[2] Two Sources of ICE Uncertainty

When comparing two treatments (**T** vs **S**)
on both effectiveness and cost, it is essential to have data from a
sample of patients on treatment **T** as well as
comparable data from a sample of patients receiving treatment **S**.
When treatment "cross-over" is ethical (usually, when the underlying
disease condition is chronic), these two samples of data can come from
the same patients. This latter situation is much easier to
treat (by forming individual differences on cost and effectiveness) but
is not common; most curable disease states are acute rather than
chronic.

The **endogenous,
statistical uncertainty** within two samples of
data about what could be the unknown, true overall average differences
due to treatment choice is **
intrinsic to scientific ICE inference**. This uncertainty can
be directly addressed using a wedge-shaped bivariate **confidence
region** ...a natural extension of a (univariate) **
confidence interval** to two-dimensional (cost and
effectiveness) data ...that has (0, 0) as a limit point (never as an
interior point) of the region. From this **purely statistical perspective**,
**Lambda**
is little more than an unimportant nuisance parameter because the
resulting confidence wedge is
**equivariant (commutative)**
under changes in
**Lambda**.

At the opposite extreme, traditional economic approaches (such
as "net-benefit") attempt to convert ICE inference into a univariate
problem by first converting effectiveness differences into measures of
cost (or utility.) Unfortunately, this introduces a **second, external source of
uncertainty** ...about choice of **Lambda**...
and, thus, about what might be a "fair" way to do the **effectiveness-to-cost conversion**!
This additional **exogenous
uncertainty** applies to **all potential
treatment comparisons** and really needs to be kept separate
and treated differently from the statistical uncertainty intrinsic to a
specific (**T** vs. **S**) treatment
comparison.

**Implied
Linear NB Preference Distribution
when Lambda = 0.26**

**More
Favorable?
Linear NB Preference Distribution
when
Lambda = 2.6 NO!!!**

The second histogram above, for **Lambda = 2.6**,
has a bigger and longer **Negative,
Left-Hand Tail **
than the first one for **Lambda = 0.26**. In
other words, while the larger numerical value for **
Lambda**
does assign higher, positive numerical preference values to some
bootstrap ICE uncertainty outcomes within the NE quadrant, it also
assigns many less positive numerical scores to more bootstrap outcomes
within the SW quadrant!!! Anyway, it is now clear that (due
to injection of exogenous, economic uncertainty and inconsistency), **
using a larger numerical value for ****Lambda****
does not automatically produce a comparison more favorable to the new
treatment, T. **

Obenchain(2008) discusses graphical ways to literally "see"
distinctions between these two alternative sources of uncertainty and,
ultimately, to **eliminate ****economic
uncertainty**** about ****Lambda****
by keeping its value held fixed.**