Question

In medicine, epidemiologists are often concerned about the accuracy of their tests for the

presence of certain diseases. That is, if a person has a disease, will our test accurately tell

us the truth? Below I will use the \+" to indicate getting a positive test back and \?" to

indicate a negative test. A positive test means the test indicates the patient has the disease.

Specically, we have the following terms:

Sensitivity: The probability that a test gives a positive result given the subject actually has

the disease; P(+j D)

Specicity: The probability that a test gives a negative result given the subject does not

have the disease; P(? j : D)

Positive Predictive Value: The probability that a subject has the disease given the test

comes back positive; P(D j +)

Negative Predictive Value: The probability that a subject does not have the disease given

the test comes back negative; P(: Dj ?)

Assuming that a disease has a known prevalence in the population of 0.10%, meaning 1 person

in 1000 has the disease, and a given test for the disease has a sensitivity value of 0.997 and a

specicity of 0.985: (18 points total).

(a) Calculate the Positive Predictive Value: Suppose a subject from our population gets a

positive test result. What is the probability this subject has the disease (9 points)?

(b) Calculate the Negative Predictive Value: Suppose a subject from our population gets a

negative test result. What is the probability this subject does not have the disease

Answer 1

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