Najera-Zuloaga Josu, Lee Dae-Jin, Arostegui Inmaculada
Basque Center for Applied Mathematics, Bilbao, Spain.
Departamento de Matemática Aplicada y Estadística e Investigación Operativa, Universidad del País Vasco UPV/EHU, Bilbao, Spain.
Biom J. 2019 May;61(3):600-615. doi: 10.1002/bimj.201700251. Epub 2018 Nov 27.
Patient-reported outcomes (PROs) are currently being increasingly used as primary outcome measures in observational and experimental studies since they inform clinicians and researchers about the health-status of patients and generate data to facilitate improved care. PROs usually appear as discrete and bounded with U, J, or inverse J shapes, and hence, exponential family members offer inadequate distributional fits. The beta-binomial distribution has been proposed in the literature to fit PROs. However, the fact that the beta-binomial distribution does not belong to the exponential family limits its applicability in the regression model context, and classical estimation approaches are not straightforward. Moreover, PROs are usually measured in a longitudinal framework in which individuals are followed up for a certain period. Hence, each individual obtains several scores of the PRO over time, which leads to the repeated measures and defines the correlation structure in the data. In this work, we have developed and proposed an estimation procedure for the analysis of correlated discrete and bounded outcomes, particularly PROs, by a beta-binomial mixed-effects model. Additionally, we have implemented the methodology in the PROreg package in R. Because there are similar approaches in the literature to address the same issue, this work also incorporates a comparison study between our proposal and alternative methodologies commonly implemented in R and shows the superior performance of our estimation procedure. This paper was motivated by the analysis of the health-status of patients with chronic obstructive pulmonary disease, where the main objective is the assessment of risk factors that may affect the evolution of the disease. The application of the proposed approach in the study leads to clinically relevant results.
患者报告结局（PROs）目前在观察性研究和实验性研究中越来越多地被用作主要结局指标，因为它们能让临床医生和研究人员了解患者的健康状况，并生成数据以促进改善护理。PROs通常呈现离散且具有U形、J形或倒J形的边界，因此，指数族成员提供的分布拟合并不充分。文献中已提出用β-二项分布来拟合PROs。然而，β-二项分布不属于指数族这一事实限制了其在回归模型中的适用性，并且经典估计方法并不直接。此外，PROs通常是在纵向框架中进行测量的，在该框架中个体被随访一段时间。因此，每个个体随时间会获得多个PRO分数，这导致了重复测量并定义了数据中的相关结构。在这项工作中，我们开发并提出了一种估计程序，用于通过β-二项混合效应模型分析相关的离散且有界结局，特别是PROs。此外，我们已在R语言的PROreg包中实现了该方法。由于文献中有类似方法来解决相同问题，这项工作还纳入了我们的方法与R中常用的替代方法之间的比较研究，并展示了我们估计程序的优越性能。本文的动机来自于对慢性阻塞性肺疾病患者健康状况的分析，其主要目标是评估可能影响疾病进展的风险因素。所提出的方法在该研究中的应用产生了具有临床相关性的结果。
