1. The prostate surface antigen test (PSA) is commonly used to detect early sign

Question

1.     The prostate surface antigen test (PSA) is commonly used to detect early signs and symptoms of prostate cancer in men. However, the PSA test has come under quite a bit of public scrutiny for its relatively high false positive rate around 25%. Assume the prevalence of prostate cancer in men above the age over 65 is 47%. Investigators looking at the performance of the PSA test sample a group of 10,000 men over the age of 65, and come up with 5,500 positive results. What percent of men taking the test with prostate cancer will get a positive result?

Explanation / Answer

probabilty of having cancer P(C)=0.47

and not having cancer =P(Cc) =1--0.47=0.53

let probabilty of true +ve =P(TP) and false +ve =P(FP) =0.25

hence probabilty of +Ve result =P(C)*P(TP|C)*P(Cc)*P(FP|Cc)

5500/10000 =0.47*P(TP|C)+0.53*0.25

P(TP|C) =0.888298

hence 88.83% of men taking the test with prostate cancer will get a positive result

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