Clinical Biochemistry of Domestic Animals (Sixth Edition) - UMK ...

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Chapter | 1 Concepts of Normality in Clinical Biochemistry
patients on the basis of analyte values, the error rates, are
shown, respectively, as vertically and horizontally shaded
areas in Figure 1-5 . The sensitivity of the diagnostic or
decision process using reference values is the probability
of deciding that a truly diseased animal is diseased on the
basis of the given reference value and is equal to 1 minus
the vertically shaded area of Figure 1-5 . The specificity
of the decision process is the probability of deciding that
a truly normal animal is normal and is equal to 1 minus
the horizontally shaded area of Figure 1-5 . It is possible to
change the reference values to increase the sensitivity of
the test, but such an action will also result in a reduction in
the specificity of the test.
Example 2
Type III diabetic dogs have the chemical form of diabetes mellitus
generally regarded as the first level of development of
the disease offering the highest likelihood “ for successful oral
hypoglycemic therapy or dietary therapy ” (Kaneko, 1977 ) . Thus,
it would be useful to distinguish type III diabetic dogs from
normal dogs. Using the sample mean [155.6mg/dl (8.63mmol/
liter)] and standard deviation [32.0mg/dl (1.77mmol/liter)]
of the plasma glucose values given by Kaneko (1977) for five
dogs with type III diabetes mellitus as reasonable estimates of
the corresponding parameters for the population of dogs with
type III diabetes mellitus, and assuming that this population
distribution is approximately Gaussian, a comparison of this
distribution of glucose values can be made with that for the
population of normal dogs described by the approximately
Gaussian distribution with parameter estimates given in
Figure 1-2 [ μ x 96.4mg/dl (5.35mmol/liter) and σ x 14.6mg/dl
(0.81 mmol/liter)]. These two distributions are those shown in
Figure 1-5 ; they have reasonably good separation with moderate
overlap. Based on this information, a diagnostic procedure
is proposed whereby a dog entering the clinic with a glucose
value above 125.1mg/dl (6.94mmol/liter), the upper limit of
the normal reference interval, will be flagged as possibly having
type III diabetes mellitus thereby indicating need for more
follow-up. (Note: This is an oversimplification of actual practice
because a diagnostic decision of this type would be based
on additional information, such as the animal’s glucose tolerance
and insulin response, making the decision rule and subsequent
error calculations more complex.) This is an example
of a one-sided diagnostic procedure because a dog with a
glucose value below the lower limit of the reference interval
would not be considered as having type III diabetes mellitus.
If a dog actually having type III diabetes mellitus has a glucose
value below the upper limit of the reference interval, the
diagnostic procedure will make a mistake in deciding that the
dog is normal. The probability of making this mistake is 0.170
or 17.0%, the area to the left of a glucose value of 125.1 mg/
dl in the distribution of glucose values for dogs having type
III diabetes mellitus or the area to the left of the corresponding
z-value, z (125.1 155.6)/32.0 0.953, for the standard
Gaussian distribution (see Section II.B).
[This probability can be found by interpolating from
Table D in Daniel (2005) or from MINITAB Release 14.13
using the reverse of the procedure described above for
generating Table 1-2 . The z -value 0.953 is placed in a
column of a MINITAB worksheet and the following commands
given:
Calc (from the main menu of MINITAB) → Probability
Distributions → Normal Distribution . Within the Normal
Distribution dialog box , Cumulative probability is
selected, Mean is set to 0.0, Standard deviation is set to
1.0, and the column of the worksheet containing the z -value
is selected and placed in the Input column : Hit OK .]
The clinician may be interested in determining the
sensitivity and the specificity of the diagnostic procedure.
The sensitivity is 1 0.170 0.830 or 83.0%. A dog that
actually is normal but has a glucose value greater than
125.1 mg/dl would be incorrectly classified by the proposed
diagnostic procedure as having type III diabetes mellitus.
The probability of making this type of error is 0.025 or
2.5%, which is the area to the right of a glucose value of
125.1 mg/dl in the distribution of glucose values for normal
dogs or the area to the right of the corresponding z-value,
z (125.1 96.4)/14.6 1.96, for the standard Gaussian
distribution (from Table 1-2 or using MINITAB as shown
earlier). The specificity of the diagnostic procedure
is 1 0.025 0.975 or 97.5%.
F . Predictive Value of a Decision Based on
a Reference Interval
A useful quantity is the probability that a patient having a
reference value outside the normal interval actually has the
disease. This is known as the predictive value of a positive
diagnosis , Prob(D | ). Interest could also be in determining
the probability that a patient having a reference value
within the normal interval is actually nondiseased or the
predictive value of a negative diagnosis , Prob(D | ). The
predictive value depends on the sensitivity, specificity, and
prevalence ( p ) of the disease as is shown in the following
equations:
Prob(D )
p sensitivity
psensitivity ( 1 p)
( 1 specificity)
Prob(D )
( 1
p)
specificity
( 1 p) specificity
p(
1sensitivity)
Figure 1-6 demonstrates the extent to which the predictive
value of a positive diagnosis changes with the prevalence.
In general, larger changes are seen in the predictive
value of a positive diagnosis for smaller changes in the