Methods for analyzing nonstandard longitudinal datasets

纵向数据分析是生物统计学中一个重要的，现在研究得很好的课题，有几个优秀的文本提供了关于这个课题的各种观点。然而，我们希望在目前的建议中强调三个主题，它们既不是这些文本的重点，也不是生物统计学和统计文献的重点。第一个是纵向数据的建模，当响应和任何时间相关的协变量(s)不是在同一时间点测量时。平滑步骤是必需的，我们将重点放在分箱方法来处理这种非典型数据结构，并允许使用传统的混合效果模型进行纵向建模。第二个主题是当纵向反应是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是前瞻性测量，即当生存过程的时钟开始时。对于这种类型的数据，有许多问题需要解决，特别是当研究参与者之间的回顾性数据量不同时，关于估计偏差的问题。第三个主题侧重于为纵向数据实现一个灵活的模型，该模型随时间从增加到减少的轨迹逐渐变化（反之亦然）。我们面临的挑战是，在不使用大量难以解释的参数过度拟合数据的同时，试图获得一个合理的平均轨迹模型，这种情况可能会出现在基于非参数曲线的方法中。我们讨论了混合效应的斜拉索回归模型，以实现这种通常令人满意的折衷。该模型还将允许我们解释轨迹中的主体间异质性，包括变化发生的位置。HQP（研究生）将在本提案中尝试解决所有这三个主题。

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.