School of Social and Community Medicine, University of Bristol, Bristol, UK.
Value Health. 2013 Jan-Feb;16(1):177-84. doi: 10.1016/j.jval.2012.07.003. Epub 2012 Sep 25.
To develop a coherent method for estimating mappings between treatment effects on disease-specific measurement (DSM) instruments and generic health-related quality-of-life (QOL) measures, when both are subject to measurement errors.
We identified three properties that must be satisfied for mappings to be logically coherent: invertability, transitivity, and invariance to linear transformation. Of the common regressions, ordinary least squares (OLS), geometric mean (GM), and orthogonal regression, only GM has all these properties, and then only in special cases. We developed a common factor model of how DSM and generic QOL scales are related, and derived expressions for coherent mapping coefficients. We showed that these are equivalent to adjusted forms of OLS or GM regressions. Where cohort data are available on just one DSM and one QOL measure, external data on the reproducibility of the DSM are required. In some circumstances, the mappings can be estimated without external data. We illustrated the estimation of mapping coefficients by using data on EuroQol five-dimensional (EQ-5D) questionnaire, 12-item short form health survey (SF-12) Mental Component Summary, and the Beck Depression Inventory (BDI), from a trial of treatments for depression.
OLS underestimates and GM overestimates mappings from DSMs to generic QOL measures. Mappings estimated by using external data on reliability were similar to those estimated by using internal data, suggesting approximate adequacy of the common factor model.
Neither OLS nor GM regression, unless corrected, is suitable for estimating mappings between disease-specific and generic QOL scales. OLS systematically underestimates mappings, but it can be adjusted by using external information on test-retest reliability.
当疾病特异性测量（DSM）工具和通用健康相关生活质量（QOL）测量都存在测量误差时，开发一种将治疗效果在这两种测量之间进行一致估计的方法。
我们确定了映射在逻辑上一致所需满足的三个属性：可反转性、传递性和线性变换不变性。在常见回归中，普通最小二乘法（OLS）、几何平均值（GM）和正交回归中，只有 GM 具有所有这些属性，但仅在特殊情况下。我们开发了一种 DSM 和通用 QOL 量表之间关系的通用因子模型，并推导出了一致映射系数的表达式。我们表明，这些与 OLS 或 GM 回归的调整形式等效。如果只有一个 DSM 和一个 QOL 测量的队列数据，则需要外部数据来重现 DSM 的可重复性。在某些情况下，可以在没有外部数据的情况下估计映射。我们使用来自抑郁症治疗试验的 EuroQol 五维（EQ-5D）问卷、12 项简短健康调查（SF-12）精神成分综合量表和贝克抑郁量表（BDI）的数据说明了映射系数的估计。
OLS 低估了 DSM 到通用 QOL 测量的映射，而 GM 则高估了。使用可靠性外部数据估计的映射与使用内部数据估计的映射相似，这表明通用因子模型的近似充分性。
除非进行校正，否则 OLS 或 GM 回归都不适合估计疾病特异性和通用 QOL 量表之间的映射。OLS 系统地低估了映射，但可以通过使用测试 - 重测可靠性的外部信息进行调整。
