Underestimation of uncertainties in health utilities derived from mapping algorithms involving health-related quality-of-life measures: statistical explanations and potential remedies.

Objectives. Mapping algorithms are being developed in increasing numbers to derive health utilities (HUs) from health-related quality-of-life (HRQOL) data. However, the variances of the mapping-derived HUs are observed to be smaller than those of the actual HUs. Methods. Two reasons are proposed: 1) the presence of important unmeasured predictors leading to a high degree of unexplained variance and 2) ignoring that the regression coefficients are random variables themselves. We derive 3 variance estimators of HUs to account for these causes: 1) R-2-adjusted estimator, 2) parametric estimator, and 3) nonparametric estimator. We tested these estimators using a simulated dataset and a real dataset involving the EQ-5D-3L and University of Washington Quality of Life questionnaire for patients with head and neck cancers. Results. The R-2-adjusted estimator can be used in ordinary least squares (OLS)-based mapping algorithms and requires only the R-2 from the derivation study. The parametric estimator can be used in OLS-based mapping algorithms and requires the mean square error (MSE) and design matrix from the derivation study. The nonparametric estimator can be used in any mapping algorithm and requires leave-one-out cross-validation MSE from the derivation study. In the simulated dataset, all 3 estimators are within 1% of the variance of the actual HUs. In the real dataset, the unadjusted variance was 45% less than the actual variance, while all 3 estimators are within 10% of the actual variance. Conclusions. When conducting cost-utility analyses (CUA) based on mapping algorithms, the variances of derived HUs should be properly adjusted using one of the proposed methods so that the results of the CUAs will correctly characterize uncertainty.