Question

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.

e) In words, define the specificity of a test like this. Define specificity in the context of this test using conditional probability notation. Calculate the specificity of this test? (you may need to look up what this term means for this context)

• Take a look at the last equation/calculation in the right hand column of the example on page 398 of the class textbook for an example of the conditional probability notation.

f) In words, define the positive predictive value of a test like this. Define positive predictive value in the contest of this test using conditional probability notation. Calculate the positive predictive value of this test? (you may need to look up what this term means)

• Take a look at the last equation/calculation in the right hand column of the example on page 398 of the class textbook for an example of the conditional probability notation.

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? (you may need to look up what this term means)

Answer 1

	Positive	Not Positive
Disease	0.009985	0.000015	0.01
Not Disease	0.00594	0.98406	0.99
	0.015925	0.984075	1

e) specificity of a test =

Specificity is the fraction of those without disease who will have a negative test result:

= 0.98406/ 0.99 =0.994

f) Positive predicted value =a person with a positive test truly has the disease

= 0.009985/ 0.015925 = 0.627

g) Negative predicted value =a person with a negative test truly has not the disease

= 0.98406/ 0.984075 = 0.99998

Please feel free to ask any doubt.