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Post by Admin on Jan 17, 2016 19:31:28 GMT
A town with 1000 citizens has a 10% prevalence of disease X. A screening test for disease X was just developed, with a sensitivity of 80% and a specificity of 70%. How many people without disease X will be falsely diagnosed positive by this screening test?
A. 20 B. 80 C. 100 D. 270 E. 630
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Post by Admin on Jan 17, 2016 19:40:44 GMT
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Post by Admin on Jan 17, 2016 19:41:47 GMT
The question is asking for the number of false-positives. Specificity = True-negatives/(True-negatives + False-positives). False-positive signifies the number of people without disease X who will be falsely diagnosed by the screening test. In this case, 900 people do not have the disease, represented by true-negatives + false-positives. Using a specificity of 70%, the number of true-negatives is 630, whereas the number of false-positives is 270. Thus, 270 people without disease X will be falsely diagnosed with this screening test (ie, they will be false-positives). The Punnett square illustrates the concept.
A is not correct. 21% chose this. The figure 20 is the number of people with the disease who will have an incorrect negative screening test result (ie, false-negatives). You know that the disease prevalence is 10%, so in a town of 1000 people 100 will have disease X and 900 will not. You can use these numbers with 80% sensitivity and 70% specificity to make the 2 × 2 table. B is not correct. 11% chose this. The figure 80 is the number of people who will have a correct positive screening test result (ie, true-positives). C is not correct. 10% chose this. The figure 100 is the number of people in the town with disease X (ie, the prevalence of disease X). E is not correct. 4% chose this. The figure 630 is the number of people who will have a correct negative screening test result (ie, true-negatives).
Bottom Line: The formulas for figuring out sensitivity, specificity, positive predictive value, and negative predictive value are important, and all of their formulas can be rearranged to solve for true-positive, false-positive, false-negative, and true-negative. Making a 2 × 2-cell chart can make it much easier to visualize what the question is asking.
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