Mapping SF-12 to EQ-5D: A Regression Analysis

For researchers and economists engaged in cost-utility analysis, the accurate measurement of health-status utilities, summarized in a single index of health-related quality of life (HR-QOL), is paramount. However, clinical studies frequently include only HR-QOL profile measures, such as the SF-36 or SF-12, rather than a direct summary HR-QOL index. This necessitates the conversion of profile data into a single index format, a process often undertaken with various ‘after-market’ tools and regression methods. Yet, a long-standing challenge has been the lack of consensus on the most appropriate regression method for this critical mapping task.

The seminal study, “Converting the SF-12 into the EQ-5D: An Empirical Comparison of Methodologies,” by Ling-Hsiang Chuang and Paul Kind, directly addresses this methodological gap. Published in Pharmacoeconomics in 2009, this research provides a comprehensive evaluation of different regression techniques and model specifications for converting SF-12 data into the EQ-5D index, utilizing a single, common dataset.

Key Aspects of the Study:

• Robust Data Source: The study leveraged data from the Medical Expenditure Panel Survey (MEPS) 2003, encompassing 19,678 adults who completed both EQ-5D and SF-12 questionnaires. This nationally representative dataset provided a strong foundation for empirical comparison.
• Comprehensive Methodological Comparison: Four econometric techniques were rigorously investigated:
  1. Ordinary Least Squares (OLS): A widely used method known for minimizing residual error.
  2. Censored Least Absolute Deviation (CLAD): Employed to account for the “ceiling effect” in EQ-5D scores, where a significant portion of the population reports full health.
  3. Multinomial Logit Model: This approach estimates responses for each EQ-5D dimension separately, thereby avoiding direct handling of the index score’s challenging distribution.
  4. Two-Part Model: A less commonly used technique that separates the estimation for individuals reporting perfect health from those reporting other health states, assuming a fundamental difference between these groups.
• Evaluation of Model Specifications: The study also compared two main types of model specifications: item-based (using individual SF-12 items as categorical variables) and summary score-based (using PCS-12 and MCS-12 scores).
• Performance Metrics: Models were judged on multiple criteria, including estimated mean, mean absolute error (MAE), mean square error (MSE), and the proportion of estimations with absolute errors exceeding 0.05 and 0.10. Subgroup analyses based on age and self-reported health conditions provided further insights into model performance in specific populations.

Groundbreaking Findings:

The research yielded crucial insights for the field of HR-QOL mapping:

• OLS for Aggregate Mean Estimation: OLS regression emerged as the most accurate model for estimating the group mean. It accurately estimated the mean observed EQ-5D index score for the overall sample and possessed the smallest mean square error (MSE), indicating its effectiveness in minimizing larger errors.
• Two-Part Model Excels in Vulnerable Subgroups: While OLS performed well overall, its accuracy deteriorated in older and less healthy subgroups. Here, the two-part model demonstrated superior performance, offering closer estimations to actual EQ-5D index scores for these vulnerable populations by effectively addressing heterogeneity.
• Superiority of Item-Based Model Specifications: Regardless of the econometric technique, models utilizing item-based model specifications consistently performed better than those based on summary scores. This finding is supported both theoretically—as item-based models avoid pre-assigned values and maintain richer information—and empirically.
• Limitations for Individual-Level Estimation: A critical conclusion is that none of the mapping methods examined in the study are suitable for accurately estimating health utility at the individual level. Even when applying these mappings for group means, caution is advised, especially for less healthy populations, given observed discrepancies between derived and actual index scores.

Implications and Recommendations:

This study strongly recommends that for the purpose of economic evaluation, clinical studies should ideally include a preference-based, single-index measure of HR-QOL directly. However, when such direct measures are unavailable, the methodology exemplified in this research has wide applicability for converting other SF-family instruments or HR-QOL profile measures. The findings underscore the importance of carefully selecting mapping methods based on the specific research question and the characteristics of the population being studied, particularly highlighting the value of item-based specifications and the two-part model for addressing population heterogeneity.

This work serves as an indispensable guide for analysts seeking to convert HR-QOL profile data into a single index, fostering more robust and reliable cost-utility analyses in health economics.

Reference for the Article:

Chuang, L.-H., & Kind, P. (2009). Converting the SF-12 into the EQ-5D: An Empirical Comparison of Methodologies. Pharmacoeconomics, 27(6), 491–505.