Two examples further illustrate these principles and show how predictive values vary with prevalence. Consider first (Example 1) an imaginary population A with 1000 people. The prevalence of disease X in this population is high—40%. You can quickly calculate that 400 of these people have X. You then set out to detect these cases with an observation that is 90% sensitive and 80% specific. Of the 400 people with X, the observation reveals .90 x 400, or 360 (the true positives). It misses the other 40 (400 - 360, the false negatives). Out of the 600 people without X, the observation proves negative in .80 x 600, or 480. These people are truly free of X, as the observation suggests (the true negatives). But the observation misleads you in the remaining 120 (600 - 480). These people are falsely labeled as having X when they are really free of it (the false positives). These figures are summarized below:
Example 1. Prevalence of Disease X = 40%
Disease X Present Absent
; 480 • total positive I observations
520 total negative observations
As a clinician who does not have perfect knowledge of who really does or does not have disease X, you are faced with a total of 480 people with positive observations. You must try to distinguish between the true and the false positives and will undoubtedly use additional kinds of data to help you in this task. Given only the sensitivity and specificity of your observation, however, you can determine the probability that a positive observation is a true positive, and you may wish to explain it to the concerned patient. This probability is calculated as follows:
360 true positive observations
120 false positive observations ab cd
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