MI 580: Principles of Epidemiology
Midterm – Fall 2023
Due: November 1 at the start of class; 90 points
Name: ____________
Instructions:
For all calculations be as explicit as possible by showing you set up all calculations related to the
final answer. Showing your work is a component of the homework grade. Please submit the
homework electronically. All calculations can be rounded to one decimal place.
Question 1 (25 points)
Read the paragraphs below and answer the following questions
In December 1982, a report in the MMWR described three persons who had developed
acquired immunodeficiency syndrome (AIDS) but who had neither of the previously known risk
factors for the disease: homosexual/bisexual activity with numerous partners and intravenous
drug use. These three persons had previously received whole-blood transfusions. By 1983,
widespread recognition of the problem of transfusion-related AIDS led to controversial
recommendations that persons in known high-risk groups voluntarily defer from donating
blood.
In June 1984, after the discovery of the human immunodeficiency virus (HIV), five
companies were licensed to produce enzyme-linked immunosorbent assay (EIA, then
called ELISA) test kits for detecting HIV antibody. A Food and Drug Administration
(FDA) spokesman stated that, "...getting this test out to the blood banks is our No. 1 priority...."
Blood bank directors were anxiously waiting to start screening blood with the new test until
March 2, 1985, the date the first test kit was approved by the FDA. In the pre-licensure evaluation,
sensitivity and specificity of the test kits were estimated using blood samples from four groups: those with
AIDS by CDC criteria, those with other symptoms and signs of HIV infection, those with various
autoimmune disorders and neoplastic diseases that could give a false-positive test result, and presumably
healthy blood and plasma donors. Numerous complex issues were discussed even
before licensure. Among them were understanding the magnitude of the problem of false-positive test
results, and determining whether test-positive blood donors should be notified.
Think back to March 2, 1985. The first HIV antibody test kits will arrive in blood banks in the state in a few
hours. Meeting with State Epidemiologist to discuss the appropriate use of this test are the Commissioner
of Health, the medical director of the regional blood bank, and the chief of the State Drug Abuse
Commission. To help in the discussions, the State Epidemiologist turns to pre-licensure information
regarding the sensitivity and specificity of test kit A. The information indicates that the sensitivity of test kit
A is 95.0% (0.95) and the specificity is 98.0% (0.98). The following table can be completed to calculate
validity measures:
Antibody Present Antibody Absent
Positive Test Result a b
Negative Test Result c d
Total
1a. In a hypothetical population of 1,000,000 blood donors, assume that 400 individuals have
HIV antibody present in this hypothetical population. Thus, 999,600 total blood donors have
the antibody absent. Use the 2 by 2 table above and the information in the article about
1
, MI 580: Principles of Epidemiology
Midterm – Fall 2023
sensitivity and specificity to calculate the positive and negative predictive values of the EIA
test (10 pts)
Antibody Present Antibody Absent Total
Positive Test Result a (380) b (19,992) a+b
Negative Test Result c (20) d (979,608) c+d
Total a+c b+d a+b+c+d
In a hypothetical population of 1,000,000 blood donors, 400 individuals have HIV antibody present.
Sensitivity (True Positive Rate) = a / (a + c) = 0.95
Specificity (True Negative Rate) = d / (b + d) = 0.98
Using this information, we can calculate the values in the table:
a = Sensitivity * (Individuals with HIV antibody) = 0.95 * 400 = 380
c = (Individuals with HIV antibody) - a = 400 - 380 = 20
b = (Individuals without HIV antibody) * (1 - Specificity) = 999,600 * (1 - 0.98) = 19,992
d = (Individuals without HIV antibody) - b = 999,600 - 19,992 = 979,608
Now, we can calculate the positive predictive value (PPV) and negative predictive value (NPV):
PPV = a / (a + b) = 380 / (380 + 19,992) ≈ 1.87%
NPV = d / (c + d) = 979,608 / (20 + 979,608) ≈ 99.99%
1b. Use the 2 by 2 table above and the information in the article about sensitivity and
specificity to calculate the positive and negative predictive values of the EIA test in a
hypothetical population of 1,000 blood donors. Assume that 100 individuals have HIV
antibody present in this hypothetical population. Show all calculations. (10 pts)
In a hypothetical population of 1,000 blood donors, 100 individuals have HIV antibody present.
Sensitivity (True Positive Rate) = 0.95 (same as in Scenario 1a)
Specificity (True Negative Rate) = 0.98 (same as in Scenario 1a)
Using the same sensitivity and specificity values, we can calculate the values in the table:
a = Sensitivity * (Individuals with HIV antibody) = 0.95 * 100 = 95
c = (Individuals with HIV antibody) - a = 100 - 95 = 5
b = (Individuals without HIV antibody) * (1 - Specificity) = 900 * (1 - 0.98) = 18
d = (Individuals without HIV antibody) - b = 900 - 18 = 882
Now, we can calculate the positive predictive value (PPV) and negative predictive value (NPV):
PPV = a / (a + b) = 95 / (95 + 18) ≈ 84.09%
NPV = d / (c + d) = 882 / (5 + 882) ≈ 99.44%
1c. Given the same sensitivity and specificity in questions 1a and 1b, why are the positive
predictive values calculated in 1a and 1b drastically different from each other? Provide a
rationale. (5 pts)
The positive predictive values in scenarios 1a and 1b are drastically different because they depend not
only on the sensitivity and specificity of the test but also on the prevalence of the condition in the
population being tested.
2
Midterm – Fall 2023
Due: November 1 at the start of class; 90 points
Name: ____________
Instructions:
For all calculations be as explicit as possible by showing you set up all calculations related to the
final answer. Showing your work is a component of the homework grade. Please submit the
homework electronically. All calculations can be rounded to one decimal place.
Question 1 (25 points)
Read the paragraphs below and answer the following questions
In December 1982, a report in the MMWR described three persons who had developed
acquired immunodeficiency syndrome (AIDS) but who had neither of the previously known risk
factors for the disease: homosexual/bisexual activity with numerous partners and intravenous
drug use. These three persons had previously received whole-blood transfusions. By 1983,
widespread recognition of the problem of transfusion-related AIDS led to controversial
recommendations that persons in known high-risk groups voluntarily defer from donating
blood.
In June 1984, after the discovery of the human immunodeficiency virus (HIV), five
companies were licensed to produce enzyme-linked immunosorbent assay (EIA, then
called ELISA) test kits for detecting HIV antibody. A Food and Drug Administration
(FDA) spokesman stated that, "...getting this test out to the blood banks is our No. 1 priority...."
Blood bank directors were anxiously waiting to start screening blood with the new test until
March 2, 1985, the date the first test kit was approved by the FDA. In the pre-licensure evaluation,
sensitivity and specificity of the test kits were estimated using blood samples from four groups: those with
AIDS by CDC criteria, those with other symptoms and signs of HIV infection, those with various
autoimmune disorders and neoplastic diseases that could give a false-positive test result, and presumably
healthy blood and plasma donors. Numerous complex issues were discussed even
before licensure. Among them were understanding the magnitude of the problem of false-positive test
results, and determining whether test-positive blood donors should be notified.
Think back to March 2, 1985. The first HIV antibody test kits will arrive in blood banks in the state in a few
hours. Meeting with State Epidemiologist to discuss the appropriate use of this test are the Commissioner
of Health, the medical director of the regional blood bank, and the chief of the State Drug Abuse
Commission. To help in the discussions, the State Epidemiologist turns to pre-licensure information
regarding the sensitivity and specificity of test kit A. The information indicates that the sensitivity of test kit
A is 95.0% (0.95) and the specificity is 98.0% (0.98). The following table can be completed to calculate
validity measures:
Antibody Present Antibody Absent
Positive Test Result a b
Negative Test Result c d
Total
1a. In a hypothetical population of 1,000,000 blood donors, assume that 400 individuals have
HIV antibody present in this hypothetical population. Thus, 999,600 total blood donors have
the antibody absent. Use the 2 by 2 table above and the information in the article about
1
, MI 580: Principles of Epidemiology
Midterm – Fall 2023
sensitivity and specificity to calculate the positive and negative predictive values of the EIA
test (10 pts)
Antibody Present Antibody Absent Total
Positive Test Result a (380) b (19,992) a+b
Negative Test Result c (20) d (979,608) c+d
Total a+c b+d a+b+c+d
In a hypothetical population of 1,000,000 blood donors, 400 individuals have HIV antibody present.
Sensitivity (True Positive Rate) = a / (a + c) = 0.95
Specificity (True Negative Rate) = d / (b + d) = 0.98
Using this information, we can calculate the values in the table:
a = Sensitivity * (Individuals with HIV antibody) = 0.95 * 400 = 380
c = (Individuals with HIV antibody) - a = 400 - 380 = 20
b = (Individuals without HIV antibody) * (1 - Specificity) = 999,600 * (1 - 0.98) = 19,992
d = (Individuals without HIV antibody) - b = 999,600 - 19,992 = 979,608
Now, we can calculate the positive predictive value (PPV) and negative predictive value (NPV):
PPV = a / (a + b) = 380 / (380 + 19,992) ≈ 1.87%
NPV = d / (c + d) = 979,608 / (20 + 979,608) ≈ 99.99%
1b. Use the 2 by 2 table above and the information in the article about sensitivity and
specificity to calculate the positive and negative predictive values of the EIA test in a
hypothetical population of 1,000 blood donors. Assume that 100 individuals have HIV
antibody present in this hypothetical population. Show all calculations. (10 pts)
In a hypothetical population of 1,000 blood donors, 100 individuals have HIV antibody present.
Sensitivity (True Positive Rate) = 0.95 (same as in Scenario 1a)
Specificity (True Negative Rate) = 0.98 (same as in Scenario 1a)
Using the same sensitivity and specificity values, we can calculate the values in the table:
a = Sensitivity * (Individuals with HIV antibody) = 0.95 * 100 = 95
c = (Individuals with HIV antibody) - a = 100 - 95 = 5
b = (Individuals without HIV antibody) * (1 - Specificity) = 900 * (1 - 0.98) = 18
d = (Individuals without HIV antibody) - b = 900 - 18 = 882
Now, we can calculate the positive predictive value (PPV) and negative predictive value (NPV):
PPV = a / (a + b) = 95 / (95 + 18) ≈ 84.09%
NPV = d / (c + d) = 882 / (5 + 882) ≈ 99.44%
1c. Given the same sensitivity and specificity in questions 1a and 1b, why are the positive
predictive values calculated in 1a and 1b drastically different from each other? Provide a
rationale. (5 pts)
The positive predictive values in scenarios 1a and 1b are drastically different because they depend not
only on the sensitivity and specificity of the test but also on the prevalence of the condition in the
population being tested.
2
