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.