Question 5: Tests with very high sensitivity and specificity sometimes have low positive predictive value. Why is this and why is positive predictive value high in this study?
The positive predictive value of a test depends not only on sensitivity and specificity, but on the prevalence of the disease in the population being tested. If this is small, most people being tested will not have the disease. Some of these disease-free people will be positive on the test, a proportion equal to one minus the specificity. Hence a lot of those who test positive will not have the disease. Few of those who test positive will actually have the disease, even if all with the disease are detected, and the positive predictive value will be low.
In this paper the population being tested is those for whom a urine sample was sent for culture for clinical reasons. They were chosen because there were clinical reasons to suspect that they would have a UTI. The prevalence would thus be high. (It appears to be 55% from the data.) Hence with a very specific test like the urine Gram stain there would be few people who did not have UTI but who tested positive. Hence we can have a high positive predictive value.
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