Methods for analyzing nonstandard longitudinal datasets

纵向数据分析是生物统计学中的一个重要课题，现在已经得到了很好的研究，有几篇优秀的文章提供了关于这个问题的各种观点。 然而，我们希望在本提案中强调三个主题，这些主题既不是这些案文的重点，也不是生物统计和统计文献的重点。 第一种是当响应和任何时间依赖性协变量未在相同时间点测量时的纵向数据建模。 需要一个平滑步骤，我们将专注于一个binning方法来处理这种非典型的数据结构，并允许使用传统的混合效应模型进行纵向建模。 第二个主题是当纵向反应被回顾性和前瞻性测量时纵向和生存数据的联合建模，而典型的安排是纵向反应仅被前瞻性测量，即，当生存过程的时钟开始时。 这种类型的数据需要解决一些问题，特别是当研究参与者之间的回顾性数据量不同时，估计偏差。 第三个主题侧重于为纵向数据实现一个灵活的模型，这些数据显示出随着时间的推移从增加到减少的轨迹（反之亦然）的逐渐变化。 挑战在于尝试获得平均轨迹的合理现实模型，同时不过度拟合具有大量难以解释的参数的数据，这可能发生在基于非参数曲线的方法中。 我们讨论的混合效应弯曲电缆回归模型，以实现这一往往令人满意的妥协。 该模型还将使我们能够解释轨迹中的受试者间异质性，包括变化发生的位置。 HQP（研究生）将积极参与试图解决所有这三个主题在这个建议。

Longitudinal data analysis is an important and now well-studied subject in biostatistics with several excellent texts providing various viewpoints on the subject. However, there are three topics that we wish to emphasize in the current proposal and which are neither part of the focus of these texts nor of the biostatistical and statistical literature. The first is the modeling of longitudinal data when the response and any time-dependent covariate(s) are not measured at the same time points. A smoothing step is required, and we will focus upon a binning approach to handle this atypical data structure and allow for longitudinal modeling using traditional mixed effects models. The second topic is joint modeling of longitudinal and survival data when the longitudinal response is measured both retrospectively and prospectively, whereas the typical arrangement is that the longitudinal response is measured only prospectively, i.e., when the start of the clock of the survival process begins. A number of issues need to be addressed with this type of data, especially as regard to estimation bias when the amount of retrospective data differs between study participants. The third topic focuses on implementing a flexible model for longitudinal data that exhibit a gradual change from an increasing to decreasing trajectory over time (or vice versa). The challenge is to try to obtain a reasonably realistic model for the mean trajectory while not overfitting the data with a high number of difficult to interpret parameters, something that may occur with a nonparametric curve-based approach. We discuss the mixed-effects bent cable regression model to achieve this often satisfying compromise. This model will also allow us to account for between-subject heterogeneity in the trajectories including where the changes occur. HQP (graduate students) will be heavily involved in attempting to address all three of these topics in this proposal.