longitudinal and survival data are required in order to obtain *unbiased results. ** There has been extensive research in the literature for *joint models of longitudinal and survival data in recent years. However, *new challenges in statistical analysis continue to arise in practice, due to*the complexity of longitudinal and survival data in many longitudinal studies. *In these cases, existing statistical models and methods cannot be used or undesirable. For example, (i)*the variables of interest may be discrete or continuous or other mixed types; (ii) the longitudinal data may be censored, e.g., viral load may drop below a limit of detection in AIDS*studies, or may be semi-continuous; (iii) the longitudinal data may contain measurement errors, missing data, and outliers;*(iv) the model parameters may be constrained by biological laws; (v) there may be spatial dependence as well as longitudinal dependence; and (vi)*the computation in statistical inference can be quite challenging. *Thus, new or better statistical models and methods need to be developed to address these issues. In this proposal, motivated by several*current HIV/AIDS datasets and cancer datasets, we propose to develop a series of new joint models and methods to *address the foregoing issues. Once developed, these new models and methods may have important*impacts in AIDS and cancer research, since they may lead to new insights and findings which are unavailable based on existing models and methods. ***