For many diseases, more than one test is available for diagnostic or screening purposes. The dilemma then becomes whether a positive result on several tests must be present before the diagnosis is confirmed, or whether a single positive test is sufficient to label the person as diseased. The various possibilities will have an impact on sensitivity and specificity if the tests are viewed separately. Consider the example in which two tests are available for the diagnosis of a disease. Three combinations can lead to an affirmative diagnosis:
1. If one of the two tests is positive, the diagnosis is made.
2. A positive result for both tests is required before the diagnosis is confirmed.
3. The second test is performed only if the first is positive, and the person is labeled as diseased only if the second is also positive.
The first combination will increase sensitivity and decrease specificity in comparison with each test alone, and the second combination will decrease sensitivity and increase specificity. These effects on sensitivity and specificity for multiple test ordering are similar to shifting the cutoff point for a single test.
The value of performing a second test only when the first is positive generally comes into play when the first test is significantly less expensive and easier to administer than the second but is less specific, although highly sensitive. The second test is highly sensitive and specific but more costly to perform on large populations, especially for screening purposes. An example is the enzyme-linked immunosorbent assay (ELISA) and Western blot test for human immunodeficiency virus (HIV) testing. The ELISA has a high sensitivity and is relatively inexpensive and easy to perform, but it is less specific. The Western blot test has high sensitivity and specificity, but it is more expensive and more difficult to perform. Using the ELISA first identifies almost everyone with the disease, whereas the Western blot excludes the fraction of persons incorrectly labeled as
P(D*): Prior probability: Pre-test probability of disease: prevalence
I I Post-test probability when the test result is positive
(positive predictive value) | | Post-test probability when the test result is negative (1 - negative predictive value)
-Results for a test with sensitivity (TP rate) = 95%, specificity (1 - FP rate) = 95%
-Results for a test with sensitivity (TP rate) = 75%, specificity (1 - FP rate) = 85%
Figure 15-3 The relationship between pretest and post-test probability of disease based on a positive or negative test result. (From Sackett DL, Haynes RB,
Guynett GH, et al. Clinical Epidemiology, 2nd ed. Boston, Little, Brown, 1991, p 92.)
having disease (false positives) by the ELISA test. This testing sequence has improved sensitivity and specificity over each test alone and is more cost-effective than initially performing both tests.
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