Epidemiologists decided to investigate the validity of new diagnostic tool for breast cancer.They used this new diagnostic tool for breast cancer in 150 women with biopsy-proven breast cancer in 300 age- and race-matched control women.The results of the new tool were positive in 136 cases and in 35 control women,all of whom showed no evidence of cancer at biopsy.Now,the epidemiologists want to use the new diagnostic tool for screening program in Cities A and B.Based on previous cross-sectional studies,the prevalence of breast cancer is 5% in City A and 1% in City B.What is the expected positive predictive value of new diagnosis tool for breast cancer in City A?

A) 30%
B) 43%
C) 81%
D) 89%
E) 91%

The sensitivity of new diagnostic test is 91%,from 136 divided by 150.The specificity of new diagnostic test is 89%,from 265 divided by 300.The prevalence of breast cancer in City A is 5%.Let us assume we have 100,000 people in City A; 5,000 individuals have breast cancer,and 95,000 individuals do not have breast cancer.The total number of people who test positive by the new diagnostic test equals the number of people who test positive from people who have cancer plus the number of people who test positive from people who do not have cancer.The number of people who test positive from people who have cancer equals 4,550 (5,000 multiplied by 0.91; the sensitivity).The number of people who test positive from people who do not have cancer equals 10,450 (95,000 multiplied by 0.11; 1 minus the specificity).The number of people who test positive by the new diagnostic test is 15,000.Therefore the positive predictive value is 0.30 (equals 4,550 divided by 15,000).