Logical inconsistencies in the health years in total and equal value of life years gained

This is the author accepted manuscriptObjectives: To assess whether recently-proposed alternatives to the quality-adjusted life year (QALY), intended to address concerns about discrimination, are suitable for informing resource allocation decisions. Methods: We consider two alternatives to the QALY: the Health Years in Total (HYT), recently proposed by Basu et al., and the Equal Value of Life Years Gained (evLYG), currently used by the Institute for Clinical and Economic Review. For completeness we also consider unweighted life years (LYs). Using a hypothetical example comparing three mutually exclusive treatment options, we consider how calculations are performed under each approach and whether the 2 resulting rankings are logically consistent. We also explore some further challenges that arise from the unique properties of the HYT approach. Results: The HYT and evLYG approaches can result in logical inconsistencies that do not arise under the QALY or LY approaches. HYT can violate the independence of irrelevant alternatives axiom, while the evLYG can produce an unstable ranking of treatment options. HYT have additional issues, including an implausible assumption that the utilities associated with healthrelated quality-of-life (HRQoL) and life years are ‘separable’, and a consideration of ‘counterfactual’ HRQoL for patients who are dead. Conclusions: The HYT and evLYG approaches can result in logically inconsistent decisions. We recommend that decision makers avoid these approaches, and that the logical consistency of any approaches proposed in future be thoroughly explored before considering their use in practice