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University Of Arizona *
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Course
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Subject
Mechanical Engineering
Date
Jan 9, 2024
Type
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BME 376: Assignment E
This assignment is focused on diagnostic tests. All answers should be entered in the space
provided below each question.
Most/each sub-question(s) will be graded as 1 (complete) or 0 (incomplete).
Upload a completed word or PDF document to D2L.
Type equations (using in-built Word features) and text. Avoid screenshots or images. You
may use the following equation (based on Bayes’ theorem) as the basis for this assignment.
Positve PredictiveValue
=
Sensitivity
∗
Prevalence
Sensitivity
∗
Prevalence
+
(
1
−
Specificity
)
(
1
−
Prevalence
)
1.
Cervical cancer is a disease for which the chance of containment is high given that it is
detected early.
The Pap Smear is a widely accepted screening procedure that can detect
cervical cancer; it has been credited with being primarily responsible for the decreasing
death rate due to cervical cancer in recent years.
The sensitivity and specificity of Pap
Smear are 83.75% and 81.36%, respectively. The prevalence of cervical cancer among
women is 8.3 cases per 100,000 women.
1.1.
[2 points]
Compute the positive predictive value of the test
1.2.
[2 points]
Compute the negative predictive value of the test
1.3.
[2 points]
Comment on the predictive values.
1
What would you suggest if the test turns out to be positive?
What would you suggest if the test turns out to be negative?
2.
A “Gold Standard” procedure is available to detect whether or not a person has tuberculosis
(TB).
Chest X-rays are routinely used as an alternative simple inexpensive procedure to
detect the presence or absence of the disease in individuals.
We would like to evaluate how
good the X-rays are as diagnostic tools. A sample of 30 people, who are known to have
tuberculosis, are given a chest x-ray. Another sample of 1,790, who are known not to have
tuberculosis, are also given a chest x-ray.
The results are summarized below.
X-ray
Tuberculosis
Yes
No
Negative
8
1739
Positive
22
51
(a)
[4 points]
Estimate the sensitivity and specificity of chest X-rays in detecting TB.
(b)
[4 points]
In USA, 9.3 people out of 100,000 have tuberculosis.
Compute the predictive
value of a positive Test and predictive value of a negative test.
2
(c)
[2 points]
Comment on the usefulness of chest X-rays as a diagnostic tool i.e., what
would you suggest if the test turns out to be positive?
What would you suggest if the
test turns out to be negative?
3.
The following data are from a study comparing self-reported smoking status with measured
serum cotinine level. In this study, cotinine level was used as a screening tool for smoking
status. For various cut-off points (for cotinine level), the observed sensitives and specificities
are given below.
Cotinine level (ng/mL)
Sensitivity
Specificity
5
0.971
0.898
7
0.964
0.931
9
0.960
0.946
11
0.954
0.951
13
0.950
0.954
14
0.949
0.956
15
0.945
0.960
17
0.939
0.963
19
0.932
0.965
a)
[3 points]
Determine the cut-off point that will yield the most optimal sensitivity and
specificity for the cotinine levels as a screening test.
3
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b)
[1 point]
Cotinine levels can be measured in both saliva and urine. A study determined
the AUC - area under the receiver operating characteristic (ROC) curve – was 0.958 and
0.973 for saliva and urine-based cotinine test, respectively. Based on the AUC, which test
is more reliable?
4
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