BPS1101 Chapter 2: Use of Natural Frequencies

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University of Ottawa
Biopharmaceutical sciences
William Ogilvie

!"#$%&$'()*+(,$-+#.*#/01#"$)%$#2(,*()#$ ")()1")10(,$1/&%+3()1%/4$ $ 1. The following data was presented in the assigned reading: a) The probability that a woman has breast cancer (prevalence) is 1 percent. b) If a woman has breast cancer, the probability that she tests positive (sensitivity) is 90 percent. c) If a woman does not have breast cancer, the probability that she nonetheless tests positive (false-positive rate) is 9 percent. (Note that b and c indicate a test accuracy of about 90 %). How to convert to Natural Frequencies: - Pick a big number of patients (100,000) then do the math. To get numbers using percentages, multiply the total by the percent and divide by 100. Using a flow-chart is helpful 100,000 women 1% have breast cancer Cancer Healthy 1000 99000 (100000 X 0.01) (100,000-1000) 90 % test positive False positive rate 9% 900 cancers 100 cances 90, 090 don't 8910 test positive detected missed have cancer for cancer but (1000 X 0.90) (1000 X 0.1) (99000 X 0.91) don't have it (99000 X 0.09) for every 9,810 positive tests (8910 + 900) only 900 actually have cancer (1 in 10) If a woman tests positive for breast cancer, hopefully her doctor does follow-up tests to make sure she actually has the disease. 2. A company with 10,000 employees is performing lie detector tests to find 100 people who have embezzled money. If the test is 99 % accurate, how many innocent people will be falsely accused? If a person tests as “guilty” what is the chance that they actually did it? Answer: There are 100 guilty people and (10000-100) 9900 innocent people 10,000 100 embezzlers Guilty Innocent 100 9900
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