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

纵向研究在实践中被广泛应用，特别是在健康相关研究中。沿纵向 研究中，我们收集了一组变量的数据，随着时间的推移， 我们经常对变量的值如何随时间变化感兴趣。 此外，我们还可以观察某些感兴趣的事件， 例如辍学和疾病感染。 在许多研究中， 这些事件是相关联的，因此一些纵向变量可以用作 感兴趣的事件的潜在标记。比如说， 在HIV/AIDS研究中，CD 4和病毒载量数据通常是随时间收集的， 并且它们的纵向轨迹可能与艾滋病或死亡的时间相关联。 在肺癌研究中，浸润前病变的病史和进展可能与 与肺癌的发病率有关。在这些研究中，重要的是在早期发现疾病 阶段，因此主要目标是确定进展的标志物或风险预测因子 艾滋病或癌症。对于这些数据的统计分析， 需要纵向和生存数据的联合模型，以便获得 公正的结果。在文献中有广泛的研究， 联合模型的纵向和生存数据近年来。然而，在这方面， 统计分析中的新挑战在实践中不断出现， 许多纵向研究中纵向和生存数据的复杂性。 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的或连续的或其它混合类型;（i i）纵向数据可以被删失，例如，艾滋病病毒载量可能降至检测限以下 （iii）纵向数据可能包含测量误差、缺失数据和离群值; (iv)模型参数可受生物学定律约束;（v）可存在空间依赖性以及纵向依赖性;以及（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。在这一提议中，出于几个方面的考虑， 目前的艾滋病毒/艾滋病数据集和癌症数据集，我们建议开发一系列新的联合模型和方法， 解决上述问题。一旦开发出来，这些新的模型和方法可能具有重要的意义。 这将对艾滋病和癌症研究产生重大影响，因为它们可能导致基于现有模型和方法无法获得的新见解和发现。

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.