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

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.