Utility functions for life years and health status: An additional remark

Utility-based measures for health-related quality of life gain more and more importance in cost-effectiveness analysis. The axiomatic foundation qualifies them as decision weights in use of the QALY concept. But their use is strained for they are loaded with assumptions to make them work. Pliskin et al. (1980) have impressively shown which assumptions might be reasonable to combine quality of life with length of life, those attributes fundamental to the QALY concept. One of those assumptions is the so called "constant proportional tradeoff". It states that people will always sacrifice the same proportion of remaining life years in order to gain better health. This assumption restricts the underlying utility functions for life years to those consistent with constant proportional risk posture, i.e. power, logarithmic and linear function. However, these types of function might be too restrictive for they do not reflect "constant absolut tradeoff". That means people might rather exchange the same number of life years for better health, independent of remaining life expectancy. Pliskin et al. mentioned that case already and suggested the exponential function as a propper function to reflect the underlying constant absolut risk posture. I will deliver its proof. In addition, a survey among Tinnitus patients is mentioned that could further stress the validity of those functions.