The Department of Health of a certain state estimates a 1010% rate of HIV for th

Question

The Department of Health of a certain state estimates a 1010% rate of HIV for the "at risk" population and a 0.30.3% rate for the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection of 5000 "at risk" people and 20,000 people from the general population results in the following table. Use the table below to complete parts (a) through (e). "At Risk" Population General Population Test Positive Test Negative Test Positive Test Negative Infected 466466 3434 4646 1414 Not Infected 232232 42684268 982982 18 comma 95818,958 a. Verify that incidence rates for the general and "at risk" populations are 0.30.3% and 1010%, respectively. Also, verify that detection rates for the general and "at risk" populations are 95%. How would you verify the incidence rates? A. Divide the number of infected patients by the total number of patients. B. Divide the number of uninfected patients by the number of infected patients. C. Divide the number of uninfected patients by the total number of patients. D. Divide the number of infected patients by the number of uninfected patients. How would you verify the detection rates? A. Divide the total number of true negatives by the total number of patients. B. Divide the total number of false negatives by the total number of patients. C. Divide the total number of true positives by the total number of patients. D. Divide the total number of false positives by the total number of patients. b. Consider a patient in the "at risk" population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different. Of the patients in the "at risk" population with HIV, nothing% test positive. Of the patients in the "at risk" population who test positive, nothing% have HIV. (Type an integer or decimal rounded to the nearest tenth as needed.) Why are these two percentages different? A. The percentages are different because there are people being accounted for that don't have HIV in the second calculation. B. The percentages are different because the people are in two different categories. C. The percentages are different because people who test positive don't always have HIV and people who have HIV don't always test positive. D. The percentages are different because the first test includes everyone who tested positive. c. Suppose a patient in the "at risk" category tests positive for the disease. As a doctor using this table, how would you describe the patient's chance of actually having the disease? Compare this figure to the overall rate of the disease in the "at risk" category. A patient in the "at risk" category who tests positive has a nothing% chance of having the disease which is less than greater than the overall "at risk" incidence rate of 1010%. (Type an integer or decimal rounded to the nearest tenth as needed.) d. Consider a patient in the general population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different. Of the patients in the general population with HIV, nothing% test positive. Of the patients in the general population who test positive, nothing% have HIV. (Type an integer or decimal rounded to the nearest tenth as needed.) Why are these two percentages different? A. The percentages are different because people who test positive don't always have HIV and people who have HIV don't always test positive. B. The percentages are different because there are people being accounted for that don't have HIV in the second calculation. C. The percentages are different because the people are in two different categories. D. The percentages are different because the first test includes everyone who tested positive. e. Suppose a patient in the general population tests positive for the disease. As a doctor using this table, how would you describe the patient's chance of actually having the disease? Compare this figure with the overall incidence rate of the disease. The chance of the patient having HIV is nothing%, compared to the overall incidence rate of 0.30.3%. (Type an integer or decimal rounded to the nearest tenth as needed.)

Explanation / Answer

At Risk" Population General Population Test Positive Test Negative Test Positive Test Negative Infected 466466 3434 4646 1414 Not Infected 232232 42684268 982982 18 comma 95818,958

The table is

How would you verify the incidence rates?

A. Divide the number of infected patients by the total number of patients.

Incidence rate for At risk population = (466+34)/(466+34+232+4269) = 0.1 = 10 %

Incidence rate for General population = (46)/(46+14) = 76.67% = 0.3%

How would you verify the detection rates?

C. Divide the total number of true positives by the total number of patients.

Detection rate for At risk population = (466)/(466+34) = 0.932 = 93.2 %

Detection rate for General population = (46+14)/(46+14+982+18958) = 0.003 = 0.3%

b. Consider a patient in the "at risk" population. Of those with HIV, what percentage test positive?

= (466)/(466+34) = 0.932 = 93.2%

Of those who test positive, what percentage have HIV? Explain why these two percentages are different.

= (466)/(466+232) = 0.6676 = 66.76%

Of the patients in the "at risk" population with HIV, nothing% test positive.

= (34)/(466+34) = 0.068 = 6.8%

Of the patients in the "at risk" population who test positive, 66.76% have HIV. (Type an integer or decimal rounded to the nearest tenth as needed.) Why are these two percentages different?

C. The percentages are different because people who test positive don't always have HIV and people who have HIV don't always test positive.

c. Suppose a patient in the "at risk" category tests positive for the disease. As a doctor using this table, how would you describe the patient's chance of actually having the disease? Compare this figure to the overall rate of the disease in the "at risk" category.

patient's chance of actually having the disease = 466 / (466 + 232) = 0.6676

A patient in the "at risk" category who tests positive has a nothing% chance of having the disease which is less than greater than the overall "at risk" incidence rate of 1010%. (Type an integer or decimal rounded to the nearest tenth as needed.)

Patients who tests positive has a nothing% chance of having the disease = 232 / (466 + 232) = 0.3323 which is greater than the overall "at risk" incidence rate of 10%.

d. Consider a patient in the general population. Of those with HIV, what percentage test positive?

= 46/ (46 + 14) = 0.7667 = 76.67%

Of those who test positive, what percentage have HIV? Explain why these two percentages are different.

= 46 / (46 + 982) = 0.0447 = 4.47 %

Of the patients in the general population with HIV, nothing% test positive.

= 14 / (46 + 14) = 0.2333 = 23.33 %

Of the patients in the general population who test positive, 4.47% have HIV. (Type an integer or decimal rounded to the nearest tenth as needed.)

Why are these two percentages different?

A. The percentages are different because people who test positive don't always have HIV and people who have HIV don't always test positive.

e. Suppose a patient in the general population tests positive for the disease. As a doctor using this table, how would you describe the patient's chance of actually having the disease? Compare this figure with the overall incidence rate of the disease.

patient's chance of actually having the disease = 46 / (46 + 982) = 0.0447 = 4.47%

The chance of the patient having HIV is 4.47%, compared to the overall incidence rate of 0.30.3%. (Type an integer or decimal rounded to the nearest tenth as needed.)

At Risk (Test Positive) At Risk (Test Negative) General Population (Test Positive) General Population (Test Negative) Infected 466 34 46 14 Not Infected 232 4268 982 18

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