Modeling Ranking, Time Trade-Off, and Visual Analog Scale Values for EQ-5D Health States: A Review and Comparison of Methods

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There is rising interest in eliciting health state valuations using rankings. Due to their relative simplicity, ordinal measurement methods may offer an attractive practical alternative to cardinal methods, such as time trade-off (TTO) and visual analog scale (VAS). In this article, we explore alternative models for estimating cardinal health state values from rank responses in a unique multicountry database. We highlight an estimation challenge pertaining to health states just below perfect health (the “nonoptimal gap”) and propose an analytic solution to ameliorate this problem.


Using a standardized protocol developed by the EuroQol Group, rank, VAS, and TTO responses were collected for 43 health states in 8 countries: Slovenia, Argentina, Denmark, Japan, Netherlands, Spain, United Kingdom, and United States, yielding a sample of 179,431 state responses from 11,483 subjects. States were described using the EQ-5D system, which allows for 3 different possible levels on 5 different dimensions of health. We estimated conditional logit and probit regression models for rank responses. The regressions included 17 health state attribute variables reflecting specific levels on each dimension and counts of different levels across dimensions. This flexible specification accommodates previously published valuation models, such as models applied in the United Kingdom and United States. In addition to fitting standard conditional logit and probit models, which assume equal variance across health states (homoscedasticity), we examined a heteroscedastic probit model that assumes no variance for the 2 points anchoring the scale (“optimal health” and “dead”) and relaxes the equal-variance assumption for all other states. Rank-based predictions for the 243 unique states defined by the EQ-5D system were compared with predictions from conventional linear models fitted to TTO and VAS responses.


By construction, the TTO and VAS models assume no variance around the anchoring states of optimal health and dead. Mimicking this assumption in the probit rank models helps dissolve the nonoptimal gap. For all other states, variances in TTO and VAS were negatively associated with mean values, which contradict the assumption of homoscedasticity. Estimated health state values from the heteroscedastic probit model for the ranking data were highly correlated with predictions from both TTO and VAS models for the 243 EQ-5D states. Between VAS and rank-based estimates, Lin's ρ, a measure of agreement, was over 0.98 with a mean absolute difference of 0.028. Corresponding measures of agreement between rank and TTO estimates were 0.96 and 0.12, which is similar to the agreement between VAS and TTO.


Rank-based valuation techniques, which offer advantages of flexibility, generalizability, and ease of administration, may be attractive substitutes for TTO and VAS in the measurement of societal values for health outcomes.

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