Innovative Analytical Methods for Repeated Measures in the OHTS Study

在眼科学研究中，经常会遇到交叉或纵向数据。自然，左和右 同一对象的眼睛是成对的和依赖的。此外，在纵向眼科研究中， 对同一主题的衡量往往是相互关联的。这些相关性（或 通常用两种统计模型描述：固定效应模型和随机效应模型 模型然而，这两种方法都有其局限性。为了在准确性和精确性之间取得适当的平衡 和效率，我们提出了一种新的方法之间的固定效应和随机效应模型，假设 每个受试者的异质性属于不同的群体。通过惩罚聚变效应（ 两个特定对象效应之间的差异），我们自动将特定对象效应分组， 提前知道受试者的组成员。因此，我们把我们的方法称为“聚变效应” 模型我们将融合效应模型应用于眼科纵向研究有三个目的：（1） 提出了融合效应模型的估计和推断方法，并应用于连续（线性）， 二元（逻辑）和事件发生时间（考克斯模型）结果;（2）考虑多种融合效应（例如，融合 拦截和融合斜率）和多层次融合效应模型;（3）开发和传播一个用户友好的 统计软件包，使研究人员能够轻松地实施这些方法。 为了说明我们的方法，我们将使用高眼压治疗研究I期和II期（OHTS）， 从1994年到2009年，对1,636名参与者的双眼进行了纵向研究。OHTS 研究具有多类型的结果和多层次的结构，这是一个理想的研究，为拟议的 research.

Clustered or longitudinal data are commonly encountered in ophthalmology studies. Naturally, left and right eyes of the same subject are paired and dependent. Also, in longitudinal ophthalmology studies, the multiple measures on the same subject tend to be correlated. These correlations (or the heterogeneity between different subjects) are usually described by two statistical models: fixed effects models and random effects models. However, both methods have their limitations. To achieve an appropriate balance between accuracy and efficiency, we propose a new approach in between the fixed effects and random effects models, assuming that the heterogeneity for each subject belongs to different groups. By penalizing the fusion effects (the differences between two subject-specific effects), we automatically group the subject-specific effects without knowing the group membership of the subjects in advance. We thus term our method as “fusion effects” models. We have three aims in utilizing the fusion effects model in longitudinal ophthalmology studies: (1) propose the estimation and inference methods for fusion effects models, with application to continuous (linear), binary (logistic), and time-to-event (Cox’s model) outcomes; (2) consider multiple fusion effects (e.g., fusion intercept and fusion slope) and multi-level fusion effects models; (3) develop and disseminate a user-friendly statistical software package that will enable researchers to implement these methods with ease. To illustrate our methods, we will use the Ocular Hypertension Treatment Study Phase I and II (OHTS), a longitudinal study with measures from both eyes of 1,636 participants followed from 1994 to 2009. The OHTS study has multiple types of outcomes and multi-level structure, which is an ideal study for the proposed research.