The purpose of this research was to develop an algorithm to allow mapping of SF-12 scores to EQ-5D index scores based on a nationally representative sample. There are 2 published algorithms to map EQ-5D index scores from the SF-12 in nationally representative data sets.^{12}^{,}^{13} The current research differs in several important respects from the previous research. First, the mapping algorithm provided in this research is based on a nationally representative US sample and maps to the EQ-5D index values based on the general US population,^{16} providing the first mapping algorithm of preference-based EQ-5D index scores that meet the criteria of the Panel on Cost-Effectiveness in Health and Medicine (PCEHM) for reference-case cost-effectiveness analyses from the societal perspective in the United States. The US and UK community-based TTO scores have been shown to differ significantly, implying that EQ-5D index scores may also differ.^{15} Although very useful to understanding the relationship between the SF-12 health status instrument and the EQ-5D index, previous algorithms mapped to EQ-5D index value based on a community sample in the United Kingdom^{14} and do not meet the PCEHM criteria for the United States.^{1} Second, the current research takes a different analytical approach, addressing the characteristics of the data (i.e., 46% censoring, nonnormality, and heteroskedasticity) and comparing different econometric approaches.

This mapping algorithm may be useful to researchers who need preference-based HRQL scores when only SF-12 scores are available. In these cases, analysts could use the algorithm from this research to derive EQ-5D index scores from available values of the SF-12.

Some comments on the practical application of this algorithm may be useful to end-users. First, in most cases, only the MCS-12 and PCS-12 scores are available, and values for sociodemographic variables are missing. In these cases, it is recommended that the CLAD MPE model with the derived constant (-0.01067) be used. This method uses the following prediction equation: EQ-5D = 0.057867 + 0.010367·PCS-12 + 0.00822·MCS-12 - 0.000034·PCS-12·MCS-12 - 0.01067. When predicting EQ-5D index scores, it is important to note that predicted scores >1.0 are possible. Hence, analysts should truncate any predicted score greater than 1 at 1.0, as was done in the empirical comparison. It is important that end-users incorporate appropriate sensitivity analyses of point estimates mapped from SF-12 scores. More detailed information on the appropriate use of sensitivity analysis is provided elsewhere.

^{33} One can use the standard error or 95% confidence intervals (CIs) of the mean predicted EQ-5D score to derive an estimate of the uncertainty in the point estimates. The mean, standard error, and 95% CI for the CLAD MPE-predicted EQ-5D score in the full MEPS sample were 0.8912, .0010636, and 0.8891-0.8933, respectively. However, an equation for calculating an adjusted standard error for mapping is provided by Franks and others:

^{12}where var is the sample variance of the individual predictions in a sample of size

*N*, and

*R*^{2} = 0.41.

Researchers can calculate EQ-5D index scores and adjusted standard erros by entering PCS-12 and MGS-12 scores and sample standard deviation at the journal’s Web site,

mdm.sagepub.com.

Although it would have been feasible to develop a model based on all 12 items of the SF-12, it may not be practical for end-users (many of whom will only have data on the PCS-12 and MCS-12 scales). In addition, the model specification becomes unwieldy and difficult for applies use, as discussed by Franks and others.^{12}

The current research compares the empirical performance of different analytic methods to estimate EQ-5D index scores in an independent, large, nationally representative valiation set, which has implications for the broader econometric analysis of preference-based HRQL scores that tend to be clustered at 1.0. In this nationally representative data set, EQ-5D index scores were found to have a high degree of censoring (46%), with erros that were not normally distributed and exhibited heteroskedasticity. Theoretically, these properties suggest that CLAD is the only unbiased estimator of EQ-5D index scores.^{25} However, given the statistical properties of EQ-5D index scores in this data set, it is surprising how well OLS performed and how poorly Tobit performed. The mean prediction error with OLS was not significantly higher than with CLAD and was lower than Tobit. The 95% CI of the prediction errors overlapped for all 3 analytic methods. Future researc is needed to examine the most appropriate theoretical approach to estimating preference-based HRQL scores with these statistical properties, as well as the relative empirical performance of analytic methods.

The current research is not without limitations. There is a significant amount of variance that is unexplained by the SF-12 and sociodemographic variables in this analysis. This uncertainty should be incorporated in probabilistic sensitivity analyses in cost-effectiveness analyses using these stimates. In addition, the methods of reducing predicted scores above 1.0 may improve the empirical performance of all 3 methods but likely improves the performance of CLAD and Tobit more than OLS. Unlike previous mapping models, the current model does not include squared PCS-12 and MCS-12 terms due to the lack of apparent nonlinearity and potential for multicollinearity. The range of predicted EQ-5D scores for the fll CLAD model ranges from 0.33 to 1.04, This range covers approximately 98% of actual EQ-5D scores in MEPS. The range for the simplified CLAD model (CLAD MPE) was .42 to 1.02, which covers >96% of all actual EQ-5D scores. If using the minimum and maximum values of actual PCS-12 and MCS-12 scores, the CLAD MPE model-predicted EQ-5D scores range from .20 to >1.0. This range covers >99.9% of actual EQ-5D scores in MEPS and demonstrates the potential range of the model given actual SF-12 scores in MEPS. Nonetheless, it should be noted that the mapping algorithms provided in this research may not provide the full range of individual EQ-5D scores possible at the lower bounds.

Although the construct validity, reliability, and responsiveness of the EQ-5D have been documented extensively in both general and specific disease populations, the EQ-5D is not without limitations. The parsimony in the 5 items and 3 levels of the EQ-5D questionnaire translates into ease of administration and efficiency of preference assessment but also results in a potential lack of discrimination. As discussed, 46% of the nationally representative MEPS sample had an EQ-5D score of 1.0. In addition, from the full health state of 1.0, the minimum possible decrement in the EQ-5D index score is 0.14. (However, it should be noted that using the mapping algorithm provied in this article will provide predicted scores within this range.) Taking these limitations into account, there is no consensus that other theoretically based MAHSCS are superior to the EQ5D.^{34}^{-}^{37} Each has its own advantages and limitations. The EQ-5D is currently the only instrument with a preference scoring algorithm based on the general US population that can be mapped from the SF-12 in a nationally representative data set.

The generalizability of the estimates provided in this research is limited to the MEPS sample of individuals with valid EQ-5D index, MCS-12, and PCS-12 scores. Individuals with complete responses for all 3 scores are likely to have slightly better health than others. MEPS is also restricted to the noninstitutionalized population. Nonetheless, it is rare to find both instruments in a nationally representative population, and the sample used in this research is likely as generalizable to the nation as is available.

In a recent examination of cost-utility analyses, 77% did not incorporate community-based preferences, and 33% used arbitrary expert or author judgment.^{38} Although not perfect, the mapping algorithm provided in this research may provide analysts an avenuwe to obtain preference-based HRQL scores appropriate for reference-case cost-effectivenjess analyses in the United States when only SF-12 scores are available.