Imagine a base rate of 2 percent for a disease, a false positive rate of 10 percent, and a sensitivity rate of 90 percent for the screening test for the disease. Which is the BEST estimate of the conditional probability that a person given a positive test result actually has the disease?

Question

Quizplus · Accepted Answer

We can use Bayes' theorem to calculate the conditional probability. Let's assume we have a population of 10,000 people. 
- 2% of the population actually has the disease, which means that 200 people have it. 
- 10% of the population (1,000 people) will get a false positive result. 
- 90% of the 200 people who have the disease will test positive, which means that 180 people will get a true positive result.

So out of the 1,180 positive results (180 true positives plus 1,000 false positives), only 180 of them actually have the disease.

Thus, the conditional probability that a person given a positive test result actually has the disease is 180/1180 = 15.25% (rounded to the nearest percent). Therefore, the best estimate would be 15 percent or choice C.

Imagine a Base Rate of 2 Percent for a Disease