, Volume 8, Issue 1, pp 31-56,
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ICE preference maps: nonlinear generalizations of net benefit and acceptability


The Net Benefit (NB) approach to Incremental Cost-Effectiveness (ICE) statistical inference uses a linear function (map) to assign a real valued, numerical preference score to every point on the 2-dimensional ICE plane. We argue that coherent ICE preferences satisfy four intuitive axioms and propose a 2-parameter family of maps that satisfy these axioms and provide highly realistic generalizations of NB. For example, nonlinear maps do not require that returns-to-scale be linear (constant) or that willingness-to-pay (WTP) and willingness-to-accept (WTA) are both equal to the shadow price of health, λ. In fact, all of our maps have the property that \( \lambda = {\sqrt {{\text{WTP}} \times {\text{WTA}}} }. \) With λ held fixed, this geometric mean relationship shows that WTA must decrease when WTP increases and vice versa. This relationship thus provides not only a polar angular measure of the size of “Bernie’s Kink,” WTP < WTA, but also the theoretical basis for Buckingham’s ALICE curve generalization of acceptability. Finally, we argue that uncertainty about economic preferences expressed by varying λ can totally swamp the statistical uncertainty in patient level data expressed by a wedge-shaped, bootstrap ICE confidence region that does not depend upon λ in the sense that it is equivariant under changes in λ.

Financial support for this research was provided entirely by Eli Lilly and Company. The author’s independence in writing and publishing his research is ensured by Lilly’s published Principles of Medical Research. The author is a retired pensioner and a stockholder of Eli Lilly and Company.
An erratum to this article can be found at http://dx.doi.org/10.1007/s10742-008-0034-y