population. This is the typical situation when
screening for a disease among asymptomatic
individuals and explains the considerable challenge
in finding sensitive screening tests that are also
specific. On the other extreme, if a clinical popula-
tion consists primarily of patients with advanced or
severe disease, almost all individual study results
will be very abnormal causing the aggregate distri-
bution of study results to be widely separated from
that of the disease-free members of the population.
At any stipulated critical value, the sensitivity of the
study will be much greater in the second population
than in the first. In addition, the specificity will
usually be less because the disease-free individuals
in the second population almost always have other
medical conditions that explain their presence in this
clinical population—conditions that will tend to
broaden the distribution of study results and thereby
lower the specificity.
Other measures of diagnostic performance
Two alternative measures of diagnostic perform-
ance need to be mentioned. Both incorporate the
effect that the prevalence of a condition, i.e. the
proportion of persons in the clinical population who
have the condition, will have upon the classification
accuracy of a diagnostic study. The first measure is
diagnostic efficiency, defined as the overall
frequency of correct diagnostic classifications when
a study is applied in a clinical setting. Thus, from
Table 3.2,
efficiency =
true negatives
+
true positives
true disease free
+
true disease
The dependence of efficiency upon disease preva-
lence is indicated by redefining it in terms of sensi-
tivity and specificity. The number of true positives
equals the sensitivity of the study times the number
of tested individuals who have the disease, the
number of tested individuals who have the disease
equals the prevalence times the number of individu-
als individuals, and the number of true negatives
equals the specificity of the study times the number
of tested individuals times one minus the prevalence.
Thus,
efficiency =
prevalence
·
sens + (1-prevalence) spec
where
sens
stands for study sensitivity and
spec
stands for study specificity. This formula reveals
the validity of a number of intuitive insights
regarding the behavior of diagnostic efficiency.
First, when the disease prevalence is low, the
efficiency of a study is determined largely by its
specificity and second, when the disease prevalence
is high, the efficiency of a study depends mostly
upon its sensitivity.
The other alternative measure of diagnostic
performance is the predictive value of a study result.
Predictive value is the frequency with which a classi-
fication study is correct in a given clinical setting,
predictive value of a positive result =
true positives
true positives
+
false positives
=
prevalence
$
sens
prevalence
$
sens
+ (
1
−
prevalence
) (
1
−
spec
)
predictive value of a negative result =
true negatives
true negatives
+
false negatives
=
(
1
−
prevalence
)
spec
(
1
−
prevalence
)
spec
+
prevalence
(
1
−
sens
)
These definitions, as well as good sense, demon-
strate that the predictive value of a positive study
result increases with increasing prevalence and with
increasing study sensitivity and specificity. When
the prevalence is low, the probability that a positive
study result is correct is small, unless the study
specificity is nearly one. This is an extremely
important point when a study is being used to
identify individuals with rare disorders. The predic-
tive value of a negative study result increases with
decreasing prevalence and with increasing study
sensitivity and specificity. When the prevalence is
low, the frequency of correct negative study results
is high even when the diagnostic performance of the
study is poor.
Repeating and combining studies
The performance of a diagnostic study can be
altered by repeating the study or by using the study
in combination with one or more other diagnostic
studies. The performance that results from such
multiple testing depends largely upon two new
considerations: the positivity rule used to make the
ultimate diagnostic classifications and the classifica-
tion correlation between repeated tests or among
combinations of tests.
Repeat testing.
The two most frequently used
positivity rules for repeat testing are illustrated in the
Diagnostic and Prognostic Classification
3-4
