Question

Statistics - Diagnostic tests of medical conditions.

Rules:

Turn in one set of solutions with names of all participating students in the group.

Graphs should be neat, clean and well-labeled. Explain how you arrived at the conclusions (functions/formulas used in calculations.)

“Explanations” and answers should given be given in the form of complete sentences.Since I give partial credit on the projects you should show your work so that some partial credit can be assigned if your answer is incorrect.

Part 1:

Diagnostic tests of medical conditions can have several results.

1) The patient has the condition and the test is positive (+)

2) The patient has the condition and the test is negative (-) – Known as “false negative”

3) The patient doesn’t have the condition and the test is negative (-)

4) The patient doesn’t have the condition and the test is positive (+) – Known as “false positive”

Consider the following:  

      Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV,  

      the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is

      not always correct. Suppose that 1% of a large population carries antibodies to HIV in their blood. Of

      those that carry the HIV antibodies in their blood, 99.85% will have a positive test result and 0.15% will

      have a false-negative test result. Of those that do not carry the HIV antibodies in their blood, 99.4% will

      have a negative test result and 0.60% will have a false-positive test result.

d) What is the sensitivity of the test? (you may need to look up what this term means for this context)

e) What is the specificity of the test? (you may need to look up what this term means for this context)

f) Given that the EIA test is negative, what is the probability that a person has the antibody?

g) In words, define the negative predictive value of a test like this. Define negative predictive value in the context of this test using conditional probability notation. Calculate the negative predictive value of this test?

Answer 1

Disease
Test	Present	%	Absent	%
Positive	True Positive, a	99.85	False Positive, c	0.6
Negative	False Negative, b	0.15	True Negative, d	99.4

d) The sensitivity is define as the result will be positive when the disease is present.

e) The specificity is define as the result will be negative when the disease is not present.

f) The probability that the result will be positivetive given the disease is not present.

g) The Negative predictive value is the probability that the disease is not present when the test is negative,