A diagnostic test for a particular disease has a sensitivity of 0.90 and a specificity of 0.80. A single test is applied to each subject in the population in which the diseased population is 30%. What is the probability that a person, negative to this test, has no disease?

a) Less than 50%

b) 70%

c) 95%

d) 72%

Correct answer : c) 95%

The probability that a person negative to this test has no disease signifies the Negative predictive value of the test.

A diagnostic test for a particular disease has a sensitivity of 0.90 and a specificity of 0.80. A single test is applied to each subject in the population in which the diseased population is 30%. What is the probability that a person, negative to this test, has no disease?

a) Less than 50%

b) 70%

c) 95%

d) 72%

Correct answer : c) 95%

How to calculate the answer?

Someone kindly post the calculations in a easy to understand method.

assume there are 1000 people .so,there are 300 diseased people among them(as it given prevalence 30%)and who doesn’t have the disease is 700.

so true positve is 270(sensitivity-90%)

false negative is 30.

true negative is 560(specificity-80%).

false positve is 140.

NEGATIVE PRED; VALUE=(TRUE NEGATIVE/TRUE NEGATIVE+FALSE NEGATIVE)*100

=(560/560+30)*100

=94.9%

assume there are 1000 people .so,there are 300 diseased people among them(as it given prevalence 30%)and who doesn’t have the disease is 700.

so true positve is 270(sensitivity-90%)

false negative is 30.

true negative is 560(specificity-80%).

false positve is 140.

NEGATIVE PRED; VALUE=(TRUE NEGATIVE/TRUE NEGATIVE+FALSE NEGATIVE)*100

=(560/560+30)*100

=94.9%