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Sensitivity and Specificity of a Diagnostic TestPart C. Positive Predictive Value and Negative Predictive Value of a Diagnostic Test in a given Population with a specified Prevalence of a DiseasePart D. Parallel testing & Serial testing
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PUBH 4233 Topics in Global Epidemiology
Instructor: Isaac Chun-Hai Fung, PhD
Homework 1b. Diagnostic tests: Sensitivity, specificity, positive predictive value, negative predictive value, serial testing,
and parallel testing
Questions
Sensitivity and Specificity of a Diagnostic Test
Imagine that your company manufactures diagnostic tests for the SARS-CoV-2 virus. You are going to test how accurate
the test is. You recruit 500 healthy individuals and 500 confirmed COVID-19 case-patients as volunteers.
B.1. Define sensitivity.
Answer:
B.2. Define specificity.
Answer:
B.3. Of the 500 case-patient volunteers, 470 receive positive test results. What is the sensitivity of the diagnostic test?
Answer:
B.4. Of the 500 healthy volunteers, 475 receive negative test results. What is the specificity of the diagnostic test?
Answer:
B.5. Define “false positive” in the context of diagnostic tests
Answer:
B.6. Define “false negative” in the context of diagnostic tests
Answer:
B.7. Define “true positive” in the context of diagnostic tests
Answer:
B.8. Define “true negative” in the context of diagnostic tests
Answer:
B.9. Given the information provided in B.3, how many “false negative” are there among the 500 case-patient volunteers?
Answer:
B.10. Given the information provided in B.4, how many “false positive” are there among the 500 healthy volunteers?
Answer:
Part C. Positive Predictive Value and Negative Predictive Value of a Diagnostic Test in a given Population with a specified
Prevalence of a Disease
C.1. In a metropolitan city of 1 million population, if the current prevalence of COVID-19 is 0.01%, how many people are
having the disease today?
Answer:
C.2. Given a population of 1 million, and the number of sick people with COVID-19 (answer to C.1), if we apply the
diagnostic test as described in Part B.3 and B.4, please complete the following 2-by-2 table.
Answer:
Diagnostic Test Results
Positive Test Results
Positive, i.e., sick
True positive =
Disease Status
Negative, i.e., healthy
False positive =
Negative Test Results
False negative =
True negative =
Total
Total number of sick
people with COVID-19 =
Total number of healthy
people (without COVID-19) =
Total
Total number of positive test
results =
Total number of negative
test results =
TOTAL POPULATION =
1000000
C.3. Calculate the Positive Predictive Value of the diagnostic test in this scenario. Please provide the equation too.
Answer:
C.4. Calculate the Negative Predictive Value of the diagnostic test in this scenario. Please provide the equation too.
Answer:
C.5. Using COVID-19 and other upper respiratory tract infections as examples, explain why in a low prevalence setting,
the positive predictive value of a diagnostic test is low.
Answer:
Part D. Parallel testing & Serial testing
D.1. If you want to reduce the number of false negatives (i.e., increase the sensitivity), and if you are allowed to perform 2
tests, would you choose “parallel testing” or “serial testing”?
Answer:
Part E. Bonus Question: The prevalence of disease X is 10%. Assuming 1000 individuals undergo a test for the disease
and 50 of them tested positive. Assuming the sensitivity of the test was 30%, (a) what is the specificity of the diagnostic
test? (b) what is the positive predictive value in this scenario? Please write all your steps and equations.
Answer:
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