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，我们通常对变量的值如何随时间变化感兴趣。此外，我们还可以观察到某些感兴趣的事件，如辍学和疾病感染。在许多研究中，事件的纵向轨迹和时间是相关的，因此一些纵向变量可以作为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着时间的推移收集的，它们的纵向轨迹可能与艾滋病或死亡的时间有关。在肺癌研究中，侵袭前病变的病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才能得到无偏的结果。

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.