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

纵向研究包括在一段时间内对同一个人的反复观察。这些研究通常在健康科学、生物化学、流行病学、工业、经济学和社会学中进行，它们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被反复测量；银行将客户的交易记录下来。混合效应模型在纵向研究中得到了广泛的应用，在R/Splus、SAS等许多统计软件中都可以使用默认函数进行混合效应模型。然而，这些模型和默认功能只适用于“完整”的数据，即没有丢失和删减的数据，没有测量误差，没有变更点。广泛的研究表明，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偏差或误导性的结果。此外，在许多纵向研究中，存在个体特定的时间到事件过程，如死亡时间。纵向流程和时间到事件流程之间经常存在关联。因此，对这两个过程进行联合建模比单独建模更可取。由于数据不完整，许多科学家和统计学家常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.