Kinky Thresholds Revisited: Opportunity Costs Differ in the NE and SW Quadrants

Historically, a kinked threshold line on the cost-effectiveness plane at the origin was suggested due to differences in willingness to pay (WTP) for health gain with trade-offs in the north-east (NE) quadrant versus willingness to accept (WTA) cost reductions for health loss with trade-offs in the south-west (SW) quadrant. Empirically, WTA is greater than WTP for equivalent units of health, a finding supported by loss aversion under prospect theory. More recently, appropriate threshold values for health effects have been shown to require an endogenous consideration of the opportunity cost of alternative actions in budget-constrained health systems, but also allocative and displacement inefficiency observed in health system practice. Allocative and displacement inefficiency arise in health systems where the least cost-effective program in contraction has a higher incremental cost-effectiveness ratio (ICER = m) than the most cost-effective program in expansion (ICER = n) and displaced services (ICER = d), respectively. The health shadow price derived by Pekarsky, $$ \left( {\frac{1}{n} + \frac{1}{d} - \frac{1}{m}} \right)^{ - 1} , $$ 1 n + 1 d - 1 m - 1 , reflects the opportunity cost of best alternative adoption and financing actions in reimbursing new technology with expected incremental costs and net effect allowing for allocative (n > m), and displacement, inefficiency (d > m). This provides an appropriate threshold value for the NE quadrant. In this paper, I show that for trade-offs in the SW quadrant, where new strategies have lower expected net cost while lower expected net effect than current practice, the opportunity cost is contraction of the least cost-effective program, with threshold ICER m. That is, in the SW quadrant, the cost reduction per unit of decreased effect should be compared with the appropriate opportunity cost, best alternative generation of funding. Consequently, appropriate consideration of opportunity cost produces a kink in the threshold at the origin, with the health shadow price in the NE quadrant and ICER of the least cost-effective program in contraction (m) in the SW quadrant having the same general shape as that previously suggested by WTP versus WTA. The extent of this kink depends on the degree of allocative and displacement inefficiency, with no kink in the threshold line strictly only appropriate with complete allocative and displacement efficiency, that is n = d = m. Copyright Springer International Publishing Switzerland 2015