A new screening test for the development of mitral regurgitation in the setting of rheumatic fever is created. A study of 1000 patients with a history of Streptococcus pyogenes infection and a diagnosis of rheumatic fever is performed using this test, which has 90% sensitivity and 85% specificity. The prevalence of mitral re- gurgitation in this population is estimated to be 40%. What is the positive predictive value of this test?
(A) 8%
(B) 20%
(C) 80%
(D) 85%
(E) 93%
The correct answer is C. Positive predictive value (PPV) is the probability that a positive test result is truly positive. It can be calculated by taking the number of true-positive results and dividing it by the total positive results. Since the prevalence is 40%, the number of positive patients will be 0.4 × 1000 = 400 and the number of negative patients will be 1000 - 400 = 600. The number of true-positives can be found by multiplying the sensitivity by this total, giving us 0.9 × 400 = 360. The number of false-positives can be found by multiplying the specificity by the total negative patients and subtracting that product from the total negatives, or 600 - (0.85 × 600) = 90. Then, 360 / (360 + 90) = 0.8, or 80%. Remember: PPV and negative predictive value change with prevalence in a population, so the esti- mated prevalence must be taken into account when calculating the number of true-positives and true-negatives.
Answer A is incorrect. Dividing the number of false-negative results by the total negative re- sults would give an answer of 8%.
Answer B is incorrect. Dividing the number of false-positive (rather than true-positive) find- ings by the total positive results would give an answer of 20%.
Answer D is incorrect. Switching the values for sensitivity and specificity would give an an- swer of 85%.
Answer E is incorrect. The negative predictive value is 93%.