Suppose that a medical test for a certain disease has a sensitivity and specificity of 93%....

Suppose that a medical test for a certain disease has a sensitivity and specificity of 93%. The test is applied to a population of which 11% are actually infected by the disease. 1. Calculate the NPV and the PPV. 2. What percent of the total population will test positive who are disease-free? 3. What percent of the total population will test negative who have the disease?

Expert Solution

From the given,
The probability of testing which has the disease, P(D) = 11% = 0.11
Assume H is the event of randomly selecting an individual who is disease-free i.e, healthy, then P(H) = 1 - P(D) = 0.89.
It is given that the sensitivity of the test is 0.93 i.e if a person has the disease, then the probability that the diagnostic blood test comes back positive is 0.93. Which is represented as P(T+| D) = 0.93
It is given that the specificity of the test is 0.93. i.e, if a person is free of the disease, then the probability that the diagnostic test comes back negative is 0.93. Which is represented as P(T− | H) = 0.93

Calculation of the percentage of the total population will test positive who are disease-free:

If a person is free of the disease, then the probability that the diagnostic test comes back positive is 1 − P(T− | H) = 1 - 0.93 = 0.07. That is, P(T+ | H) = 0.07.
Therefore, the percentage of the total population will test positive who are disease-free is 7%.

Calculation of the percentage of the total population will test negative who have the disease:

If a person has the disease, then the probability that the diagnostic test comes back negative is 1 − P(T+ | D) = 1 - 0.93 = 0.07. That is, P(T− | D) = 0.07.
Therefore, the percentage of the total population will test negative who has the disease is 7%.

Calculation of the Negative predicted value (PPV):

Negative predicted value refers to the post-test probability of no disease given a negative test result.

Calculation of the Positive predicted value (PPV):

Positive predicted value refers to the post-test probability of disease providing a positive result.

ekkarill92 answered 1 year ago

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