#medicine #bayes
"Manrai AK, Bhatia G, Strymish J, Kohane IS, Jain SH. "Medicine's uncomfortable relationship with math: calculating positive predictive value." JAMA Intern Med. 2014;174(6):991-993. Note: this is JAMA Internal Medicine, not NEJM - the brief was widely miscited; the NEJM attribution in the brief is wrong. Question posed (replicating Casscells 1978): "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?" Of 61 respondents: 14 (23%) gave the correct answer of ~2%; 27 (44%) answered 95% - the modal response. Median answer 66%, i.e. 33× the true value. Original: Casscells W, Schoenberger A, Graboys TB. N Engl J Med. 1978;299(18):999-1001 (where 11/60 gave the correct answer)."
"Hoffrage U, Gigerenzer G. "Using natural frequencies to improve diagnostic inferences." Acad Med. 1998;73(5):538-540. Physicians averaging 14 years' experience, mammography problem: with natural frequencies, 16/24 found the Bayesian answer; with conditional probabilities, only 1/24 did."
"Manrai AK, Bhatia G, Strymish J, Kohane IS, Jain SH. "Medicine's uncomfortable relationship with math: calculating positive predictive value." JAMA Intern Med. 2014;174(6):991-993. Note: this is JAMA Internal Medicine, not NEJM - the brief was widely miscited; the NEJM attribution in the brief is wrong. Question posed (replicating Casscells 1978): "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?" Of 61 respondents: 14 (23%) gave the correct answer of ~2%; 27 (44%) answered 95% - the modal response. Median answer 66%, i.e. 33× the true value. Original: Casscells W, Schoenberger A, Graboys TB. N Engl J Med. 1978;299(18):999-1001 (where 11/60 gave the correct answer)."
"Hoffrage U, Gigerenzer G. "Using natural frequencies to improve diagnostic inferences." Acad Med. 1998;73(5):538-540. Physicians averaging 14 years' experience, mammography problem: with natural frequencies, 16/24 found the Bayesian answer; with conditional probabilities, only 1/24 did."