Question

**Cancer Screening ~** Breast cancer is the most
common cancer in females in the United States and throughout the
world. Digital mammography test (the process of using low-energy
X-rays to examine the human breast for diagnosis and screening) is
one of the typical techniques for early detection of breast cancer
in recent years. According to a study, digital mammography test has
a sensitivity of 0.97, and a specificity of 0.63 for breast cancer
detection.

**Round all numeric answers to four decimal
places.**

1. Given a theoretical population of 10,000, assume that the base
rate of this population is 0.06. Complete the table below for this
scenario. .

Test Positive | Test Negative | Total | |

Have Breast Cancer | |||

Do not have Breast Cancer | |||

Total | 10,000 |

2. In what proportion of cases do we expect the test will
indicate the patient does **not** have breast
cancer?

3. Among the cases where the test indicates the patient has breast cancer, what proportion of patients would we expect to actually have the disease?

4. Among the cases where the test indicates the patient does not have breast cancer, what proportion of patients would we expect to actually be healthy?

5. Consider a second scenario with a base rate of 0.14, does the probability of actually having breast cancer if someone tests positive increase, decrease or remain the same?

Answer #1

Mammography is used as a form of early detection of breast
cancer in women. We know that if a woman has breast cancer,
mammography will detect it 90% of the time. If the woman does not
have breast cancer, then mammography will give a positive result 7%
of the time. We also know that there is a 0.8% chance that any
given woman has breast cancer.
What is the probability that a woman has breast cancer if she
has a...

Suppose that a screening test for breast cancer has 95%
sensitivity and 90% specificity. Assume 1% of the population being
screened truly has breast cancer.
a. If you really do have breast cancer, what is the probability
that the test says you do?
b. If you really do not have breast cancer, what is the
probability that the test says you do?
c. The screening test is applied to a total of 15 people; 5 who
really do have cancer...

Question 1.
The main purpose of screening is to identify symptomatic disease
using tests, exams, or other procedures.
True
False
Question 2.
The detectable pre-clinical phase of a disease starts when the
disease can be identified by a screening test and ends when the
disease produces symptoms.
True
False
Question 3
.Diseases that are appropriate for screening…
a.
Have serious consequences
b.
Have a treatment that is more effective at an earlier stage
c.
Have a detectable preclinical phase that...

A 2011 article in the British Medical Journal attempts to
elucdiate Bayes' Rule for the medical profession. It's well worth
reading and has some illuminating graphics. In this exercise you
will confirm a result stated in the article. Useful terminology:
The sensitivity of a test for a medical condition is the proportion
of correctly diagnosed patients among those who have the condition.
The specificity of the test is the proportion of correctly
diagnosed patients among those who do not have...

Assume breast cancer affects 0.005 of the Female
population between 45 and 55 years of age.
There are two kinds of positive test results:
True positive (the test indicates you have a disease, and you
actually have it)
False positive (the test indicates you have a disease, but you
actually do not).
Assume mammograms are
0.90 accurate detecting people who actually have breast cancer
(true positive rate)
0.91 accurate for people who do not have breast cancer (true
negative rate)....

Suppose a particular woman tests positive; what is the
probability that she has breast cancer?
To pin this question , please consider a population in which 1%
of women have breast cancer, and a mammography test which has a 90%
chance of returning a correct result. That is, if a woman has
cancer then there is a 90% chance the test will be positive, and if
a woman does not have cancer then there is a 90% chance the test...

A 2011 article in the British Medical Journal attempts to
elucdiate Bayes' Rule for the medical profession. It's well worth
reading and has some illuminating graphics. In this exercise you
will confirm a result stated in the article. Useful terminology:
The sensitivity of a test for a medical condition is the proportion
of correctly diagnosed patients among those who have the condition.
The specificity of the test is the proportion of correctly
diagnosed patients among those who do not have...

One of the most common screening tests for epithelial
ovarian cancer involves the use of biomarkers. Biomarkers have been
applied in the management of epithelial ovarian cancer in several
different ways, including predicting primary disease at an early
stage, distinguishing malignant from benign pelvic masses,
monitoring responses to treatment, and estimating prognosis. A
number of proteins present in either blood or urine have been
identified as specific markers for epithelial ovarian cancer. Let’s
say that you collected data from patients...

A new, non-invasive colon cancer screening method boasts a
sensitivity of 99%. That is, given that a patient has colon cancer,
the screening method has a 0.99 probability of yielding a
positive test. The test is also 90% specific, meaning that if a
person without colon cancer is screened, there is a 0.9 probability
of a negative test result. Among the population of adults
over 45 years of age, the proportion who have colon cancer is
0.0013 (thirteen out of...

Suppose a test for cancer is given. If a person has cancer, the
test will detect it in 96% of the cases; if the person does not
have cancer, the test will show a positive result 1% of the time.
If we assume that 12% of the population taking the test actually
has cancer, what is the probability (rounded to the nearest
percent) that a person taking the test and obtaining a positive
actually has cancer?

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