Question

Based on all the information currently available, you estimate that the patient in your office has a one in four chance of having a serious disease. You order a diagnostic test with sensitivity of 95% and specificity of 90%. The result comes back negative. Based on all the information now available, the chance your patient really has the disease is closest to:

Select one:

a. 1.5%

b. 3%

c. 5%

d. 25%

Answer 1

Let the total population be 1000

1 out of 4 chances of having the disease = 25% chance means 250 people will have the disease

Specificity of test = 90%

Sensitivity of test = 95%

So people with disease = 250

People without disease = 750

Because of 95% sensitivity,

True positive result = 95% of 250 = 238

False negative result = 12

Specificity is 90%,

So out of 750 people, 90% of 750 = 675 people will show true negative results.

Therefore,

Chance of having the disease now (PPV) = 12/(12+675)

= 0.017 x 100% = 1.7% roughly 1.5%

The correct answer is : 1.5%