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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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OK, let's do it

you have to construct a 2X2 Table to determine the sensitivity and the specificity of the test.
They've done it on 2000 people 1000 with disease and 1000 without the disease and it was positive in 250 in diseased people and 100 in non diseased people.
So your 2X2 table look like this

Font Electric blue Rectangle Parallel Screenshot

click to enlarge

Sensitivity = TP/TP+FN = 250/250+750 = .25 or 25%
Specificity = TN/TN+FP = 900/900+100 = .9 or 90%

Now in the new population you also have to construct a new 2X2 table
They told you the prevalence is 80/100,000 so your total diseased people is 80 and the rest (100,000-80=99,920) are not diseased.
since we know the sensitivity is 25% so we expect quarter of the 80 to test positive that is 20 and the rest (80-20=60) to test negative.
since we know the specificity is 90% so we expect that 90% of the 99,920 to test negative and 10% (99,920X10%=9992) to test falsely positive.
so your 2X2 table should will be

Font Screenshot Electric blue Rectangle Parallel

click to enlarge

Obviously the answer is A. In fact you don't need to bother yourself with the specificity calculation because there's only one option with 20 as true positives so calculation of the sensitivity part would have been enough to answer the question :eek:
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