ICEepmap: Set Parameter Values defining ICE Economic Preference Maps

Description Usage Arguments Details Value Author(s) References See Also Examples


ICEepmap() and ICEomega() set numerical values for lambda (the full, fair shadow price of health) and for the two so-called power-parameters of a parametric ICE Preference Map. These functions return a value, epm, that is an output list object of class ICEepmap for display using print(epm) or plot(epm, xygrid). The primary purpose of such plots is to allow the user to more easily visualize the profound effects that changing numerical values for lambda, beta and either gamma or eta = gamma / beta can have on the iso-preference contours (level curves) of an ICE map.

From the statistical prospective championed here, lambda is little more than a nusiance parameter. For example, the wedge-shaped ICE confidence regions formed by ICEwedge() are equivariant under changes in lambda. Unfortunately, the resulting economic preferences that can be visualized using ICEcolor() can change drastically with changes in lambda.

A stardardized ICE map results when the specified value of lambda is used to assure that the x effe difference and the y cost difference are both expressed in the same units (i.e. both in cost units or else both in effe units.) Unfortunately, the only way to assure display of this particular sort of rescaling in ICE plane depictions is to use alibi = TRUE in plot.ICEuncrt(). Both plot.ICEwedge() and plot.ICEcolor() always default to alias axis scaling. Thus the equivariance property of the ICE confidence wedge is depicted as if the rays determining its upper and lower limits are invariant under changes in lambda.

The easy way to visualize a standardized ICE map is to always use the default value of lambda = 1 in ICEepmap() and ICEomega(). A standardized ICE map always has the following two characteristics: [i] it always assigns a zero overall preference to all (x, y) outcomes everywhere along the x = y ICE diagonal, and [ii] its iso-preference contours are always exactly symmetric about the x = -y (upper-left to lower-right) ICE diagonal.


  ICEepmap(lambda = 1, beta = 1, gamma = 3+2*sqrt(2)) 
  ICEomega(lambda = 1, beta = 1, eta = 3+2*sqrt(2))



Positive value for the fair, full-retail Shadow Price of Health.


Positive Returns-to-Scale Power parameter for the ICE Preference Map. beta = 1 implies linear (constant) Returns-to-Scale. A beta > 0 and < 1 implies diminishing Returns-to-Scale. A beta > 1 implies increasing Returns-to-Scale.


Positive Directional Power parameter for ICEepmap(). The smallest reasonable value for gamma is usually gamma = beta, which yields a (generalized) linear map. The largest reasonable value for gamma is usually gamma = beta*(3+2*sgrt(2)), which yields a map that satisfies Cartesian Monotonicity and also yields WTP and WTA values within [0, +Inf).


Positive Power Parameter Ratio for ICEomega(). Generalized linear maps result when eta = 1. The eta for the more realistic Nonlinear maps is greater than one, but not greater than the ICE Omega limit of (3+2*sgrt(2)), which is approximately 5.828. This upper limit on eta is required to assure that Cartesian Monotonicity of preferences holds.


The ICEepmap() and ICEomega() functions specify numerical values for the Shadow Price of Health Parameter, lambda, for the Returns to Scale Power Parameter, beta, and for either the Directional Power Parameter, gamma, or else the Power Parameter Ratio, eta = gamma / beta.


Object of class ICEepmap containing an output list with the following items:


Saved positive value of Shadow Price of Health, lambda, read by the print and plot methods for objects of class ICEepmap.


Saved Positive Returns-to-Scale Power parameter, beta, read by the print and plot methods for objects of class ICEepmap.


Saved Positive Directional Power parameter, gamma, read by the print and plot methods for objects of class ICEepmap.


Bob Obenchain <>


Cook JR, Heyse JF. Use of an angular transformation for ratio estimation in cost-effectiveness analysis. Statistics in Medicine 2000; 19: 2989-3003.

Obenchain RL. Incremental Cost-Effectiveness (ICE) Preference Maps. 2001 JSM Proceedings (Biopharmaceutical Section) on CD-ROM. (10 pages.) Alexandria, VA: American Statistical Association. 2002.

Obenchain RL. ICE Preference Maps: Nonlinear Generalizations of Net Benefit and Acceptability. Health Serv Outcomes Res Method 2008; 8: 31-56. DOI 10.1007/s10742-007-0027-2. Open Access.

See Also

plot.ICEepmap and print.ICEepmap


 pm <- ICEomega(beta=0.8)

Example output

Loading required package: lattice

ICEinfer documentation built on Oct. 23, 2020, 8:31 p.m.