Slide 1: A question for you: 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?

Slide 2: Did you try to draw out a 2×2 box? Try it this way instead! If prevalence = 1/1000, out of 1000 people 1 will be diseased and 999 healthy. Assuming 100% sensitivity, the 1 diseased person tests positive. A 5% false positive rate (aka 95% specificity) means of the 999 healthy people, 50 test positive, 949 test negative.

Slide 3: 1 true positive divided by (1 true + 50 false positives) = positive predictive value of only ~2%!

Slide 4: How did you do? Most people get it wrong! A study done at Harvard and BU that asked this exact question of medical students, residents, and attendings found the most common given answer was 95%!

Slide 5: Lesson Learned. When considering the results of a test, even one with an excellent sensitivity and specificity, one must take into account the underlying prevalence of a disease to determine the likelihood of a true positive!


  • Manrai AK, Bhatia G, Strymish J, Kohane IS, Jain SH. Medicine’s uncomfortable relationship with math: calculating positive predictive value. JAMA Intern Med. 2014 Jun;174(6):991-3. PMID 24756486

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