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Updated: Jan 8, 2026

Measuring Delay Discounting in Humans Using an Adjusting Amount Task
Published on: January 9, 2016
GRACEユーティリティと支払い意思額補正の推定に関する実用的な方法
Anirban Basu1, Darius Lakdawalla1
1The CHOICE Institute University of Washington, National Bureau of Economic Research, Seattle, Washington, USA; Schaeffer Center for Health Policy and Economics, University of Southern California, National Bureau of Economic Research, Los Angeles, California, USA.
Objective:
Commonly used health-related utility measures fail to account for risk preferences. Generalized Risk-Adjusted Cost-Effectiveness (GRACE) solves this problem, but it currently requires visual analogue scale (VAS) measures of health states, which may not be available to the analyst. We develop an empirically based approach for constructing GRACE utilities from existing time tradeoff (TTO) utilities.
Methods:
Using nationally representative patient-level data on both VAS and TTO measures of health states, we estimate a mapping from TTO to VAS. Using published estimates of GRACE utility over the VAS domain, we present estimates allowing analysts to map from existing TTO utility to GRACE and to make corresponding willingness-to-pay threshold corrections.
Results:
Compared to expo-power and hyperbolic absolute risk-aversion (HARA) models, a linear model provides the best mapping from TTO utilities to VAS measures of health state. We find TTO utilities approximate VAS reasonably well for moderate health state utilities but suffer from more approximation error elsewhere. Notably, TTO underestimates VAS health for the sickest health states, e.g., for TTO levels below 0.4.
Conclusion:
A straightforward linear mapping permits analysts to estimate GRACE using traditional TTO health state utilities. Many existing studies use time tradeoff (TTO) utilities in place of VAS. Our results suggest that this existing approach underestimates the GRACE value of health improvements for the sickest patients. Our study provides a solution without requiring generation of new data.
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