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A screening test for colon cancer is administered to 1000 people with biopsy -proven colon cancer and to 1000 people without colon cancer. The test results are positive for 250 people of proven cases and 100 of those without colon cancer.The screening test is now to be used on a population of 100,000 with a known prevalence rate of colon cancer of 80 per 100,000. Which of the following is the expected number of true positives and false positives in this population of 100,000 people?


True Positives - False positives

a. 20 - 9992
b. 20 - 89,928
c. 40 - 9992
d. 50 - 89,928
e. 60 - 9992
f. 60 - 89,928
g. 80 - 9992
h. 80 - 89,928
 

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Sorry, I meant A, I tried drawing a 4x4 table but I could not do it. In fact, to answer this question you would need two 4x4 tables, one with the initial information and the other with what you could reason from it.
 

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I got A.
First calculate sensitivity and specificity, in this case is 25% and 90%, respectively.

For the case with 10,000 ppl in which 80 ppl definitely have cancer, just apply the sensitivity, 80*25%=20(true positive), and the remaining 99920 ppl are definitely without cancer, and here just apply specificity, 99920*90%=89928, substract 99920 by 89928 and then get the false positive 9992.
 
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