Ordinal Regression Models for Continuous Scales
Ordinal Regression Models for Continuous Scales
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DOI：
10.2202/1557-4679.1230
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发表时间：
2010-01-01
影响因子：
1.2
通讯作者：
Heller, Gillian Z.
中科院分区：
文献类型：
--
作者：
Manuguerra, Maurizio;Heller, Gillian Z.
在协变量存在的情况下，有序回归分析是一种方便的分析有序响应变量的工具。在本文中，我们将这种方法扩展到连续自评量表的情况下，如用于疼痛评估的视觉模拟量表（VAS），或生活质量研究中的线性模拟自评量表（LASA）。这些量表测量受试者对无形量的感知，由于其固有的非线性，不能作为比率变量处理。我们用连接刻度和潜在连续变量的函数来表示似然，并以参数或非参数方式近似该函数。在此基础上，提出了连续尺度的一般半参数回归框架。分析了两个数据集，将我们的方法与标准离散有序回归模型进行比较，并将模型的参数版本与非参数版本进行比较。第一个数据集使用来自低水平激光治疗慢性颈部疼痛疗效研究的VAS数据；第二份来自一项关于晚期乳腺癌化疗治疗的研究，研究了不同药物对患者生活质量的影响。有序回归模型的连续公式的优点是不会因为分数的分类而导致精度的损失，也不会任意选择类别的数量和边界。该模型的半参数形式使其成为分析连续有序尺度的灵活方法。
Ordinal regression analysis is a convenient tool for analyzing ordinal response variables in the presence of covariates. In this paper we extend this methodology to the case of continuous self-rating scales such as the Visual Analog Scale (VAS) used in pain assessment, or the Linear Analog Self-Assessment (LASA) scales in quality of life studies. These scales measure subjects' perception of an intangible quantity, and cannot be handled as ratio variables because of their inherent nonlinearity. We express the likelihood in terms of a function connecting the scale with an underlying continuous latent variable and approximate this function either parametrically or non-parametrically. Then a general semi-parametric regression framework for continuous scales is developed. Two data sets have been analyzed to compare our method to the standard discrete ordinal regression model, and the parametric to the non-parametric versions of the model. The first data set uses VAS data from a study on the efficacy of low-level laser therapy in the treatment of chronic neck pain; the second comes from a study on chemotherapy treatments in advanced breast cancer and looks at the impact of different drugs on patients' quality of life. The continuous formulation of the ordinal regression model has the advantage of no loss of precision due to categorization of the scores and no arbitrary choice of the number and boundaries of categories. The semi-parametric form of the model makes it a flexible method for analysis of continuous ordinal scales.