Estimating the Fuzzy Trade-Offs Between Health Dimensions with Standard Time Trade-Off Data

  • Michał JakubczykEmail author
  • Dominik Golicki
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 642)


Optimizing health provision requires measuring health, best using societal preferences. Health-related quality of life is evaluated with multiple criteria (e.g. feeling pain or being depressed), and their importance must be quantified. In a time trade-off (TTO) elicitation method, worsening in various attributes is compared with shortening the duration of life—a task unlike everyday experience. Therefore, we claim the trade-off coefficients should be treated as fuzzy numbers to allow imprecision. Additionally, a typical TTO protocol allows only limited number of final outcomes, enforcing approximate answers. In our model, we assume the respondent terminates TTO when the implied utility falls within the 1-cut of the true fuzzy disutility (normal and rectangular, simplifying). We show how to estimate such disutilities with standard TTO data (existing datasets can be used) in the hierarchical Bayesian setting. We test our approach on data collected in Poland with EQ-5D-3L descriptive system. For example, the disutility of worsening mobility to level 2 or 3 results (on average) in a disutility with 1-cut equal to [0.076–0.089] or [0.398–0.483], respectively. Standard errors of interval bounds estimates amount to ca. 5%–15% of their values. We construct a fuzzy value set assigning fuzzy utilities to all 243 EQ-5D-3L health states. The fuzzy disutilities tend to be larger than the standard, crisp ones (e.g. the crisp parameters for mobility amount to 0.056 and 0.313, respectively), and the resulting fuzzy value set assigns lower values to utilities than the crisp one.


Preference elicitation Utility Fuzzy numbers Time trade-off Imprecise preferences Multiple-criteria decision making 



The research was financed by the funds obtained from National Science Centre, Poland, granted following the decision number DEC-2015/19/B/HS4/01729. We would like to thank Juan-Manuel Ramos Goñi for comments on the initial results presented during the EuroQol Group Meeting in Berlin, 2016.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Decision Analysis and Support UnitSGH Warsaw School of EconomicsWarsawPoland
  2. 2.Department of Experimental and Clinical PharmacologyMedical University of WarsawWarsawPoland

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