# Fuzzy approach to decision analysis with multiple criteria and uncertainty in health technology assessment

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## Abstract

Decision making in health technology assessment (HTA) involves multiple criteria (clinical outcomes vs. cost) and risk (criteria measured with estimation error). A survey conducted among Polish HTA experts shows that opinions how to trade off health against money should be treated as fuzzy. We propose an approach that allows to introduce fuzziness into decision making process in HTA. Specifically, in the paper we (i) define a fuzzy preference relation between health technologies using an axiomatic approach; (ii) link it to the fuzzy willingness-to-pay and willingness-to-accept notions and show the survey results in Poland eliciting these; (iii) incorportate uncertainty additionally to fuzziness and define two concepts to support decision making: *fuzzy expected net benefit* and *fuzzy expected acceptability* (the counterparts of expected net benefit and cost-effectiveness acceptability curves, CEACs, often used in HTA). Illustrative examples show that our fuzzy approach may remove some problems with other methods (CEACs possibly being non-monotonic) and better illustrate the amount of uncertainty present in the decision problem. Our framework can be used in other multiple criteria decision problems under risk where trade-off coefficients between criteria are subjectively chosen.

## Keywords

Multiple criteria decision making Fuzzy preferences Uncertainty Health technology assessment Willingness to pay Preference elicitation## Notes

### Acknowledgments

It would not have been possible to collect the survey results presented in the paper without the help from M. Niewada, who facilitated the contact with the respondents. We would like to acknowledge the help of HTA experts who participated in the survey: K. J. Filipiak, K. Jahnz-Różyk, and the others, who opted to remain anonymous. We also express our gratitude to D. Golicki, T. Macioch, W. Wrona, and again M. Niewada, who commented on the first version of the survey.

## References

- Arrow, K. (1963). Uncertainty and the welfare economics of medical care.
*The American Economic Review*,*53*(5), 141–149.Google Scholar - Arrow, K., & Lind, R. (1970). Uncertainty and the evaluation of public intervention decisions.
*The American Economic Review*,*60*, 364–378.Google Scholar - Billingsley, P. (1999).
*Convergence of probability measures*(2nd ed.). New York: Wiley.CrossRefGoogle Scholar - Black, W. (1990). The CE Plane: A graphic representation of cost-effectiveness.
*Medical Decision Making*,*10*, 212–214.CrossRefGoogle Scholar - Bleichrodt, H., Wakker, P., & Johannesson, M. (1997). Characterizing QALYs by risk neutrality.
*Journal of Risk and Uncertainty*,*15*, 107–114.CrossRefGoogle Scholar - Briggs, A., Claxton, K., & Sculpher, M. (2006).
*Decision modelling for health economic evaluation*. Oxford: Oxford University Press.Google Scholar - Briggs, A., & Fenn, P. (1998). Confidence intervals or surfaces? Uncertainty on the cost-effectiveness plane.
*Health Economics*,*7*(8), 723–740.CrossRefGoogle Scholar - Briggs, A., Weinstein, M. C., Fenwick, E. A., Karnon, J., Sculpher, M. J., & Paltiel, A.D., on behalf of the ISPOR-SMDM Modeling Good Research Practices Task Force. (2012). Model parameter estimation and uncertainty analysis: A report of the ISPOR-SMDM Modeling Good Research Practices Task Force Working Group-6.
*Medical Decision Making*,*32*(5), 722–732.Google Scholar - Claxton, K. (1999). The irrelevance of inference: A decision-making approach to the stochastic evaluation of health care technologies.
*Journal of Health Economics*,*18*(3), 341–364.CrossRefGoogle Scholar - Devlin, N., & Parkin, D. (2004). Does NICE have a cost-effectiveness threshold and what other factors influence its decisions? A binary choice analysis.
*Health Economics*,*13*, 437–452.CrossRefGoogle Scholar - Eckermann, S., & Willan, A. (2011). Presenting evidence and summary measures to best inform societal decisions when comparing multiple strategies.
*Pharmacoeconomics*,*29*(7), 563–577.Google Scholar - Eichler, H. G., Kong, S., Gerth, W., Mavros, P., & Jönsson, B. (2004). Use of cost-effectiveness analysis in health-care resources allocation decision-making: How are cost-effectiveness thresholds expected to emerge?
*Value in Health*,*7*(5), 518–528.CrossRefGoogle Scholar - Fenwick, E., Claxton, K., & Sculpher, M. (2001). Representing uncertainty: The role of cost-effectiveness acceptability curves.
*Health Economics*,*10*(8), 779–787.CrossRefGoogle Scholar - Fenwick, E., O’Brien, B., & Briggs, A. (2004). Cost-effectiveness acceptability curves facts, fallacies and frequently asked questions.
*Health Economics*,*13*, 405–415.CrossRefGoogle Scholar - Gafni, A., & Birch, S. (2006). Incremental cost-effectiveness ratios (ICERs): The silence of the lambda.
*Social Science & Medicine*,*62*, 2091–2100.CrossRefGoogle Scholar - Garber, A. (2000). Advances in cost-effectiveness analysis of health interventions. In A. J. Culyer (Ed.),
*Handbook of health economics*(Vol. 1A, pp. 181–221). Amsterdam: North-Holland.Google Scholar - Gold, M., Siegel, J., Russell, L., & Weinstein, M. (Eds.). (1996).
*Cost-effectiveness in health and medicine*. Oxford: Oxford University Press.Google Scholar - Hunink, M. G., Bult, J. R., de Vries, J., & Weinstein, M. C. (1998). Uncertainty in decision models analyzing cost-effectiveness: The joint distribution of incremental costs and effectiveness evaluated with a nonparametric bootstrap method.
*Medical Decision Making*,*18*(3), 337–346.CrossRefGoogle Scholar - Jakubczyk, M., & Kamiński, B. (2010). Cost-effectiveness acceptability curves-caveats quantified.
*Health Economics*,*19*, 955–963.CrossRefGoogle Scholar - Kahneman, D., Knetsch, J., & Thaler, R. (2009). Experimental tests of the endowment effect and the coase theorem. In E. L. Khalil (Ed.),
*The new behavioral economics. Volume 3. Tastes for endowment, identitiy and the emotions*(Vol. 3, pp. 119–142). London: Elgar.Google Scholar - Klir, G., & Yuan, B. (1995).
*Fuzzy sets and fuzzy logic: Theory and applications*. Englewood Cliffs NJ: Prentice Hall.Google Scholar - Lee, K. (2005).
*First course on fuzzy theory and applications*. Berlin: Springer.Google Scholar - Löthgren, M., & Zethraeus, N. (2000). Definition, interpretation and calculation of cost-effectiveness acceptability curves.
*Health Economics*,*9*, 623–630.CrossRefGoogle Scholar - Moreno, E., Girón, F., Vázquez-Polo, F., & Negrín, M. (2010). Optimal healthcare decisions: Comparing medical treatments on a cost-effectiveness basis.
*European Journal of Operational Research*,*204*, 180–187.CrossRefGoogle Scholar - Moreno, E., Girón, F., Vázquez-Polo, F., & Negrín, M. (2013). Optimal treatments in cost-effectiveness analysis in the presence of covariates: Improving patient subgroup definition.
*European Journal of Operational Research*,*226*, 173–182.CrossRefGoogle Scholar - Obenchain, R. (1997). Issues and algorithms in cost-effectiveness inference.
*Biopharmaceutical Report*,*5*(2), 1–7.Google Scholar - Obenchain, R. (2008). ICE preference maps: Nonlinear generalizations of net benefit and acceptability.
*Health Services and Outcomes Research Methodology*,*8*, 31–56.CrossRefGoogle Scholar - O’Brien, B., Gertsen, K., Willan, A., & Faulkner, L. (2002). Is there a kink in consumers’ threshold value for cost-effectiveness in health care?
*Health Economics*,*11*, 175–180.CrossRefGoogle Scholar - Pliskin, J., Shepard, D., & Weinstein, M. (1980). Utility functions for life years and health status.
*Operations Research*,*28*(1), 206–224.CrossRefGoogle Scholar - Sadatsafavi, M., Najafzadeh, M., & Marra, C. (2008). Acceptability curves could be misleading when correlated strategies are compared.
*Medical Decision Making*,*28*(3), 306–307.CrossRefGoogle Scholar - Severens, J., Brunenberg, D., Fenwick, E., O’Brien, B., & Joore, M. (2005). Cost-effectiveness acceptability curves and a reluctance to lose.
*Pharmacoeconomics*,*23*(12), 1207–1214.CrossRefGoogle Scholar - van Hout, B., Al, M., Gordon, G., & Rutten, F. (1994). Costs, effects and C:E-ratios alongside a clinical trial.
*Health Economics*,*3*, 309–319.CrossRefGoogle Scholar - Weinstein, M., & Zeckhauser, R. (1973). Critical ratios and efficient allocation.
*Journal of Public Economics*,*2*, 147–157.CrossRefGoogle Scholar - Zaric, G. (2010). Cost-effectiveness analysis, health-care policy, and operations research models. In
*Wiley Encyclopedia of operations research and management science*, Wiley. doi: 10.1002/9780470400531.eorms0202. - Zivin, J., & Bridges, J. (2002). Addressing risk preferences in cost-effectiveness analysis.
*Applied Health Economics and Health Policy*,*1*(3), 135–139.Google Scholar