Methods for analyzing nonstandard longitudinal datasets

纵向数据分析是生物统计学中一个重要且现在研究得很好的主题，有几篇优秀的文本提供了关于这一主题的各种观点。然而，我们希望在目前的提案中强调三个主题，它们既不是这些文本的重点的一部分，也不是生物统计和统计文献的一部分。第一种是纵向数据的建模，当响应和任何随时间变化的协变量(S)没有在同一时间点测量时。需要一个平滑步骤，我们将重点介绍一种装箱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果模型进行纵向建模。第二个主题是纵向和生存数据的联合建模，当纵向响应被回顾和前瞻性地测量时，而典型的安排是只前瞻性地测量纵向响应，即，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，特别是在研究参与者之间回溯数据量不同时的估计偏差。第三个主题集中于为纵向数据实现灵活的模型，这些数据显示出随着时间的推移从增加到减少(或相反)的逐渐变化。挑战是试图获得平均轨迹的合理现实模型，同时不用大量难以解释的参数来过度拟合数据，这可能会发生在基于非参数曲线的方法中。我们讨论了混合效应弯曲电缆回归模型来实现这一通常令人满意的折衷。这个模型还将使我们能够考虑到研究对象之间在轨迹上的异质性，包括变化发生在哪里。HQP(研究生)将积极参与本提案中所有这三个主题的讨论。

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.