Resubmission: Latent Class Trajectory Analysis in the OHTS Study

高眼压治疗研究（OHTS）是一项纵向研究， 药物治疗可延迟或预防原发性开角型青光眼（POAG）的发作。表征 视野变化的纵向轨迹和危险因素对轨迹的影响具有较高的公信力。 健康意义。视力丧失的进展因患者而异。因此有 重要的是识别更有可能快速进展的患者，以防止不可逆的视力丧失。 功能另一方面，对于青光眼保持稳定的患者，应避免过度治疗， 降低成本、副作用和不便。例如，在OHTS中，将感兴趣的是将 以不同的发展速度分成几组。在这个建议中，我们将使用潜在的 类混合模型（LCMM）来表征视野变化轨迹的异质性。LCMM是一个 数据驱动的分类方法，而不预先指定每个潜在类在其他模型中的临界点。 此外，LCMM是非常全面的，因为它包括了几个常用的方法， 例我们将扩展LCMM来解决一些具有挑战性的问题，在建模视野轨迹 在OHTS中：（1）开发平均偏差（MD，一种视觉损失的定量测量， （2）使用（稀疏组）Lasso方法进行变量分析， 选择，以达到准确性和效率之间的适当平衡;（3）联合模型的MD和其他 POAG转换前的疾病进展指标，例如，模式标准差轨迹 同时预测POAG的时间;（4）用泛函分析方法考虑视野逐点回归 主成分分析我们对LCMM的扩展将更好地捕捉 平均偏差时间趋势和促进青光眼的循证精确医学， 眼科和其他医疗条件。

The Ocular Hypertension Treatment Study (OHTS) is a longitudinal study that tested whether topical ocular hypotensive medication delays or prevents the onset of primary open-angle glaucoma (POAG). Characterizing the longitudinal trajectory of visual field change and the effect of risk factors on the trajectory has high public health significance. The progression of visual loss varies substantially from patient to patient. Therefore, it is important to identify patients who are more likely to progress rapidly to prevent irreversible loss of visual function. On the other hand, for patients whose glaucoma remains stable, over-treatment should be avoided to reduce costs, side-effects, and inconvenience. For example, in OHTS, it would be of interest to classify the trajectories into several groups with different rates of progression. In this proposal we will employ the latent class mixed model (LCMM) to characterize the heterogeneity in the trajectory of visual field change. LCMM is a data-driven classification approach, without pre-specifying the cut-point of each latent class as in other models. Furthermore, LCMM is very comprehensive in that it includes several commonly used approaches as special cases. We will extend the LCMM to address a number of challenging issues in modeling visual field trajectory in OHTS: (1) develop a latent class joint model of mean deviation (MD, a quantitative measure of vision loss in the visual field) trajectory to predict time to POAG; (2) use the (sparse group) Lasso method for variable selection to achieve a proper balance between accuracy and efficiency; (3) jointly model of MD and other measures of disease progression prior to POAG conversion, e.g., pattern standard deviation trajectories simultaneously to predict time of POAG; (4) consider pointwise regression of visual field using functional principal component analysis. Our extensions to LCMM will better capture individual heterogeneity in the temporal trends of mean deviation and facilitate evidence-based precision medicine in glaucoma, in ophthalmology, and other medical conditions.