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.
Repeated measures data are prevalent in ophthalmology studies, e.g., left and right eyes of the same subject are paired and correlated. The correlation of repeated measures (or the heterogeneity between different subjects) needs to be accounted for - failure to do so will result in less efficient regression estimates and incorrect inference. We propose a new ?fusion effects? approach in between the commonly used fixed effects and random effects models. Our methods will be illustrated using the Ocular Hypertension Treatment Study (OHTS), a longitudinal study with measures from both eyes from 1,636 participants.