A doctor examines a patient and thinks the patient might have a disease that is very...
A doctor examines a patient and thinks the patient might have a disease that is very rare -- 1 in 5 million. The patient goes for a test which is 99.9% accurate -- meaning false positives as well as false negatives occur only .1 percent of the time. a) If the test comes back positive, what is the probability that the patient has the disease? b) If, after seeing the test results, the patient decides to have another lab administer the same test and the test results come back positive again, what is the probability that he has the disease now?
Hint: You can use a Bayesian calculator such as: http://psych.fullerton.edu/mbirnbaum/bayes/BayesCalc.htm
Homework Answers
Add Answer to:
A doctor examines a patient and thinks the patient might have a
disease that is very...
A disease affects 16% of the population. There is a test (not perfect) that detects disease...
A disease affects 16% of the population. There is a test (not perfect) that detects disease with a probability of 98% (i.e comes back positive when the person has the disease). However, the test produces 5% false positives, i.e comes back positive even though the person does not have the disease. i) A person who has the disease is tested, what is the probability that the test will come back negative. ii) What is the probability that a randomly selected...
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D...
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) = δ, with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D'l+). For this screening to be useful at a given δ, what is required of e ?
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D...
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D|+). For this screening to be useful at a given δ, what is required of ε ?
A diagnostic test for a certain disease is applied to n individuals known to not have the disease.
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the...
A diagnostic test for a certain disease is applied to n individuals known to not have...
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than...
Consider a small town that has a population of 1,000 people. It is known that in...
Consider a small town that has a population of 1,000 people. It is known that in this town, 10 people are infected with a rare disease. The remaining 990 people are NOT infected with the disease. This data is known with certainty. Recently, The FDA (Food and Drug administration) developed a test that determines if a person is infected with this disease. However, as with most test of this nature, it is not foolproof proof as there are a certain...
Suppose next that we have even less knowledge of our patient, and we are only given...
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 98 percent reliable, this means that the test will yield an accurate positive result in 98% of the cases where the disease is actually present. Gestational diabetes affects 9 percent of the population in our patient’s age group, and that our test...
2. Suppose next that we have even less knowledge of our patient, and we are only...
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 90 percent reliable, this means that the test will yield an accurate positive result in 90% of the cases where the disease is actually present. Gestational diabetes affects 0+1 percent of the population in our patient’s age group, and that our...
Suppose next that we have even less knowledge of our patient, and we are only given...
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 96 percent reliable, this means that the test will yield an accurate positive result in 96% of the cases where the disease is actually present. Gestational diabetes affects 7 percent of the population in our patient’s age group, and that our test...
2. Suppose next that we have even less knowledge of our patient, and we are only...
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 99 percent reliable, this means that the test will yield an accurate positive result in 9 of the cases where the disease is actually present. Gestational diabetes affects #.1 percent of the population in our patient's age group, and that our...
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) = δ, with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D'l+). For this screening to be useful at a given δ, what is required of e ?
4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D) with δ small. The test for this disease is accurate such that the probability of a correct result is 1-e, with e small. Derive formulas for the probabilities of a true positive P(D|+) and a false positive, P(D|+). For this screening to be useful at a given δ, what is required of ε ?
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the...
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than...
Consider a small town that has a population of 1,000 people. It is known that in this town, 10 people are infected with a rare disease. The remaining 990 people are NOT infected with the disease. This data is known with certainty. Recently, The FDA (Food and Drug administration) developed a test that determines if a person is infected with this disease. However, as with most test of this nature, it is not foolproof proof as there are a certain...
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 99 percent reliable, this means that the test will yield an accurate positive result in 9 of the cases where the disease is actually present. Gestational diabetes affects #.1 percent of the population in our patient's age group, and that our...
Most questions answered within 3 hours.
-
convert grams into vloume with the density of water being at
.997514 g/cm^3 at 23.1 Celsuis...
asked 1 hour ago -
Foreman company obtained a $20,000, 6% loan on May 1, 2018.
Principal and interest will be...
asked 1 hour ago -
5. Problem 11.05 (Discounted Payback)
eBook
Project L costs $60,000, its expected cash inflows are $14,000
per...
asked 2 hours ago -
1. Which of the following is true about politics and health
organizations?
A. Health organizations are...
asked 2 hours ago -
A space vehicle is coasting at a constant velocity of 18.1 m/s
in the +y direction...
asked 3 hours ago -
5) Use the following balanced equation to answer questions
(a)-(i).
3 Cu(s) + 8 HNO3(aq) →...
asked 3 hours ago -
A three-year maturity bond with a 12% annual coupon rate is
currently traded at par $1000...
asked 3 hours ago -
1.
What is the minimum volume to use in the Spec 20 cuvette in order
to...
asked 3 hours ago -
A builder wants to install wall-to-wall carpeting in a living
room of length 8.87 m and...
asked 3 hours ago -
Organizational change can produce anxiety in those affected by
the change. In what ways can change...
asked 3 hours ago -
Ozone in the atmosphere may react with nitric oxide.
From the following data, calculate the DG...
asked 3 hours ago -
Steven Long, a bond analyst, is analyzing a convertible bond.
The characteristics of the bond are...
asked 3 hours ago