Quality-Adjusted Life-Years without Constant Proportionality

Background: A quality-adjusted life-year is a common unit of measurement in health valuation. Under its constant proportionality assumption, the value of a quality-adjusted life span is defined as the product of preference weight and life span. Objectives: To empirically identify an alternative functional relationship between life span and value by relaxing the constant proportionality assumption. Methods: Using an online survey, 5367 respondents completed 30 to 40 paired comparisons where each involved a choice between two health outcomes: one with a longer life span and health problems (five-level EuroQol five-dimensional questionnaire) and the other with a shorter life span and no problems (time trade-off pair). Using 2670 pairs, a saturated model with indicator variables for 27 life spans and 90 health problems of varying duration and severity was estimated by maximum likelihood. Its coefficients empirically illustrate the relationship between life span and value on a quality-adjusted life-year scale. Results: The results reject constant proportionality (P < 0.01) and support the use of a power function to describe the relationship between life span and value, namely, value = preference weight x life span(beta) The estimate of power (beta = 0.415; 95% confidence interval 0.41-0.42) appears to depend on whether life span was expressed in a temporal unit of days (0.403), weeks (0.509), months (0.541), or years (0.654). Conclusions: Raising life span to a power less than 1 implies decreasing marginal value of life span and greatly improved model fit, and confirms previous violations of proportionality. This power function may replace conventional assumptions in health valuation studies. Nevertheless, governmental agencies may favor a longer time horizon than that of the general population.