Question

A psychiatrist devised a short screening test for depression. In order to determine this new test’s validity, an independent blind comparison was made with a gold standard for diagnosis of depression among a group of 200 psychiatric outpatients. Among the 50 outpatients found to be depressed according to the gold standard, 35 patients were positive for the test. Among 150 patients found not to be depressed according to the gold standard, 30 patients were found to be positive for the test.

What is the sensitivity?

What is the specificity?

What is the positive predictive value?

What is the negative predictive value?

Answer 1

A study was done among a group of 200 psychiatric outpatients.

Among them 50 outpatients found to be depressed according to the gold standard, 35 patients were positive for the test.

Among 150 patients found not to be depressed according to the gold standard, 30 patients were found to be positive for the test.

So,

	depressed	not depressed
positive for the test	35 (TP)	30 (FP)
negative for the test	15 (FN)	120 (TN)

a. Sensitivity:-

True positive /(True positive + False negative)

35:35 + 15) = 0.7

Answer- The sensitivity of the test is 70%.

b. Specificity:-

True negative / (true negative + false positive)

120: (120 +30) = 0.8

Answer- The specificity of the test is 80%.

c. Positive predictive value

True positive / (true positive + false positive)

35:35 +30) = 0.53

Answer- The positive predictive value of the test is 53%.

d. Negative predictive value

True negative / (false negative + true negative)

120 : (15+ 120) = 0.88

Answer- The negative predictive value of the test is 88%.