The overall detection rate of breast cancer using a mammogram is approximately 8

Question

The overall detection rate of breast cancer using a mammogram is approximately 80%. The false positive rate is approximately 7%. The prevalence of breast cancer in 40 year old women is approximately 1.47%.
a. (3 marks) Compute the positive predictive value of a mammogram for 40 year old women.
b. (2 marks) Approximately 50% of women who get mammograms annually will receive a false positive result over a 10 year period. Given that the false positive rate for a single mammogram is 7%, shouldn’t this value be 10×7% = 70% ? Explain.

Explanation / Answer

a) probabilty of postive test =0.0147*0.8+(1-0.0147)*0.07=0.0807

hence positive predictive value =true postive/probabilty of positive =0.0147*0.8/0.0807=0.1457

b)

probabilty of false positive rate =not having breast cancer*probability of false postive =(1-0.0147)*0.07=0.0689

hence probabilty to get at least one false postive over 10 years =1-P(getting none false postive)

=1-(1-0.0689)10 =1-0.4894 =0.5106~=51.06%~50%

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