Biology Reference
In-Depth Information
1. The range of scores in the hypoglycemic range is much smaller than
the range of hyperglycemic scores; and
2. The target range is not in the center of the data range.
We want to convert this scale to a scale as shown in Figure 5-5. The idea
is to expand the hypoglycemic range, squeeze the hyperglycemic range,
and position the target BG range symmetrically about zero. More
specifically, we want the transformed scale to satisfy the following
conditions:
1. The directions of the original and transformed scales are the same;
2. The target range is centered at 0; and
3. The entire BG range is centered at 0.
First, we must find such a transformation, and, second, establish the
transformation's validity by testing it with BG reading samples from a
sufficiently large number of people.
We seek a transformation in the form:
ÞÞ
a
b; a; b >
f
ð
BG
;
a
; bÞ¼½ð
ln
ð
BG
0
:
(5-1)
Why choose this particular analytic expression? Such a question is not
always easy to answer. Developing a good mathematical model may
sometimes border on artistic creativity, and it may not always be
possible to retrace every single step of the process. In the case of model
(5-1), we began with a widely accepted skewness correction formula,
and then modified it to fit our needs. The specific details can be found in
Kovatchev et al. (1997).
Actual BG Scale
1.1
3.9
10
33.3
Hypo
Target
Hyper
−
a
a
−
b
0
b
Transformed BG Scale
FIGURE 5-5.
Conversion of the BG scale.
