My statistical perspective on methods for ICE inference is that they address
a **fundamentally two-dimensional problem**. In fact, I believe that ICE
inference represents the single, most important and challenging area for practical
application of basic concepts from **multivariate analysis** in health care
today.

Introduction to Key Topics in ICE Graphical Perception and Interpretation:

The above pair of
graphical displays can be generated using the ICEwedge( ) and ICEcolor( )
functions contained within my **
ICEinfer
R-package. **The two
graphs above show essentially the "same"**
Bootstrap Count-Outwards Wedge-Shaped 95% Confidence Region **for the high-uncertainty
numerical example of Obenchain(2008) and
Obenchain, Robinson and Swindle(2005.)
Due to high-uncertainty, this
**statistical region**
has an incredibly wide central-polar-angle of 237.^{o} In other
words, this particular confidence "wedge" is actually more than half of the
whole bootstrap resampling pie! Yet, this 95% confidence region is at
least somewhat restrictive in the sense that it spans only 66% (237 out of
360-degrees) of the total
**ICE plane.**

Mathematically, the
approach to defining a statistical confidence region illustrated here is said to
be
**"equivariant"** under changes in
the** Shadow Price of Health**,
usually denoted by the Greek symbol**
****
Lambda. **
Here, outcomes for the
two numerical values of 0.26 and 2.6 are illustrated and compared.
Technically, equivariance means that the operations of [a] changing
**Lambda **
and [b] forming the
confidence wedge are
**commutative**.
One gets the same final wedge either when performing operation [b] then [a] or
when performing operation [a] first and only then [b].

Actually, the above
graphs (somewhat cunningly) use the so-called
**"alias" perspective**
(quite commonly used in both physics and computer science) where the bootstrap
re-sampling scatter
literally appears to be essentially unchanged between the left-hand and right-hand panels.
However, because
**Lambda** increases by a factor of ten
in the second analysis, note that the** scale changes** along the horizontal axis
(effectiveness in cost units); the left-hand effectiveness range of (-10 to +10)
becomes (-100 to +100) in the right-hand graphic. Another difference that
may emerge only upon quite careful examination of the above graphics is that
(due to differences in **R's initial random-number-generator "seed" value**
specified in two consecutive but separate analyses) the two scatters actually
are not **exactly identical! **Still, up to this point in our
discussion of the above graphics, there really are no important differences
between them.

And now, the Kicker!!!
When the bootstrap resampled outcomes within the above confidence wedges get
**
COLORED** with
somewhat contradictory
**linear NB preferences**
(Beta = Gamma = Eta = 1) implied by two very different numerical values for
**Lambda**,
considerable additional **
economic variation**** (uncertainty)**
gets injected
into the "Are there Differences?" question. See discussion **Topic Two**
below for more information on this pivotal complication!

Topic One: Why Attempt to Exclude (0, 0)?

Topic Two: Two Sources of ICE Uncertainty

Topic Three: ICE Angle Serendipity

Topic Four: ICE Fieller's Theorem Wedges

Topic Five: ICE Preference Axioms

Topic Six: Variation in Willingness-to-Pay/Accept

Topic Seven: Eliminating Bias in Acceptability Curves