QALYs, HYEs and individual preferences-- A graphical illustration

The choice of outcome measure in cost-utility analysis has been a matter of concern. In particular the theoretical properties of quality-adjusted life-years (QALYs) and healthy-years equivalents (HYEs) have been debated. In this paper the underlying preference assumptions of QALYs and HYEs are illustrated graphically. For QALYs the assumptions of mutual utility independence, constant proportional trade-off, and risk neutrality are explained and illustrated. Mutual utility independence is shown to guarantee that the quality weight with the standard gamble method is independent of the number of years in the health state and constant proportional trade-off is shown to guarantee that the quality weight with the time-trade-off method is independent of the number of years in the health state. Together these two assumptions leads to a utility function over life-years that exhibits constant proportional risk posture, which is the basis for the risk-adjusted QALY model. The more commonly used risk-neutral QALY model is shown to be a valid cardinal utility function if risk neutrality over life-years holds for all health states. For HYEs to be a valid cardinal utility function the somewhat less restrictive assumption of risk neutrality over life-years in full health has to be made. It is also shown graphically that the proposed two-stage procedure to measure HYEs in theory gives the same result as directly using the time-trade-off method. Finally, it is shown that by estimating the certainty-equivalent number of HYEs it is possible in theory to obtain a measure that will always rank risky health profiles according to individual preferences. It is concluded that further empirical work should be undertaken to test the ranking properties of the different measures.