Are Utilities Bounded at 1.0? Implications for Statistical Analysis and Scale Development

Acareful consideration of the fundamental characteristics of preference-based QALY weights (hereafter referred to as utilities for simplicity) can help us better understand how we should approach their statistical estimation. In an article in this issue, Pullenayegum and others 1 argue: ‘‘Although negative utilities are allowed because there are health states worse than death, utilities cannot exceed 1 because you cannot do better than full health.’’ Based on this argument, the authors suggest that censored regression models (such as Tobit and CLAD) are biased and that specific statistical analyses and/or manipulations should be used to estimate marginal coefficients. In this commentary, I argue the opposing view that the basic characteristics of utilities require that scores can exceed 1.0. As a result, censored regression models such as Tobit or CLAD should be used to estimate unbiased estimates of utilities that can exceed 1.0. By convention, utilities are anchored at 0.0 (death) and 1.0 (full health). Theoretically, utilities are interval scaled and could take on any 2 arbitrary values as the anchors for death and full health as long as the value for death is below that for full health. 2 An analogous interval scale is temperature, with reference points at freezing and boiling. Temperatures can exceed the boiling point and the freezing point. Within the context of QALYs, selecting reference points at death and full health is particularly convenient and meaningful. Assigning a value of 0.0 for death ensures that when a patient enters the death state, QALYs cease to accrue. (If death