Medicine’s Uncomfortable Relationship With Math: Calculating Positive Predictive Value

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In 1978, Casscells et al1 published a small but important study showing that the majority of physicians, house officers, and students overestimated the positive predictive value (PPV) of a laboratory test result using prevalence and false positive rate. Today, interpretation of diagnostic tests is even more critical with the increasing use of medical technology in health care. Accordingly, we replicated the study by Casscells et al1 by asking a convenience sample of physicians, house officers, and students the same question: “If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person’s symptoms or signs?”

Approximately three-quarters of respondents answered the question incorrectly (95% CI, 65% to 87%). In our study, 14 of 61 respondents (23%) gave a correct response, not significantly different from the 11 of 60 correct responses (18%) in the Casscells study (difference, 5%; 95% CI, −11% to 21%). In both studies the most common answer was “95%,” given by 27 of 61 respondents (44%) in our study and 27 of 60 (45%) in the study by Casscells et al1 (Figure).

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