Skip to main content
SpringerLink
Log in

Estimating the Crossover Point of a Fuzzy Willingness-to-Pay/Accept for Health to Support Decision Making

  • Conference paper
  • First Online:
Recent Advances in Mathematical and Statistical Methods (AMMCS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 259))

  • 855 Accesses

Abstract

Selecting health technologies to finance with public money requires juxtaposing their cost and health gains. Determining the exact values of willingness-to-pay/willingness-to-accept (WTP/WTA) may be difficult and considered unethical. As a solution, both may be treated as fuzzy sets. Then, a crossover-point (CP) of a fuzzy WTP is such a value that a decision maker is just as convinced as unconvinced it is worth paying for a unit of health (analogously for fuzzy WTA). In this fuzzy approach, I motivate why health technologies should be compared using CPs. I introduce three statistical methods of assessing the CP based on random-samples, survey data: using hypothesis testing, Bayesian hierarchical modelling, and frequentist estimation. I use the previously published dataset for Poland and show how the methods may be employed. The results suggest no (significant) difference in CPs for fuzzy WTP and WTA, but more stochastic uncertainty regarding the latter. The estimation methods can be used to assess the fuzzy preferences in other decision problem contexts.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In applied CEA it is more common to calculate the incremental cost-effectiveness ratios and compare them with WTP, algebraically equivalent to maximizing NB [5].

  2. 2.

    This approach can also be seen (not pursued formally, for brevity) as applying the Orlovsky-score [11]: maximizing the degree to which a given alternative is not dominated by others.

  3. 3.

    The explanation is done for WTP, but refers to WTA mutatis mutandis.

  4. 4.

    Example 1: if the respondent selected option 4 for \(\lambda =100\), option 3 for \(\lambda =125\) and \(\lambda =150\), and option 2 for \(\lambda =175\), then \(C\!R=[112.5; 162.5]\). Example 2: if the respondent selected option 4 for \(\lambda =100\) and immediately switched to option 2 for \(\lambda =125\), then \(C\!R=[106.25; 118.75]\).

  5. 5.

    1 \(\nicefrac {{\text {PLN}}}{{\text {QALY}}}\) added, to avoid \(\ln (0)\).

  6. 6.

    Taking the logs, conveniently, allows using a normal distribution, as the non-log CR are bounded by zero from below.

References

  1. Bellavance, F., Dionne, G., Lebeau, M.: The value of a statistical life: a meta-analysis with a mixed effects regression model. J. Health Econ. 28(2), 444–464 (2009)

    Article  Google Scholar 

  2. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  3. Dykstra, R., Kochar, S., Robertson, T.: Likelihood ratio tests for symmetry against one-sided alternatives. Ann. Inst. Stat. Math. 47(4), 719–730 (1995)

    Article  MathSciNet  Google Scholar 

  4. Jakubczyk, M., Kamiński, B.: Fuzzy approach to decision analysis with multiple criteria and uncertainty in health technology assessment. Ann. Oper. Res. 251, 301–324 (2017)

    Article  MathSciNet  Google Scholar 

  5. Jakubczyk, M.: Using a fuzzy approach in multi-criteria decision making with multiple alternatives in health care. Multiple Criteria Decis. Making 10, 65–81 (2015)

    Google Scholar 

  6. Jakubiak-Lasocka, J., Jakubczyk, M.: Cost-effectiveness versus cost-utility analyses: what are the motives behind using each and how do their results differ?-a Polish example. Value Health Reg. Issues 4C, 66–74 (2014)

    Article  Google Scholar 

  7. Lee, C., Chertow, G., Zenios, S.: An empiric estimate of the value of life: updating the renal dialysis cost-effectiveness standard. Value Health 12(1), 80–87 (2009)

    Article  Google Scholar 

  8. Lindhjem, H., Navrud, S., Braathen, N., Biausque, V.: Valuing mortality risk reductions from environmental, transport, and health policies: a global meta-analysis of stated preference studies. Risk Anal. 31(9), 1381–1407 (2011)

    Article  Google Scholar 

  9. Matell, M., Jacoby, J.: Is there an optimal number of alternatives for Likert-scale items? effects of testing time and scale properties. J. Appl. Psychol. 56(6), 506–509 (1972)

    Article  Google Scholar 

  10. Neumann, P., Cohen, J., Weinstein, M.: Updating cost-effectiveness-the curious resilience of the $50,000-per-QALY threshold. N. Engl. J. Med. 371(9), 796–797 (2014)

    Article  Google Scholar 

  11. Orlovsky, S.: Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1, 155–167 (1978)

    Article  MathSciNet  Google Scholar 

  12. Whitehead, A.: Meta-Analysis of Controlled Clinical Trials, 1st edn. Wiley (2002)

    Google Scholar 

  13. Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

Download references

Acknowledgements

The research was financed by the funds obtained from National Science Centre, Poland, granted following the decision number DEC-2015/19/B/HS4/01729.

Author information

Authors and Affiliations

  1. Decision Analysis and Support Unit, SGH Warsaw School of Economics, Al. Niepodległości 162, 02-554, Warsaw, Poland

    Michał Jakubczyk

Authors
  1. Michał Jakubczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michał Jakubczyk .

Editor information

Editors and Affiliations

  1. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    D. Marc Kilgour

  2. Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada

    Herb Kunze

  3. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roman Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roderick Melnik

  5. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Xu Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jakubczyk, M. (2018). Estimating the Crossover Point of a Fuzzy Willingness-to-Pay/Accept for Health to Support Decision Making. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_39

Download citation

Publish with us

Policies and ethics

Search

Navigation