Complex Longitudinal Data with Changepoints, Informative Dropouts, Measurement Errors, and Time-to-events

纵向研究涉及对同一个体随时间的重复观察。这类研究通常在健康科学、生物化学、流行病学、工业、经济学和社会学领域进行，通常被称为小组研究。例如，在艾滋病毒研究中，每个病人的病毒载量都是随着时间的推移而反复测量的;银行记录了客户随着时间的推移而进行的交易。混合效应模型在纵向研究中得到了广泛的应用，许多统计软件如R/Splus、SAS等都可以通过默认函数进行混合效应分析。然而，这些模型以及默认函数仅适用于“完整”数据，即，无缺失和删失数据，无测量误差，无变化点。大量的研究表明，在统计分析中忽略上述任何一个或多个问题都可能导致严重的偏倚或误导性结果。此外，在许多纵向研究中，存在个体特异性的事件发生时间过程，例如死亡时间。在纵向过程和事件发生时间过程之间经常存在关联。因此，这两个过程的联合建模优于单独建模。在数据不完整的情况下，许多科学家和统计学家经常因现有统计方法和相关计算工具的局限性而感到沮丧。

Longitudinal studies involve repeated observations of the same individual over time. Such studies are commonly conducted in health sciences, biochemistry, epidemiology, industry, economics and sociology where they are often called panel studies. For example, in HIV studies, the viral load of each patient is measured repeatedly over time; the banks record the transactions of clients over time. Mixed-effects models have been widely applied in longitudinal studies and can be conducted by the default functions in many statistical softwares, such as R/Splus and SAS. However, these models as well as the default functions are feasible only to "complete" data, i.e., no missing and censored data, no measurement errors, and no changepoints. Extensive research has demonstrated that ignoring any one or more of above problems in statistical analyses may lead to severely biased or misleading results. Moreover, in many longitudinal studies, there exists an individual-specific time-to-event process such as time to death. There is often association between the longitudinal and the time-to-event processes. Therefore, joint modeling for these two processes is preferable to separate modeling. With the incomplete data, many scientists and statisticians are often frustrated by the limitations of the existing statistical methods and the relevant computing tools.