Question

Most medical tests used today have about a 5% false positive rate, which some doctors will take to mean that if a patient’s test comes back positive, that the patient has a 95% chance of having the disease. A 95% chance is very high, and so the doctor will assume that the patient has the disease and will start an aggressive and potentially dangerous course of treatment. For your first problem, you will show that, for rare diseases, this common assumption is not even close to accurate.

1. A certain disease is present in 1 out of 1000 people, the probability that a randomly choosen person has this disease is 0.001. A hospital uses a particular test to detect the presence of this disease. If a person has the disease, then the test will detect it 100% of the time, and if a person does not have the disease, the test will detect it 5% of the time. If a patient’s test comes back positive, what is the probability that the patient actually has the disease? Is your answer close to 95% or 0.95? Round your answer to two decimal places. (Proper work includes a tree-diagram for the given scenario and any formulas that are needed.)

One reason for the low probability of a “true” positive result is that the disease is so rare. It is only present in 0.1% of the population, whereas the test will detect it in about 5.1% of the population.

2. Assume that we have the same scenario from Problem 1, except that this time the disease is present in 1 out of 3 people, so that the probability that a randomly choosen person has this disease is 1/3. If a patient’s test comes back positive this time, what is the probability that the patient actually has the disease? Is your answer closer to 95% or 0.95 than last time? Round your answer to two decimal places. (Proper work includes a tree-diagram for the given scenario and any formulas that are needed.)

Answer #1

1) A certain disease is present in 1 out of 1000 people, the probability that a randomly choosen person has this disease is 0.001. The prevelance of the disease is . Define the events

The given conditional probabilities are . Using total probability theorem,

If a patient’s test comes back positive, the probability that the patient actually has the disease is the conditional probability

It is far lesser than 95%.

2) When . Recalculate all the probabilities.

It is closer to 95%.

A rare disease exists in 3% of the population. A medical
test exists that can detect (positive
results) this disease 98% of the time for those who do,
in fact have this disease. On the other hand, 5% of the time
positive results will come back for those who do not have this
disease.
a. Draw a "tree diagram" illustrating this scenario. b.
Determine the probability that a person will test positive. C.
Determine the probability that a person who...

A diagnostic test for disease X correctly identifies the disease
94% of the time. False positives occur 14%. It is estimated that
0.95% of the population suffers from disease X. Suppose the test is
applied to a random individual from the population. Compute the
following probabilities. (It may help to draw a probability
tree.)
The percentage chance that the test will be positive = %
The probability that, given a positive result, the person has
disease X = %
The...

A virus has a rare occurrence: the virus
occurs, on average, 20 out of
every 200000 people.
An antibody test has been devised. Among those
with the virus, the test correctly detects the
person has been infected with probability
0.95.
Among those without the virus, the test correctly
identifies the person as virus free 0.95 % of the time.
Suppose you have tested positive for the
disease. How worried should you be?
Answer this by computing your probability of
having the...

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...

Mr. Smith goes to his doctor and is told that he just tested
positive for some fatal and rapidly progressing disease. Patients
with this disease have a life expectancy exponentially distributed
with mean 1 year. Patients of Mr. Smith's age without this disease
have a life expectancy exponentially distributed with mean 20
years. 0.1% of the population (i.e., one person in a thousand)
suffers from this disease. There is no known treatment that can
alter its progression.
This test (like...

1) The reliability of a particular skin test for tuberculosis
(TB) is as follows: the sensitivity of the test is 0.9 (the test
comes back positive 90% of the time if the subject has TB) and the
specificity of the test is 0.95 (if the subject does not have TB,
the test comes back negative 95% of the time). In a large
population, only 0.3% (0.003) of the people have TB. A person is
selected at random and given the...

2. Suppose next that we have even less knowledge of our patient,
and we are only given the accuracy of the blood test and prevalence
of the disease in our population. We are told that the blood test
is 95 percent reliable, this means that the test will yield an
accurate positive result in 95% of the cases where the disease is
actually present. Gestational diabetes affects 6% of the population
in our patient’s age group, and that our test...

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...

QUESTION 5
Imagine a test that's 100% sensitive and 80% specific and it's
testing for something that has a 5% chance of occurring. What's the
chance that a test result will come back positive (remember, there
are two ways to get a positive result: a true positive and a false
positive). Express your answer as a value between 0 and 1 to two
decimal places.
QUESTION 6
Suppose you're hiring a new worker for your business. You'd like
someone reliable....

Say I bought two tests for lead in water: X and Y . Test X
indicates there’s lead in the water 95% of the time when it is
present but has a 10% false positive rate (the times when it
detects lead, but it’s not actually there). Test Y is 90% effective
at recognizing lead but has a 5% false positive rate. The tests use
independent methods of identifying lead which occurs in 3% of
houses.
(a) Write the statements...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 16 minutes ago

asked 43 minutes ago

asked 53 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago