[7] ICE Acceptability: VAGR versus ALICE?
The concept of ICE "acceptability" originated in the publication: Van Hout BA, Al MJ, Gordon GS, Rutten FFH. Costs, effects and C/E ratios alongside a clinical trial. Health Econ 1994; 3: 309319.
The alternative (Acceptability Levels In Cost Effectineness) definition is newer; see Figures 7 and 8 of Obenchain RL. Issues and algorithms in costeffectiveness inference. Biopharmaceutical Reports 1997; 5(2): 17. Washington, DC: American Statistical Association.
As is clear from the following table, the only difference in definitions of "acceptability" between these two alternative approaches occurs within the SouthWest ICE Quadrant:
ICE quadrant 
VAGR Definition 
ALICE Definition

DeltaC > 0, DeltaE > 0 NE quadrant

Acceptable if DeltaC / DeltaE is less than Lambda times s. 
Acceptable if DeltaC / DeltaE is less than Lambda times s = WTP. 
DeltaC < 0, DeltaE > 0 SE quadrant 
All outcomes are Acceptable. 
All outcomes are Acceptable. 
DeltaC < 0, DeltaE < 0 SW quadrant

Acceptable if DeltaC / DeltaE is greater than Lambda times s. 
Acceptable if DeltaC / DeltaE is greater than Lambda /s = WTA. 
DeltaC > 0, DeltaE < 0 NW quadrant 
No outcomes are Acceptable. 
No outcomes are Acceptable. 
DeltaC = Incremental Difference in Average Cost (Treated minus Control.)
DeltaE = Incremental Difference in Average Effectiveness (Treated minus Control.)
Lambda is a fixed value for the "Shadow Price of Health"
expressed in DeltaC / DeltaE units.
The standardized ICE slope, s = x/y, is a positive, unitless scalar that is
forced to vary between zero and infinity.
Note that the ALICE approach uses a "kinked frontier" ...with the WTP ray in the NE quadrant having slope Lambda times s while the WTA ray in the SW quadrant has slope Lambda / s. The product of the WTP and WTA slopes thus clearly satisfies Bob O's "LINK" function:
See equation (5) and Section 7 of Obenchain RL. [ICE Preference Maps: Nonlinear Generalizations of Net Benefit and Acceptability. Health Services and Outcomes Research Methodology 2008; 8: 3156] for a discussion of the following "highuncertainty" numerical example. Note that the VAGR acceptability curve is nonmonotone here and is badly biased relative to the (always monotone) ALICE curve. My ICEinfer Rpackage contains functions to make bootstrap acceptability calculations and produce the following graphical / tabular displays:
The horizontal axis of an ALICE plot displays ICE angle, theta = 45 + ArcTan(s).
Note that theta increases only from 45 degrees to 135 degrees (a finite range) as
s and WTP increase from 0 to infinity (an infinite range) and as 1/s and WTA decrease from
infinity to 0 (an infinite range.) In fact, WTP = WTA = Lambda only when theta = 90 degrees.