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When evaluating a new diagnostic test, researchers compare the results of the new test to the diagnotic results produced by the recognized "gold standard" in the area. For example, a new test for diagnosing ectoptic pregnancy would be compared to transvaginal ultrasonography.
Positive Predictive Value
The Positive Predictive Value of a test is the number of times the disease was present according to the gold standard as a percentage of the number of times the new test came back positive. In the above example, the Positive Predictive Value would be 900/(900 +100) or 90%.
Negative Predictive Value
The Negative Predictive Value of a test is the number of times the disease is absent according to the gold standard as a percentage of the number of times the new test comes back negative. In the above example, the Negative Predictive Value would be 800/(800+200)) or 80%.
The prevalance of a disease is the percentage of people with a particular disease within a given population. In the above example, the prevalance would be 900/(900+100+200+800) or 45%.
Positive and Negative Predictive Values are highly influenced by the prevalance of a disease. So researchers began to look for qualities that would not be so easily influenced.
The Sensitivity of a test is the number of times a test came back positive as a percentage of the times the disease was present according to the gold standard. In the above example, the Sensitivity would be (900/900+200) or 81%.
The Specificity of a test is the number of times a test comes back negative as a percentage of the times the disease was negative according to the gold standard. In the above example, the Specificity would be (800/800+100) or 88%.
While Sensitivity and Specificity are useful in that they are unaffected by prevalance, they are qualities of the test and not patient-related the way we would like evidence-based practice to be. So researchers came up with another quality that would satisfy both demands of being patient-centered and minimally affected by prevalance.
Pre- and Post-Test Probability
First, it is important to note that no test tells us absolutely whether a disease is present (This is not, strictly speaking. true. A pathologist performing an autopsy knows exactly what disease killed a patient, but by then it's too late). A diagnostic test simply tells us something about the probability that a disease is present. Evidence-based practice encourages the practitioner to assign a value to the probability that a disease is present, based on the practitioners's clinical judgment. This number is likely to be related to the prevalance of the disease in a particular population. As the prevalance of ectoptic pregnancies in men over 50 is 0%, that would be the pre-test probability. The results of a test raise or lower this number to a post-test probability that the condition is present. If the TVU for the 50-year old man comes back positive, the post-test probability is 100% that you need a new sonograph.
The positive and negative likelihood ratios of a test gauge the test's ability to bring the pre-test probability and post-test probability into allignment.
The likelihood ratio for the positive test measures the test's ability to raise the pre-test probability to a level high enough that a practioner feels comfortable choosing one therapy over another. It is computed with the following equation: Sensitivity/(1-Specificity) [where specificity and sensitivity are expressed as decimals rather than percentages].
The likelihood ratio for the negative test measures the test's ability to lower the pre-test probability to a level low enough that a practitioner feels comfortable in choosing not to apply the therapy for the suspected disease. It is computed with the following equation: (1-Sensitivity)/Specificity [where sensitivity and specificity are expressed as decimals rather than percentages].
The Likelihood Nomagram
The Likelihood Nomagram developed by T.J. Fagan (Fagan TJ. Letter: Nomogram for Bayes theorem. N Engl J Med 293. 257(1975)) is the tool used to make use of likelihood ratios. Find your pre-test probability on the left-hand column. Draw a line through the likelihood ratio of the test as reported in the study and find the post-test probability that the condition is present. As can be seen from the nomagram, a likelihood ratio of 1 is not at all effective. On the whole, a positive likelihood ratio (LR+) of greater than 10 and a negative likelihood ratio (LR-) of less than 0.1 provide the greatest results.