A flexible formula for incorporating distributive concerns into cost-effectiveness analyses: Priority weights

Autoři: Øystein Ariansen Haaland aff001;  Frode Lindemark aff001;  Kjell Arne Johansson aff001
Působiště autorů: Bergen Centre for Ethics and Priority Setting (BCEPS), Department of Global Public Health and Primary Care, University of Bergen, Bergen, Norway aff001;  Department of Addiction Medicine, Haukeland University Hospital, Bergen, Norway aff002
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: 10.1371/journal.pone.0223866



Cost effectiveness analyses (CEAs) are widely used to evaluate the opportunity cost of health care investments. However, few functions that take equity concerns into account are available for such CEA methods, and these concerns are therefore at risk of being disregarded. Among the functions that have been developed, most focus on the distribution of health gains, as opposed to the distribution of lifetime health. This is despite the fact that there are good reasons to give higher priority to individuals and groups with a low quality adjusted life expectancy from birth (QALE). Also, an even distribution of health gains may imply an uneven distribution of lifetime health.


We develop a systematic and explicit approach that allows for the inclusion of lifetime health concerns in CEAs, by creating a new priority weight function, PW = α+(t-γ)·C·e-β·(t-γ), where t is the health measure. PW has several desirable properties. First, it is continuous and smooth, ensuring that people with similar health characteristics are treated alike. For example, those who achieve 50 QALE should be treated similarly to those who achieve 49.9 QALE. Second, it is flexible regarding shape and outcome measure (i.e., caters to other measures than QALE), so that a broad range of values may be modelled. Third, the coefficients have distinct roles. This allows for the easy manipulation of the PW’s shape. In order to demonstrate how PW may be applied, we use data from a previous study and estimated the coefficients of PW based on two approaches.


Equity concerns are important when conducting CEAs, which means that suitable PWs should be developed. We do not intend to determine which PW is the most appropriate, but to illustrate how a flexible general PW can be estimated based on empirical data.

Klíčová slova:

Cost-effectiveness analysis – Curve fitting – Finance – Global health – Health economics – Child health – Life expectancy – Public and occupational health


1. Johri M, Norheim OF: Can cost-effectiveness analysis integrate concerns for equity? Systematic review. Int J Technol Assess Health Care 2012, 28(2):125–132. doi: 10.1017/S0266462312000050 22494637

2. A QALY is a QALY is a QALY—or is it not? In: Measuring and valuing health benefits for economic evaluation. Edited by Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Oxford: Oxford University Press; 2007: 287–298.

3. Baltussen R, Youngkong S, Paolucci F, Niessen L: Multi-criteria decision analysis to prioritize health interventions: Capitalizing on first experiences. Health Policy 2010, 96(3):262–264.

4. National Institute for Health and Clinical Excellence: Guide to the methods of technology appraisal 2013. In. London; 2013.

5. Claxton K, Sculpher M, Palmer S, Culyer AJ: Causes for concern: is NICE failing to uphold its responsibilities to all NHS patients? Health Econ 2015, 24(1):1–7. doi: 10.1002/hec.3130 25488707

6. Cookson R: Justice and the NICE approach. J Med Ethics 2015, 41(1):99–102. doi: 10.1136/medethics-2014-102386 25516947

7. Morland B, Ringard A, Rottingen JA: Supporting tough decisions in Norway: a healthcare system approach. Int J Technol Assess Health Care 2010, 26(4):398–404. doi: 10.1017/S0266462310001030 20942984

8. Svensson M, Nilsson FO, Arnberg K: Reimbursement Decisions for Pharmaceuticals in Sweden: The Impact of Disease Severity and Cost Effectiveness. Pharmacoeconomics 2015, 33(11):1229–1236. doi: 10.1007/s40273-015-0307-6 26093889

9. van de Wetering EJ, Stolk EA, van Exel NJ, Brouwer WB: Balancing equity and efficiency in the Dutch basic benefits package using the principle of proportional shortfall. Eur J Health Econ 2013, 14(1):107–115. doi: 10.1007/s10198-011-0346-7 21870179

10. Franken M, Stolk E, Scharringhausen T, de Boer A, Koopmanschap M: A comparative study of the role of disease severity in drug reimbursement decision making in four European countries. Health Policy 2015, 119(2):195–202. doi: 10.1016/j.healthpol.2014.10.007 25456017

11. Grocott R, Metcalfe S, Alexander P, Werner R: Assessing the value for money of pharmaceuticals in New Zealand—PHARMAC's approach to cost-utility analysis. N Z Med J 2013, 126(1378):60–73. 24045316

12. Ngo P: The Influence of Cost-Effectiveness Evaluations on Reimbursement in Australia: A Retrospective Study of Decisions made by the Pharmaceutical Benefits Advisory Committee. Pharmaceutical Medicine 2014, 28(4):187–193.

13. Norges offentlige utredninger. Åpent og rettferdig—prioriteringer i helsetjenesten. NOU 2014:12. In: Norges offentlige utredninger; NOU 2014:12. 218 s.

14. Paulden M: Recent amendments to NICE's value-based assessment of health technologies: implicitly inequitable? Expert Rev Pharmacoecon Outcomes Res 2017, 17(3):239–242. doi: 10.1080/14737167.2017.1330152 28490259

15. Drummond MF, Sculpher M, Torrance G, O'Brien B, Stoddart G: Methods for the economic evaluation of health care programmes, 3rd ed. edn. Oxford: Oxford University Press; 2005.

16. Brock DW, Wikler D: Ethical Issues in Resource Allocation, Research, and New Product Development. In: Disease Control Priorities in Developing Countries. Edited by Jamison DT, Breman JG, Measham AR, Alleyne G, Claeson M, Evans DB, Jha P, Mills A, Musgrove P, 2nd edn. Washington (DC): World Bank; 2006: 259–270.

17. Cookson R, Drummond M, Weatherly H: Explicit incorporation of equity considerations into economic evaluation of public health interventions. Health Econ Policy Law 2009, 4(Pt 2):231–245. doi: 10.1017/S1744133109004903 19216834

18. Parfit D: Equality and priority. Ratio 1997, 10(3):202–221.

19. Adler MD, Holtug N: Prioritarianism: A response to critics. Polit Philos Econ 2019, 18(2):101–144.

20. Choudhry N, Slaughter P, Sykora K, Naylor CD: Distributional dilemmas in health policy: large benefits for a few or smaller benefits for many? Journal of health services research & policy 1997, 2(4):212–216.

21. Olsen JA: A note on eliciting distributive preferences for health. J Health Econ 2000, 19(4):541–550. 11010240

22. Ottersen T: Lifetime QALY prioritarianism in priority setting. J Med Ethics 2012.

23. Lindemark F, Norheim OF, Johansson KA: Making use of equity sensitive QALYs: a case study on identifying the worse off across diseases. Cost effectiveness and resource allocation: C/E 2014, 12:16. doi: 10.1186/1478-7547-12-16 25089121

24. Williams A: Intergenerational equity: an exploration of the 'fair innings' argument. Health Econ 1997, 6(2):117–132. 9158965

25. Norheim OF, Asada Y: The ideal of equal health revisited: definitions and measures of inequity in health should be better integrated with theories of distributive justice. Int J Equity Health 2009, 8:40. doi: 10.1186/1475-9276-8-40 19922612

26. Dolan P, Tsuchiya A: It is the lifetime that matters: public preferences over maximising health and reducing inequalities in health. J Med Ethics 2012, 38(9):571–573. doi: 10.1136/medethics-2011-100228 22493185

27. Bleichrodt H, Doctor J, Stolk E: A nonparametric elicitation of the equity-efficiency trade-off in cost-utility analysis. J Health Econ 2005, 24(4):655–678. doi: 10.1016/j.jhealeco.2004.10.001 15960990

28. Ottersen T, Maestad O, Norheim OF: Lifetime QALY prioritarianism in priority setting: quantification of the inherent trade-off. Cost Eff Resour Alloc 2014, 12(1):2. doi: 10.1186/1478-7547-12-2 24418267

29. Atkinson AB: On the measurement of inequality. J Econ Theory 1970, 2(3):244–263.

30. Bleichrodt H, van Doorslaer E: A welfare economics foundation for health inequality measurement. J Health Econ 2006, 25(5):945–957. doi: 10.1016/j.jhealeco.2006.01.002 16466818

31. Wagstaff A: Health care: QALYs and the equity-efficiency tradeoff. In: Cost-benefit analysis. Edited by Layard PRG, Glaister S, 2nd edn. Cambridge: Cambridge University Press; 1994: 428–447.

32. Bleichrodt H: Health utility indices and equity considerations. J Health Econ 1997, 16(1):65–91. 10167345

33. Olsen JA: Persons vs years: two ways of eliciting implicit weights. Health Econ 1994, 3(1):39–46. 8167798

34. Rodriguez-Miguez E, Pinto-Prades JL: Measuring the social importance of concentration or dispersion of individual health benefits. Health Econ 2002, 11(1):43–53. 11788981

35. Murray CJ: Rethinking DALYs. In: The global burden of disease: a comprehensive assessment of mortality and disability from diseases, injuries, and risk factors in 1990 and projected to 2020. Edited by Murray CJL, Lopez AD. Cambridge, MA: Published by the Harvard School of Public Health on behalf of the World Health Organization and the World Bank; Distributed by Harvard University Press; 1996: 1–98.

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2019 Číslo 10