Question

**Part 1:**

Diagnostic tests of medical conditions can have several results.

1) The patient has the condition and the test is positive (+)

2) The patient has the condition and the test is negative (-) – Known as “false negative”

3) The patient doesn’t have the condition and the test is negative (-)

4) The patient doesn’t have the condition and the test is positive (+) – Known as “false positive”

Consider the following:

Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV,

the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is

not always correct. Suppose that 1% of a large population carries antibodies to HIV in their blood. Of

those that carry the HIV antibodies in their blood, 99.85% will have a positive test result and 0.15% will

have a false-negative test result. Of those that do not carry the HIV antibodies in their blood, 99.4% will

have a negative test result and 0.60% will have a false-positive test result.

- Draw a tree diagram for selecting a person from this population and testing his or her blood.

b) Construct a probability table that shows the probabilities for individuals in this population with

respect to the presence of antibodies and test results.

c) What is the probability the EIA is positive for a randomly chosen person from this population?

d) In words, define the sensitivity of a test like this. Define the sensitivity in the context of this test using conditional probability notation. Calculate the sensitivity of this test? (you may need to look up what this term means for this context)

e) In words, define the specificity of a test like this. Define specificity in the context of this test using conditional probability notation. Calculate the specificity of this test? (you may need to look up what this term means for this context)

- f) In words, define the positive predictive value of a test like this. Define positive predictive value in the contest of this test using conditional probability notation. Calculate the positive predictive value of this test? (you may need to look up what this term means)

g) In words, define the negative predictive value of a test like this. Define negative predictive value in the context of this test using conditional probability notation. Calculate the negative predictive value of this test? (you may need to look up what this term means)

Answer #1

Diagnostic tests of medical conditions can have several
results.
1) The patient has the condition and
the test is positive (+)
2) The patient has the condition and the test is
negative (-) – Known as “false negative”
3) The patient doesn’t have the condition and the test is
negative (-)
4) The patient doesn’t have the condition and the test is
positive (+) – Known as “false positive”
Consider the following:
Enzyme immunoassay (EIA) tests
are used...

Statistics - Diagnostic tests of medical conditions.
Rules:
Turn in one set of solutions with names of all participating
students in the group.
Graphs should be neat, clean and well-labeled. Explain how you
arrived at the conclusions (functions/formulas used in
calculations.)
“Explanations” and answers should given be given in the form of
complete sentences.Since I give partial credit on the projects you
should show your work so that some partial credit can be assigned
if your answer is incorrect.
Part...

Diagnostic tests of medical conditions can have several types of
results. The test result can be positive or negative, whether or
not a patient has the condition. A positive test (+) indicates that
the patient has the condition. A negative test (−) indicates that
the patient does not have the condition. Remember, a positive test
does not prove the patient has the condition. Additional medical
work may be required. Consider a random sample of 200 patients,
some of whom have...

Diagnostic tests of medical conditions have several results. The
rest result can be positive or negative. A positive test (+)
indicates the patient has the condition. A negative test (–)
indicates the patient does not have the condition. Remember, a
positive test does not prove the patient has the condition.
Additional medical work may be required. Consider a random sample
of 201 patients, some of whom have a medical condition and some of
whom do not. Results of a new...

Suppose that a medical test run on 372 people resulted in 38
positive results. Of those, 22 people were eventually confirmed to
have the illness. Among the people who tested negative, 3 were
eventually diagnosed through other means, and the rest were
healthy. Find the sensitivity of the test, the specificity of the
test, and the positive and negative predictive values. The positive
predictive value is the probability that a person is ill given that
they tested positive, and the...

According to Bendavid et al. (2020), 2.8% of residents in the
Santa Clara County, California have antibodies to SARS-CoV-2.
BioMedomics Covid-19 IgM/IgG Rapid Test has 88.7% sensitivity and
90.6% specificity. If a resident of Santa Clara County tested
positive for the SARS-CoV-2 antibody from that test, what is the
probability that the person actually has the antibody? Clearly
define the events of interest using the context of the problem to
receive full credit.
Hint: (1) Sensitivity measures how often a...

3. A diagnostic test has 95% sensitivity (the probability a
person with the condition tests positive = 0.95) and 95%
specificity (the probability a person without the condition tests
negative = 0.95). In a population of people given the test, 1% of
the people have the condition (probability a person has the
condition = 0.01). (a) What proportion of the people will test
positive? (b) Given a person has tested positive, what is the
probability he/she has the condition?

We have the following statements:
1 percent of the population is infected by a disease.
We have a test, a, that has a sensitivity of 90% and a
specificity of 95%.
Sensitivity means that a person will test positive IF they are
in fact infected.
Specificity means that a person will test negative IF they are
in fact not infected.
The question is:
What is the probability that a random tested person gets
a positiv result?
And what is the...

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...

what is the correct answer..
1- In raising the cutoff point for a screening test, which of
the following is the likely result?
A
An increase in sensitivity
B
An increase in specificity
C
An increase in false positives
D
An increase in prevalence
E
An increase in lead time bias
2- If the screening test does not delay the time of death from a
condition but makes survival appear longer because of earlier
detection of disease, there is evidence...

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