# ICEpref: Compute ICE Economic Preference Scores from Numeric Cost and... In ICEinfer: Incremental Cost-Effectiveness Inference using Two Unbiased Samples

## Description

This function calculates Incremental Net Monetary Benefit (INMB) Scores that are expressed in Cost units. While these scores are of "linear" form, (lambda * Effe) - Cost, when eta == gamma / beta == 1, they are "Nonlinear" when eta is either > 1 or < 1.

## Usage

 `1` ``` ICEpref(tr, ex, cy, lambda = 1, beta = 1, eta = 3 + 2 * sqrt(2)) ```

## Arguments

 `tr` Binary [0 or 1] indicator of Treatment Regimen received by each patient [Experimental Unit]: tr == 0 denotes the "Standard" Regimen, tr == 1 denotes a "New" Regimen. `ex` Numeric vector representing Effe measures observed for 2 or more experimental units. `cy` Corresponding numeric vector reporting Total Cost Incurred by patients during treatment. The tr, ex and cy vectors must be of the same length, n >= 2, and 1 < sum(tr) < n. `lambda` Positive value for the fair, full-retail Shadow Price of Health. When ex is measured in QALYs and cy in U.S. Dollars, lambda = 50000 is traditionally assumed appropriate. `beta` Positive Returns-to-Scale Power parameter for ICE Preference calculations. beta = 1 implies Linear (Constant) Returns-to-Scale. A beta > 0 but < 1 implies Returns-to-Scale that are Diminishing and tend to be highly Realistic. Any beta > 1 implies Increasing Returns-to-Scale. `eta` Positive Power Parameter Ratio: gamma / beta. Generalized "linear" maps result when eta = 1. An eta ratio > 1 can yield a realistic "Nonlinear" map, but maps with eta > 3+2*sqrt(2) = 5.828 (Obenchain's "Omega") violate the "Cartesian Monotonicity" Axiom.

## Value

Object of class "numeric" of the same length as the tr, ex and cy vectors input:

 `pref` Computed ICE Economic Preference Scores.

## Author(s)

Bob Obenchain <wizbob@att.net>

## References

Hoch JS, Briggs AH, Willan AR. Something old, something new, something borrowed, something blue: a framework for the marriage of health econometrics and cost-effectiveness analysis. Health Economics 2002; 11: 415-430.

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.

`plot.ICEepmap` and `print.ICEepmap`
 ```1 2 3 4``` ``` data(sepsis) attach(sepsis) icedr <- ICEpref(tr=icu, ex=qalypres, cy=totcost, lambda=50000, beta=0.6) # Diminishing Returns. summary(icedr) ```