Question

A 2011 article in the British Medical Journal attempts to elucdiate Bayes' Rule for the medical profession. It's well worth reading and has some illuminating graphics. In this exercise you will confirm a result stated in the article. Useful terminology: The sensitivity of a test for a medical condition is the proportion of correctly diagnosed patients among those who have the condition. The specificity of the test is the proportion of correctly diagnosed patients among those who do not have the condition. Read those definitions a couple of times and note that a good test should have high values of both sensitivity and specificity. In the section Special Cases, the authors consider a 45-year-old woman who has a 1% chance of getting breast cancer in the subsequent five years. The article says, "The sensitivity of routine screening mammography ranges from 71% to 96% and the specificity ranges from 94% to 97%. Using values of 80% for sensitivity and 96% for specificity, a positive test increases the probability to 17%." For this problem, show your work in finding each probability and box the final decimal answer.
(iv) the chance that the woman's test result is negative

Answer 1

If sensitivity = 80%,specificity = 96%,prevalence = 17% as given

so

chance that the woman's test result is negative = NPV =

(0.96*(1-0.17))/((1-0.8)*0.17+0.96*(1-0.17))

=0.9590756

chance that the woman's test result is negative = PPV =

=0.8*0.17/(0.8*0.17+(1-0.96)*(1-0.17))

=0.8037825