Question

A serologic test is being devised to detect a hypothetical chronic disease.Three hundred individuals were referred to a laboratory for testing. Onehundred diagnosed cases were among the 300. A serologic test yielded200 positives, of which one-fourth were true positives. Calculate thesensitivity, specificity, and predictive value of this test.

Answer 1

Answer:

sensitivity = 0.5

specificity = 0.25

Predictive value = 0.5

Explanation:

Given data:

Total number of cases = 300

Total number of positively predicted = 200

Total number of actual positive = 100

NOte : 1/4th yield true positives

confusion matrix for given condition is given below

                                 predicted: yes               predicted: NO

actual: Yes               TP = 50                           FN = 50       =   100

actual: NO                FP = 150                        TN = 50

                               = 200                                  = 100                        

TP - true positive

FP - false positive

TN - true negative

FN - false negative

sensitivity  $=\frac{TP}{TP +FN} = \frac{50 }{50 + 50} = 0.5$

specificity $= \frac{TN}{TN +FP} = \frac{50 }{50 + 150} = 0.25$

Predictive value  $= \frac{TP}{TP +FP} = \frac{50 }{50 + 50} = 0.5$