How Much Better is Faster? Value Adjustments for Health-Improvement Sequences

While the quality-adjusted life-year construct has advantages of simplicity and consistency, simplicity requires strong assumptions. In particular, standard assumptions result in health-state utility functions that are unrealistically linear and separable in risk and duration. Consequently, sequencing of a series of health improvements has no effect on the total value of the sequence because each increment is assessed independently of previous increments. Utility functions in nearly all other areas of applied economics are assumed to be nonlinear with diminishing marginal utility so it matters where an improvement occurs in a sequence. We construct a conceptual framework that that demonstrates how diminishing marginal utility for health improvements could affect preferences for different sequence patterns. Using this framework, we derive conditions for which the sum of conventional health-state utilities understates, overstates, or approximates the sequence-sensitive value of health improvements. These patterns suggest the direction and magnitude of possible adjustments to conventional value calculations. We provide numerical examples and identify recent studies whose results are consistent with the conceptual model.