Transcript HW 7a

Homework 7
How do we judge efficacy
of a screening test?
Solve the following problems
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1. To evaluate the performance of a new diagnostic test, the developer
checks it out on 100 known cases of the disease for which the test was
designed, and on 200 controls known to be free of the disease. Ninety of
the known cases yield positive tests, as do 30 of the controls. Based on
these data, what is the sensitivity and specificity of the test?
•
2. A diagnostic test is 95% sensitive and 80% specific. The test group is
comprised of 500 people known to have the disease and 500 people known
to be free of the disease. How many of the known positives would actually
test positive? How many of the known negatives would actually test
negative?
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3. A test with 99.9% sensitivity and 99% specificity is used to screen a
population of 100000 people for a disease with 1% prevalence. What would
be the positive predictive value of this test?
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4. A test with 97% sensitivity and 98% specificity is used to screen a
population of people for a disease with a 3% prevalence rate. What is the
positive predictive value of this test?
Sensitivity and Specificity
PPV and HIV status
World Prevalence Rates
Welcome to the sensitivity, specificity, and positive predictive value calculator.
This calculator explores the effects of sensitivity and specificity with a disease prevalence of 1%
Directions: In this spreadsheet you are asked to choose a sensitivity and specificity. Try using different percentages to investigate how these affect
the number of false positives and false negatives. Start with 100% sensitivity and specificity and note that with 1000 people, 10 have the disease and
990 do not. There are no false negatives nor false positives. Now change the sensitivity and watch what happens to the false test results. Now
change the specificity and note the resulting changes.
PLEASE NOTE: ONLY ENTER NUMBERS IN THE AREAS THAT ARE BLUE!
What is the sensitivity of your test?
Enter your percentage here--->
100%
What is the specificity of your test?
Enter your percentage here--->
100%
Total number of people tested
1000
THE TEST RESULT
positive
negative
Positive Predictive Value : TP/(TP+FP)
100%
Probability that a person who tests positive actually has the disease
Actual Status
positive
negative
true positive
false positive
Tested positive
Sensitivity
10
0
10
100.0%
false negative
true negative
Tested negative
Specificity
0
990
990
100.00%
total with disease total without disease
Total number
10
990
1000
Negative Predictive Value : TN/(TN+FN)
100%
Probability that a person who tests negative is disease-free
Assignment:
(1) Make a graph of the false positives and the false negatives as sensitivity is varied from 0-100% while specificity is held at 100%.
(2) Make a graph of the false positives and the false negatives as specificity is varied from 0-100% while sensitivity is held at 100%.
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Welcome to the HIV positive predictive value calculator.
This calculator explores the effects of prevalence rate on positive predictive value
How many people do you want to test for HIV infection?
For reference, the population of the US (July 2003) is 290,342,554 people.
Enter your number here--->
1000
For reference, the prevalence of HIV in different populations:
Blood donors in the US (due to screening)
0.1%
Drug rehabilitation units in US for I.V. drug users
10%
US adult prevalence rate
0.6%
Botswana adult prevalence rate
38.8%
What is the prevalence of the disease in the population you wish to test?
Enter your percentage here--->
According to the parameters you have chosen, this is the number of tested patients who are actually HIV positive:
1.00%
10
The most common HIV test used in the United States is the ELISA screen which has a sensitivity of 91.3% and a specificity of 99.7%. Those are the values used
in this introductory spreadsheet.
Total number of people tested
1000
THE TEST RESULT
positive
negative
Positive Predictive Value : TP/(TP+FP)
75%
Probability that a person who tests positive actually has the disease
Actual HIV Status
positive
negative
true positive
false positive
Tested positive
Sensitivity
9.13
2.97
12.1
91.3%
false negative
true negative
Tested negative
Specificity
0.87
987.03
987.9
99.70%
total with disease total without disease
Total number
10
990
1000
Negative Predictive Value : TN/(TN+FN)
100%
Probability that a person who tests negative is disease-free
Assignment:
(1) Make a graph of positive predictive values vs. prevalence from 0.0 to 10.0%. (Note that the number of people does not make a difference as PPV is a %)
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