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Max Hodak - Medical math

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1% of women at age 40 who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer? There’s a long history of studies that ask physicians this question and repeatedly find that only about 15% of doctors get it right, with most guessing in the 75% - 85% range. The correct answer is 7.8% and requires the use of Bayes’ theorem. 7.8%! No wonder doctors don’t want to do unnecessary tests, right? The vast majority of people with positive results are false positives! The question is interesting because it highlights one of the common and more valid reasons to resist greater levels of routine testing: every test has some non-zero false positive and false negative rates, meaning that all else equal you’re going to end up doing

Max Hodak - Medical math Max Hodak - Writings Medical math May 2020 1% of women at age 40 who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer? There’s a long history of studies that ask physicians this question and repeatedly find that only about 15% of doctors get it right, with most guessing in the 75% - 85% range.

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