A major manufacturing company with 10,000 employees introduces
mandatory drug testing for all its workers. A urine test has been
selected for screening the workers. The test has 99% sensitivity and
97% specificity for detecting cocaine metabolites. A previous crosssectional study in the area indicated a prevalence of cocaine use of
2%.
a)
Construct a 2 X 2 table for these data:
Truly
Positive
Tested
Positive
Tested
Negative
Truly
Negative
Tested
Positive
Tested
Negative
Truly
Positive
198 (a)
Truly
Negative
294 (b)
492
2 (c)
9506 (d)
9508 (c + d)
200 (a + c)
9800 (b+d)
(a + b)
10,000
Calculate and interpret the number of false positives:
A) There were 294 people who tested positive for cocaine but in fact
were not drug users and did not have cocaine metabolites in their
urine.
B) There were 2 people who tested positive for cocaine but in fact
were not drug users and did not have cocaine metabolites in their
urine.
C) There were 198 people who tested positive for cocaine but in fact
were not drug users and did not have cocaine metabolites in their
urine.
Tested
Positive
Tested
Negative
Truly
Positive
198 (a)
Truly
Negative
294 (b)
492
2 (c)
9506 (d)
9508 (c + d)
200 (a + c)
9800 (b+d)
(a + b)
10,000
Calculate and interpret the number of false negatives:
A) There were 198 people who tested negative for cocaine but in fact
were drug users with cocaine metabolites present in their urine.
B) There were 2 people who tested negative for cocaine but in fact
were drug users with cocaine metabolites present in their urine.
C) There were 294 people who tested negative for cocaine but in fact
were drug users with cocaine metabolites present in their urine.
Tested
Positive
Tested
Negative
Truly
Positive
198 (a)
Truly
Negative
294 (b)
492
2 (c)
9506 (d)
9508 (c + d)
200 (a + c)
9800 (b+d)
(a + b)
10,000
Calculate and interpret the Positive Predictive Value:
A) Positive Predictive Value = a / (a+b) = 198 /492 = 0.402.
The probability that a person is using cocaine given that he or she has
a positive urine test for the drug is 40.2%.
B) Positive Predictive Value = a / (total) = 2 /10000 = 0.0002.
The probability that a person is using cocaine given that he or she has
a positive urine test for the drug is 0.020%.
C) Positive Predictive Value = a / (a+c) = 198 /200 = 0.99.
The probability that a person is using cocaine given that he or she has
a positive urine test for the drug is 99.0%.
A major manufacturing company with 10,000 employees introduces
mandatory drug testing for all its workers. A urine test has been
selected for screening the workers. The test has 99% sensitivity and
97% specificity for detecting cocaine metabolites. A previous crosssectional study in the area indicated a prevalence of cocaine use of
2%.
Construct a 2 X 2 table for these data:
Prevalence =2% means 200 of 10,000 employees will be true
positives
Sensitivity = a / (a+c) = 0.99
a / (200) = 0.99
a = 198 this goes in cell ‘a’ in 2 X 2 table
Specificity = d / (b+d) = 0.97
d / (9800) = 0.97
d = 9506 this goes in cell ‘d’ in 2 X 2 table
Tested
Positive
Tested
Negative
Truly
Positive
198 (a)
Truly
Negative
294 (b)
492
2 (c)
9506 (d)
9508 (c + d)
200 (a + c)
9800 (b+d)
10,000
(a + b)
Tested
Positive
Tested
Negative
Truly
Positive
198 (a)
Truly
Negative
294 (b)
492
2 (c)
9506 (d)
9508 (c + d)
200 (a + c)
9800 (b+d)
(a + b)
10,000
Calculate and interpret the number of false positives:
A) There were 294 people who tested positive for cocaine but in
fact were not drug users and did not have cocaine metabolites in
their urine.
B) There were 2 people who tested positive for cocaine but in fact
were not drug users and did not have cocaine metabolites in their
urine.
C) There were 198 people who tested positive for cocaine but in fact
were not drug users and did not have cocaine metabolites in their
urine.
Calculate and interpret the number of false negatives:
A) There were 198 people who tested negative for cocaine but in fact
were drug users with cocaine metabolites present in their urine.
B) There were 2 people who tested negative for cocaine but in
fact were drug users with cocaine metabolites present in their
urine.
C) There were 294 people who tested negative for cocaine but in fact
were drug users with cocaine metabolites present in their urine.
Tested
Positive
Tested
Negative
Truly
Positive
198 (a)
Truly
Negative
294 (b)
492
2 (c)
9506 (d)
9508 (c + d)
200 (a + c)
9800 (b+d)
(a + b)
10,000
Calculate and interpret the Positive Predictive Value:
A) Positive Predictive Value = a / (a+b) = 198 /492 = 0.402.
The probability that a person is using cocaine given that he or
she has a positive urine test for the drug is 40.2%.
B) Positive Predictive Value = a / (total) = 2 /10000 = 0.0002.
The probability that a person is using cocaine given that he or she has
a positive urine test for the drug is 0.020%.
C) Positive Predictive Value = a / (a+c) = 198 /200 = 0.99.
The probability that a person is using cocaine given that he or she has
a positive urine test for the drug is 99.0%.