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

纵向研究包括随着时间的推移对同一个人进行重复观察。此类研究通常在健康科学、生物化学、流行病学、工业、经济学和社会学中进行，在这些领域中，它们通常被称为小组研究。例如，在艾滋病毒研究中，每个患者的病毒载量都会随着时间的推移而重复测量；银行会记录客户随着时间的推移进行的交易。混合效应模型在纵向研究中得到了广泛的应用，可以通过R/sPlus、SAS等统计软件的默认功能进行。然而，这些模型以及默认函数只适用于“完整”数据，即没有缺失和删失的数据，没有测量误差，也没有变点。广泛的研究表明，在统计分析中忽视上述任何一个或多个问题都可能导致严重的偏见或误导性结果。此外，在许多纵向研究中，存在个体特定的事件发生时间过程，例如死亡时间。纵向流程和事件发生时间流程之间往往存在关联。因此，这两个过程的联合建模比单独建模更可取。在数据不完整的情况下，许多科学家和统计学家经常对现有统计方法和相关计算工具的局限性感到沮丧。 我的研究兴趣是针对事件间隔时间数据和具有不完全特征的长期纵向数据提出创新的统计方法以及相应的计算实现。如果开发出来，这些新的统计方法和软件包可以对纵向研究做出重大贡献。典型的方法包括基于随机或蒙特卡罗EM算法的“精确”似然推断，以及基于观测数据似然的一阶或更高阶泰勒/拉普拉斯近似的计算效率更高的近似方法。

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. My research interests aim at the proposal of innovative statistical methods for time-to-event data and long-term longitudinal data with some incomplete features as well as the corresponding computational implement. If developed, these novel statistical methods and software packages can make significant contributions to longitudinal studies. The typical proposed approaches include "exact" likelihood inferences based on stochastic or Monte-Carlo EM algorithms and computationally more efficient approximate methods based on first- or higher-order Taylor/Laplace approximations to the observed-data likelihoods.