Information Technology Reference
In-Depth Information
20
Probability, Fuzziness and Information:
Defining Missions in Medicine
Luis Argüelles Méndez
20.1
Probability and Perception in Medicine
Like a representation of probabilistic concepts in formal terms, probability theory
is a well developed area of mathematics, and an extensive number of physiological,
biochemical and biophysical magnitudes closely adhere to probability distributions,
specially to the Gaussian or Normal distribution,
N
2
(
μ
,
σ
)
, defined by its intrinsic
2
)
parameters mean,
. When both parameters are known, that is,
if the Gaussian distribution representing a subject of interest in medicine is well
defined, the probability of appearance of a given observed value can be easily cal-
culated. In particular, every health sciences practitioner knows that an observed
feature with value
x
in a patient obeys the following probabilistic expressions:
μ
, and variance,
σ
P
(
μ
−
σ
≤
x
≤
μ
+
σ
)
≈
0
.
6827
P
(
μ
−
2
σ
≤
x
≤
μ
+
2
σ
)
≈
0
.
9545
P
(
μ
−
3
σ
≤
x
≤
μ
+
3
σ
)
≈
0
.
9973
That is, a direct interpretation can be made in order to know how far is the observed
value
x
from the mean in the population following a Gaussian distribution [3].
Very interestingly, probability laws produce numerical results that, as real num-
bers, generate a conscience of precision and accuracy that usually affects the per-
ception and confidence of a physician, generating absolute and ultimate reference
values. However, and as a philosophical reflection, we should ask ourselves about
absolute probability and more precisely, about its own existence, or in other words:
does absolute probability in medicine really exist? An example on autosomal reces-
sive diseases will help us to clarify this point.
As it is well known, an autosomal recessive mechanism is one of several ways
that a trait, disorder, or disease can be passed down through families. In these in-
stances, two copies of an abnormal gene must be present in order for the disease
or trait to develop [9]. If we name the following elements,
A
=
“to be an affected
