Quality of Life Research

, Volume 25, Issue 7, pp 1667–1678 | Cite as

Health state utility instruments compared: inquiring into nonlinearity across EQ-5D-5L, SF-6D, HUI-3 and 15D

  • Thor Gamst-Klaussen
  • Gang Chen
  • Admassu N. Lamu
  • Jan Abel Olsen



Different health state utility (HSU) instruments produce different utilities for the same individuals, thereby compromising the intended comparability of economic evaluations of health care interventions. When developing crosswalks, previous studies have indicated nonlinear relationships. This paper inquires into the degree of nonlinearity across the four most widely used HSU-instruments and proposes exchange rates that differ depending on the severity levels of the health state utility scale.


Overall, 7933 respondents from six countries, 1760 in a non-diagnosed healthy group and 6173 in seven disease groups, reported their health states using four different instruments: EQ-5D-5L, SF-6D, HUI-3 and 15D. Quantile regressions investigate the degree of nonlinear relationships between these instruments. To compare the instruments across different disease severities, we split the health state utility scale into utility intervals with 0.2 successive decrements in utility starting from perfect health at 1.00. Exchange rates (ERs) are calculated as the mean utility difference between two utility intervals on one HSU-instrument divided by the difference in mean utility on another HSU-instrument.


Quantile regressions reveal significant nonlinear relationships across all four HSU-instruments. The degrees of nonlinearities differ, with a maximum degree of difference in the coefficients along the health state utility scale of 3.34 when SF-6D is regressed on EQ-5D. At the lower end of the health state utility scale, the exchange rate from SF-6D to EQ-5D is 2.11, whilst at the upper end it is 0.38.


Comparisons at different utility levels illustrate the fallacy of using linear functions as crosswalks between HSU-instruments. The existence of nonlinear relationships between different HSU-instruments suggests that level-specific exchange rates should be used when converting a change in utility on the instrument used, onto a corresponding utility change had another instrument been used. Accounting for nonlinearities will increase the validity of the comparison for decision makers when faced with a choice between interventions whose calculations of QALY gains have been based on different HSU-instruments.


Health state utility instruments Crosswalks Nonlinearity Exchange rates Health-related quality of life Economic evaluation 


  1. 1.
    Weinstein, M. C., Torrance, G., & McGuire, A. (2009). QALYs: The basics. Value in Health, 12, S5–S9. doi: 10.1111/j.1524-4733.2009.00515.x.CrossRefPubMedGoogle Scholar
  2. 2.
    Brazier, J. (2007). Measuring and valuing health benefits for economic evaluation. New York: OUP Oxford.Google Scholar
  3. 3.
    Richardson, J., Iezzi, A., & Khan, M. (2015). Why do multi-attribute utility instruments produce different utilities: The relative importance of the descriptive systems, scale and ‘micro-utility’ effects. Quality of Life Research,. doi: 10.1007/s11136-015-0926-6.PubMedCentralGoogle Scholar
  4. 4.
    Richardson, J., McKie, J., & Bariola, E. (2014). Multi attribute utility instruments and their use. In C. Aj (Ed.), Encyclopedia of health economics (pp. 341–357). San Diego: Elsevier Science.CrossRefGoogle Scholar
  5. 5.
    Wisloff, T., Hagen, G., Hamidi, V., Movik, E., Klemp, M., & Olsen, J. A. (2014). Estimating QALY gains in applied studies: a review of cost-utility analyses published in 2010. Pharmacoeconomics, 32(4), 367–375. doi: 10.1007/s40273-014-0136-z.CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Brazier, J. E., Yang, Y., Tsuchiya, A., & Rowen, D. L. (2010). A review of studies mapping (or cross walking) non-preference based measures of health to generic preference-based measures. The European Journal of Health Economics, 11(2), 215–225. doi: 10.1007/s10198-009-0168-z.CrossRefPubMedGoogle Scholar
  7. 7.
    Mortimer, D., & Segal, L. (2008). Comparing the incomparable? A systematic review of competing techniques for converting descriptive measures of health status into QALY-weights. Medical Decision Making, 28(1), 66–89. doi: 10.1177/0272989x07309642.CrossRefPubMedGoogle Scholar
  8. 8.
    Chen, G., Khan, M. A., Iezzi, A., Ratcliffe, J., & Richardson, J. (2015). Mapping between 6 multiattribute utility instruments. Medical Decision Making,. doi: 10.1177/0272989x15578127.Google Scholar
  9. 9.
    Fryback, D. G., Palta, M., Cherepanov, D., Bolt, D., & Kim, J. S. (2010). Comparison of 5 health-related quality-of-life indexes using item response theory analysis. Medical Decision Making, 30(1), 5–15. doi: 10.1177/0272989x09347016.CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Rowen, D., Brazier, J., Tsuchiya, A., & Alava, M. H. (2012). Valuing states from multiple measures on the same visual analogue sale: A feasibility study. Health Economics, 21(6), 715–729. doi: 10.1002/hec.1740.CrossRefPubMedGoogle Scholar
  11. 11.
    Seymour, J., McNamee, P., Scott, A., & Tinelli, M. (2010). Shedding new light onto the ceiling and floor? A quantile regression approach to compare EQ-5D and SF-6D responses. Health Economics, 19(6), 683–696. doi: 10.1002/hec.1505.PubMedGoogle Scholar
  12. 12.
    Richardson, J., Kahn, M., Lezzi, A., & Maxwell, A. (2012). Cross-national comparison of twelve quality of life instruments: MIC Paper 1: Background, questions, instruments. Research paper 76. http://www.aqol.com.au/papers/researchpaper76.pdf. Accessed May 14, 2014.
  13. 13.
    Devlin, N., & van Hout, B. (2014). An EQ-5D-5L value set for England. Office of Health Economics (OHE), London. http://www.slideshare.net/ScHARR-HEDS/ohe-seminar-5-l-value-set-oct-30-2014-final-version-031114-1. Accessed January 20, 2015.
  14. 14.
    van Hout, B., Janssen, M. F., Feng, Y. S., Kohlmann, T., Busschbach, J., Golicki, D., et al. (2012). Interim scoring for the EQ-5D-5L: Mapping the EQ-5D-5L to EQ-5D-3L value sets. Value Health, 15(5), 708–715. doi: 10.1016/j.jval.2012.02.008.CrossRefPubMedGoogle Scholar
  15. 15.
    Dolan, P. (1997). Modeling valuations for EuroQol health states. Medical Care, 35(11), 1095–1108.CrossRefPubMedGoogle Scholar
  16. 16.
    Brazier, J., Roberts, J., & Deverill, M. (2002). The estimation of a preference-based measure of health from the SF-36. Journal of Health Economics, 21(2), 271–292. doi: 10.1016/S0167-6296(01)00130-8.CrossRefPubMedGoogle Scholar
  17. 17.
    Feeny, D., Furlong, W., Torrance, G. W., Goldsmith, C. H., Zhu, Z., DePauw, S., et al. (2002). Multiattribute and single-attribute utility functions for the health utilities index mark 3 system. Medical Care, 40(2), 113–128.CrossRefPubMedGoogle Scholar
  18. 18.
    Sintonen, H., & Pekurinen, M. (1993). A fifteen-dimensional measure of health-related quality of life (15D) and its applications. In S. Walker & R. Rosser (Eds.), Quality of life assessment: Key issues in the 1990s (pp. 185–195). Netherlands: Springer.CrossRefGoogle Scholar
  19. 19.
    Koenker, R., & Hallock, K. F. (2001). Quantile regression. Journal of Economic Perspectives, 15(4), 143–156. doi: 10.1257/jep.15.4.143.CrossRefGoogle Scholar
  20. 20.
    Chen, G., Flynn, T., Stevens, K., Brazier, J., Huynh, E., Sawyer, M., et al. (2015). Assessing the health-related quality of life of Australian adolescents: An empirical comparison of the child health utility 9D and EQ-5D-Y instruments. Value Health, 18(4), 432–438. doi: 10.1016/j.jval.2015.02.014.CrossRefPubMedGoogle Scholar
  21. 21.
    Gheorghe, L., & Baculea, S. (2010). Cost-effectiveness of peginterferon alpha-2a and peginterferon alpha-2b combination regimens in genotype-1 naive patients with chronic hepatitis C. Hepato-Gastroenterology, 57(101), 939–944.PubMedGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thor Gamst-Klaussen
    • 1
  • Gang Chen
    • 2
  • Admassu N. Lamu
    • 1
  • Jan Abel Olsen
    • 1
  1. 1.Department of Community MedicineUniversity of TromsøTromsøNorway
  2. 2.Flinders Centre for Innovation in Cancer and Flinders Health Economics GroupFlinders UniversityAdelaideAustralia

Personalised recommendations