Generalizability and Unaddressed Issues in Mapping

Abstract

Health utility measures are used in economic analysis to provide estimates of cost-effectiveness in terms of costs per quality-adjusted life years (QALYs). Some studies measure health-related quality of life but do not use preference-based health utility measures. A common method for estimating health utilities in these studies is to use a mapping function. Mapping, also known as cross-walking, uses a data set containing the health utility measure and health-related quality-of-life measure to estimate a function and can then be applied to other data sets that contain only the health-related qualityof-life measure to estimate health utilities in costeffectiveness analysis. A number of methodological issues have been recognized in mapping studies; these include whether there is sufficient overlap between the health utility and quality-of-life instruments, appropriate methodology and model specification, and measuring uncertainty. In their article on uncertainty, Chan and others focus on the last of these, specifically the underestimation of the variance in mapping functions, resulting in tighter confidence intervals around utility estimates than if utilities had been observed directly. The authors state that this is due to the presence of important unmeasured predictors and assuming regression coefficients are fixed. They provide mathematical explanations as to why this will underestimate the variance and then provide 3 solutions: 1) R adjustment to account for unmeasured variables, 2) a parametric method for mapping functions fitted using ordinary least squares regression, and 3) a nonparametric general case method that can be used across all types of mapping model. Methods are illustrated with both real and simulated examples and demonstrate that all 3 methods correct for the underestimation of the variance. The 3 proposed solutions by Chan and others are also generalizable beyond mapping. For example, the tariffs (algorithms) used to derive health utility indices used in economic evaluations are based on mathematical models with regression coefficients, and the 2 factors identified by Chan and others that underestimate uncertainty in mapping models will also occur in the derivation of health utility indices. The models used to derive the tariffs are likely to exclude unmeasured/unknown factors that people participating in the valuation may take into account. Furthermore, when these tariffs are applied to other data sets, the coefficients in the scoring algorithm are regarded as fixed rather than random. Authors of some of the tariffs already provide sufficient information to make these adjustments. For example, for the EQ-5D York modeling valuations (MV) tariff, Dolan provides R for the tariff to estimate the R adjustment, and in their National Institute for Health and Care Excellence (NICE) technical support document on health state utility values in decision models, Ara and Wailoo provide the variance-covariance matrix for the York MV tariff, which can be used to correct the variance using Chen and others’ proposed parametric solution. Chan and others point out that although it is possible to account for the uncertainties from unaccounted predictors, ‘‘this does not affect the accuracy of the mapping algorithm itself,’’ and if the mapping algorithm is poor at predicting utility values, it will remain poor after allowing for unaccounted predictors. When constructing mapping algorithms, the researcher is making the assumption that there is sufficient overlap of the constructs (domains/dimensions) between the utility measure Received 11 June 2014 from University of Sheffield School of Health and Related Research, Sheffield, UK. Revision accepted for publication 11 August 2014.