R: Set Parameter Values defining ICE Economic Preference Maps

ICEepmap

R Documentation

Set Parameter Values defining ICE Economic Preference Maps

Description

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 use alias axis rescaling so that the equivariance property of the
wedge-shaped ICE confidence region is depicted as if it were 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.

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

beta

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.

gamma

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).

eta

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.

Details

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.

Value

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

lambda

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

beta

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

gamma

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

Author(s)

Bob Obenchain <wizbob@att.net>

References

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. 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.

Obenchain RL. ICEinR.pdf Vignette-like documentation for ICEinfer
stored in the R library/ICEinfer/doc folder. 2009; 30 pages.

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'license()' or 'licence()' for distribution details.
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Type 'contributors()' for more information and
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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(ICEinfer)
Loading required package: lattice
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/ICEinfer/ICEepmap.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ICEepmap
> ### Title: Set Parameter Values defining ICE Economic Preference Maps
> ### Aliases: ICEepmap ICEomega
> ### Keywords: methods
>
> ### ** Examples
>
> pm <- ICEomega(beta=0.8)
> require(lattice)
> plot(pm)
>
>
>
>
>
> dev.off()
null device
1
>