Description Details Author(s) References Examples

Functions in the ICE Statistical Inference package make head-to-head comparisons between patients in two treatment cohorts (assumed to be unbiased samples) in two distinct dimensions, cost and effectiveness.

Bootstrap resampling methods quantify the endogenous Distribution of ICE Uncertainty and define Wedge-Shaped Statistical Confidence Regions equivariant relative to exogenous choice for the numerical Shadow Price of Health, lambda.

Preference maps with (linear or nonlinear) indiference curves can be viewed or superimposed upon endogenous confidence wedges to illustrate that considerable additional, potentially self-contradictory Economic Preference Uncertainty results from deliberately varying lambda.

Package: | ICEinfer |

Type: | Package |

Version: | 1.3 |

Date: | 2020-10-10 |

License: | GNU GENERAL PUBLIC LICENSE, Version 2, June 1991 |

Statistical inference using functions from the ICEinfer package usually starts with (possibly multiple) invocations of ICEscale() to help determine a reasonable value for the Shadow Price of Health, lambda. This is invariably followed by a single call to ICEuncrt to generate the Bootstrap Distribution of ICE Uncertainty corresponding to the chosen value of lambda. The print() and plot() functions for objects of type ICEuncrt have optional arguments, lfact and swu, to help users quantify and visualize the consequences of changing lambda and switching between cost and effe units.

A single call to ICEwedge() then yields the equivariant, wedge-shaped region of specified statistical confidence within [.50, .99] ...by computing ICE Angle Order Statistics around a circle with center at the ICE Origin: (DeltaEffe, DeltaCost) = (0, 0).

Researchers wishing to view alternative ICE Acceptability Curves would then envoke ICEalice().

Finally, multiple calls to ICEcolor for different values of lambda and/or different forms of (linear or nonlinear) ICE Preference Maps are typically used to illustrate the considerable additional Economic Preference Uncertainty that can be introduced in these ways. This Economic Preference uncertainty is superimposed on top of the inherent Statistical Uncertainty contained within even unbiased, patient level data on the relative cost and effectiveness of two treatments for the same disease or health condition.

Bob Obenchain <wizbob@att.net>

Black WC. The CE plane: a graphic representation of cost-effectiveness. *Med
Decis Making* 1990; **10**: 212-214.

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.

Laupacis A, Feeny D, Detsky AS, Tugwell PX. How attractive does a new technology have
to be to warrant adoption and utilization? Tentative guidelines for using clinical
and economic evaluations. *Can Med Assoc J* 1992; **146(4)**: 473-81.

O'Brien B, Gersten K, Willan A, Faulkner L. Is there a kink in consumers' threshold
value for cost-effectiveness in health care? *Health Economics* 2002; **11**:
175-180.

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. (2020) *ICEinfer_in_R.PDF* ICEinfer package vignette-like document.
http://localcontrolstatistics.org

Stinnett AA. Adjusting for Bias in C/E Ratio Estimates. *Health Economics* LETTERS
Secton. 1996; **5**: 470-472.

Stinnett AA, Mullahy J. Net health benefits: a new framework for the analysis of
uncertainty in cost-effectiveness analysis. *Medical Decision Making*, Special
Issue on Pharmacoeconomics 1998; **18**: s68-s80.

1 |

```
Loading required package: lattice
demo(fluoxpin)
---- ~~~~~~~~
> library(ICEinfer)
> # input the fluoxpin data of Sacristan et al. (2000).
> data(fluoxpin)
> # Effectiveness = respond, Cost = cost, trtm = flxpin where
> # flxpin = 1 ==> fluoxetine plus pindolol and flxpin = 0 ==> fluoxetine plus placebo
>
> cat("\n Display of Lambda => Shadow Price Summary Statistics...\n")
Display of Lambda => Shadow Price Summary Statistics...
> ICEscale(fluoxpin, flxpin, respond, cost)
Incremental Cost-Effectiveness (ICE) Lambda Scaling Statistics
Specified Value of Lambda = 1
Cost and Effe Differences are both expressed in cost units
Effectiveness variable Name = respond
Cost variable Name = cost
Treatment factor Name = flxpin
New treatment level is = 1 and Standard level is = 0
Observed Treatment Diff = 0.156
Std. Error of Trtm Diff = 0.089
Observed Cost Difference = -29361.751
Std. Error of Cost Diff = 15438.192
Observed ICE Ratio = -188012.873
Statistical Shadow Price = 173534.734
Power-of-Ten Shadow Price= 1e+05
> ICEscale(fluoxpin, flxpin, respond, cost, lambda=100000)
Incremental Cost-Effectiveness (ICE) Lambda Scaling Statistics
Specified Value of Lambda = 1e+05
Cost and Effe Differences are both expressed in cost units
Effectiveness variable Name = respond
Cost variable Name = cost
Treatment factor Name = flxpin
New treatment level is = 1 and Standard level is = 0
Observed Treatment Diff = 15616.883
Std. Error of Trtm Diff = 8896.312
Observed Cost Difference = -29361.751
Std. Error of Cost Diff = 15438.192
Observed ICE Ratio = -1.88
Statistical Shadow Price = 1.735
Power-of-Ten Shadow Price= 1
> cat("\nBootstrap ICE Uncertainty calculations with R=25000 can be lengthy...\n")
Bootstrap ICE Uncertainty calculations with R=25000 can be lengthy...
> fpunc <- ICEuncrt(fluoxpin, flxpin, respond, cost, lambda=100000, R=5000)
> fpunc
Incremental Cost-Effectiveness (ICE) Bivariate Bootstrap Uncertainty
Shadow Price = Lambda = 1e+05
Bootstrap Replications, R = 5000
Effectiveness variable Name = respond
Cost variable Name = cost
Treatment factor Name = flxpin
New treatment level is = 1 and Standard level is = 0
Cost and Effe Differences are both expressed in cost units
Observed Treatment Diff = 15616.883
Mean Bootstrap Trtm Diff = 15582.662
Observed Cost Difference = -29361.751
Mean Bootstrap Cost Diff = -29526.386
Consistent (Biased) ICER = -0.5319
Bootstrap Mean ICE ratio = -0.5278
Unbiased ICER estimate = -0.536
> cat("\nDisplay the Bootstrap ICE Uncertainty Distribution...\n")
Display the Bootstrap ICE Uncertainty Distribution...
> plot(fpunc)
> fpwdg <- ICEwedge(fpunc)
> fpwdg
ICEwedge: Incremental Cost-Effectiveness Bootstrap Confidence Wedge...
Shadow Price of Health, lambda = 1e+05
Shadow Price of Health Multiplier, lfact = 1
ICE Differences in both Cost and Effectiveness expressed in cost units.
ICE Angle of the Observed Outcome = -16.809
ICE Ratio of the Observed Outcome = -1.88013
Count-Outwards Central ICE Angle Order Statistic = 2472 of 5000
Counter-Clockwise Upper ICE Angle Order Statistic = 4847
Counter-Clockwise Upper ICE Angle = 26.292
Counter-Clockwise Upper ICE Ratio = -0.33863
Clockwise Lower ICE Angle Order Statistic = 97
Clockwise Lower ICE Angle = -51.278
Clockwise Lower ICE Ratio = 9.08941
ICE Angle Computation Perspective = alibi
Confidence Wedge Subtended ICE Polar Angle = 77.571
> plot(fpwdg)
> cat("\nComputing VAGR Acceptability and ALICE Curves...\n")
Computing VAGR Acceptability and ALICE Curves...
> fpacc <- ICEalice(fpwdg)
> plot(fpacc, show="VAGR")
> plot(fpacc, show="Alice")
> cat("\nColor Interior of Confidence Wedge with LINEAR Economic Preferences...\n")
Color Interior of Confidence Wedge with LINEAR Economic Preferences...
> fpcol <- ICEcolor(fpwdg, gamma=1)
> plot(fpcol, show="RBOW")
> plot(fpcol, show="Hist")
> cat("\nIncrease Lambda and Recolor Confidence Wedge with NON-Linear Preferences...\n")
Increase Lambda and Recolor Confidence Wedge with NON-Linear Preferences...
> fpcol <- ICEcolor(fpwdg, lfact=10)
> plot(fpcol, show="RBOW")
> plot(fpcol, show="Hist")
```

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