Question

"To diagnose colorectal cancer, the hemoccult test is
conducted to detect occult

blood in the stool. For symptom-free people over 50 years old who
participate in

screening using the hemoccult test, the following information is
available.

The probability that one of these people has colorectal cancer is
0.3 percent. If a

person has colorectal cancer, the probability is 50 percent that he
will have a

positive hemoccult test. If a person does not have colorectal
cancer, the

probability is 3 percent that he will still have a positive
hemoccult test. Imagine a

person (over age 50, no symptoms) who has a positive hemoccult test
in your

screening. What is the probability that this person actually has
colorectal

cancer?"

using the above paragraphs

Identify the base rate (or prevalence in medical literature),
sensitivity (the

percentage of individuals with a disease who are correctly
classified as having the

disease), and false positive rate in this case. Provide a brief and
clear description

of these terms using your own words.

Answer #1

"To diagnose colorectal cancer, the hemoccult test is
conducted to detect occult
blood in the stool. For symptom-free people over 50 years old who
participate in
screening using the hemoccult test, the following information is
available.
The probability that one of these people has colorectal cancer is
0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that he
will have a
positive hemoccult test. If a person does not have colorectal
cancer, the
probability is 3...

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...

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?

A blood test to diagnose a disease was performed on a
number of patients. Given the following information:
Number of patients who have a positive test result and
have the disease = 1,491
Number of patients who have a negative test result =
3,149
Number of patients who have a positive test result but
don’t have the disease = 89
Number of patients who do not have the disease =
3,017
Construct, label, and completely fill in a 2 x...

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...

The prevalence of a disease D among the population is 3%. There
is a diagnostic test for disease D. The sensitivity of this test is
99%, this means that the test is positive given that the person has
the disease. The specificity of this test is 98%, this means that
the test is negative given that the person does not have the
disease.
a) Given that a person tests positive, what is the probability
that the person does not have...

Suppose that, of men
who undergo routine screening, 1/501 have prostate cancer. Of the
men who undergo screening and do have prostate cancer, 80% will
have a positive test. Of the men who undergo screening but don’t
have prostate cancer, only 5% have a positive test. A man of this
age undergoes routine screening and has a positive test. What is
the probability that he has prostate cancer?
(a) 0 to 0.2
0.21 to 0.8
0.81 to 0.9
0.91 to...

The American Disease X Foundation reports that 6% of
the population over 50 years of age has Disease X. You inquire as
to the source of their information, and they cite disease
population screening data in the literature which reports that 6%
of that population was positive when screened. Referring to the
literature, you discover that the screening test used had
sensitivity of 95% and specificity of 98%. What proportion of the
population over 50 years of age do you...

The American Disease X Foundation reports that 6% of
the population over 50 years of age has Disease X. You inquire as
to the source of their information, and they cite disease
population screening data in the literature which reports that 6%
of that population was positive when screened. Referring to the
literature, you discover that the screening test used had
sensitivity of 95% and specificity of 98%. What proportion of the
population over 50 years of age do you...

Use Bayes theorem to answer the following question. A screening
test for Hepatitis B in blood donors has been determined to have a
sensitivity of 0.97 and a specificity of 0.96. If the prevalence
(what is exist) of hepatitis B in the Canadian population is 10 out
of 1000 people what is the predictive value of this test for a
positive result?

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