3. The standard blood test screen for the Human Immunodeficiency Virus (HIV) det

Question

3.   The standard blood test screen for the Human Immunodeficiency Virus (HIV) detects antibodies to the virus using a laboratory test known as ELISA (enzyme-linked immunosorbent assay). If the ELISA test is run properly under recommended conditions, it has a sensitivity of 99% and a specificity of 99%.

a) (4 pts) Assume the HIV-ELISA test is administered to a low-risk community of 100,000 people. By low-risk we mean a population which has an HIV prevalence of 1%. Construct the appropriate 2 X 2 table, determine the number of false positives and false negatives, and calculate the positive predictive value of the ELISA test in this population.

b) (4 pts) Assume the same ELISA test with the same sensitivity and specificity is used to screen a high-risk population (a population of 100,000 people with an HIV prevalence of 12%), Construct the appropriate 2 X 2 table, determine the number of false positives and false negatives, and calculate the positive predictive value of the ELISA test.   

Explanation / Answer

a) The total population is 100,000. Prvalance of HIV in this population is 1%.

False positives = 990

False negative = 10

Positive predictive value = True positive / (true positive + false positive)

= 990 / (990 + 990)

= 990 / 1980

= 0.5

= 50%

b)

False positives = 880

false negatives = 120

Positive predictive value =

True positive / (true positive + false positive)

= 880 / (11880 + 880)

= 880 / 12760

= 0.0689

= 6.89%

Disease present Disease absent Total ELISA positive 990 990 1980 ELISA negative 10 98010 98020 1000 99,000 1,00,000

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