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

sensitivity = 0.5

specificity = 0.25

Predictive value = 0.5

Step-by-step 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
`=(TP)/(TP +FN) = (50 )/(50 + 50) = 0.5`

specificity
`= (TN)/(TN +FP) = (50 )/(50 + 150) = 0.25`

Predictive value
`= (TP)/(TP +FP) = (50 )/(50 + 50) = 0.5`