resolution. Transferrin saturation, which is the ratio
of plasma iron concentration to plasma total iron-
binding capacity, is a more reliable marker of iron
deficiency than either measure taken separately
because as the plasma iron concentration declines
with iron deficiency, the total iron-binding capacity
increases. Consequently, the ratio of the two dimin-
ishes markedly.
Ordinarily, diagnostic ratios are not the best way
to achieve maximum diagnostic discrimination
because the line separating the diagnostic classes
must necessarily pass through the origin. In
contrast, the line of separation defined by a linear
discriminant function is free to have a nonzero inter-
cept and, therefore, has the positional flexibility to
optimally separate the diagnostic classes. Thus,
linear discriminant functions make for better positiv-
ity rules than diagnostic ratios.
If the result frequency distributions of the
diagnostic classes are bivariate lognormal, the
discriminant function, which is linear in the
log-transformed diagnostic space, can be written as a
ratio in the untransformed diagnostic space
discriminant ratio
=
result
1
b
1
result
2
−
b
2
Because of their superior diagnostic accuracy,
discriminant ratios are preferable to diagnostic ratios
as the bases for positivity rules.
Diagnostic plots.
Positivity rules for two-study
test combinations can be very effectively presented
graphically in what are called diagnostic plots. In
such plots, the result combinations that are consid-
ered negative are indicated by one enclosed region
and the result combinations that are positive are
indicated by another. The diagnostic regions are
generally nonoverlapping.
In addition to simplifying the application of
individual positivity rules, diagnostic plots can incor-
porate multiple positivity rules, a feature that is
extremely useful when the same pair of laboratory
studies is used to diagnose a multiplicity of clinical
conditions. Perhaps the premier example of this
functionality are diagnostic plots of acid-base status
based on blood pCO
2
and hydrogen ion concen-
tration.
THE PROBABILITY OF DISEASE IN AN
INDIVIDUAL PATIENT
There is usually some degree of uncertainty in
the diagnostic classification of a patient. It arises
from an inability to separate completely the presence
of a condition from its absence on the basis of clini-
cal or laboratory findings. This means that the
presence of a disorder can be expressed only as a
probability: “It is quite likely that you are affected,”
“There is a fifty-fifty chance you have this
disorder,” “You could be suffering from,” and so
forth. When expressed quantitatively, the probabil-
ity of a diagnosis being correct has a value between
zero, which means that the condition is definitely not
present, and one, which means that the condition is
unarguably present.
Bayes' formula
Formal approaches exist for estimating the
probability of a diagnosis. One of these, the Bayes-
ian approach, is a well studied general method for
making decisions in the face of uncertainty. Even in
its formal realization, it is clinically practicable and
it is one of the most common methods used in
computer-based medical decision support. The
Bayesian approach has informal counterparts in the
diagnostic decision making of many clinicians,
although not all clinicians agree that it is a good
model of, or for, the diagnostic process (for
example, Feinstein 1979).
Prior probability.
The prior probability of a
disorder in a patient, P[pre], is the estimate of the
probability of the disorder arrived at prior to the
performance of a stipulated diagnostic study. Thus,
it is the pre-test probability. At the time of initial
presentation of a patient, the prior probability is
equivalent to the disease prevalence in the clinical
population to which the patient belongs. That
Diagnostic and Prognostic Classification
3-8
Study 1 result
Study 2 result
positive
negative
Figure 3.8
Diagnostic ratio positivity rule for the interpreta-
tion of a two-test combination.
