Question

Suppose that a medical test run on 372 people resulted in 38 positive results. Of those, 22 people were eventually confirmed to have the illness. Among the people who tested negative, 3 were eventually diagnosed through other means, and the rest were healthy. Find the sensitivity of the test, the specificity of the test, and the positive and negative predictive values. The positive predictive value is the probability that a person is ill given that they tested positive, and the negative predictive value is the probability they are healthy if they tested negative.

Answer 1

from given data:

	have disease	not have disease	total
tested positive	22	16	38
tested negative	3	331	334
total	25	347	372

sensitivity of the test =P(tested positive |have disease) =22/25 =0.88 ~ 88%

specificity of the test =P(tested negative | not have disease) =331/347 =0.9539 ~ 95.39%

positive  predictive values =P(have disease |tested positive) =22/38 =0.5789 ~ 57.89%

negative predictive value =P(not have disease |tested negative)=331/334 =0.9910 ~ 99.10%