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4 When the prevalence of a disease in the population is very low, such as HIV infection or certain cancers, there is controversy about the benefits of screening everyone for the disease. In this problem, you will see why this is the case. The table below shows what is likely to happen if all roughly 300,000,000 Americans each were given an inexpensive enzyme immunoassay screening test for HIV infection. Test Positive 1,339,370 4,479,849 5,819,219 Test Negative 4,030 Total Have HIV 1,343,400 Do Not Have HIV 294,176,751 298,656,600 Total 294,180,781 300,000,000 Sources: www.cdc.gov, R. Chou et al. (July 2005). "Screening for HIV: A Review of the Evidence for the U.S. Preventive Services Task Force," Annals of Internal Medicine, Vol. 143, July 2005, pp. 55-73, www.annals.org/content/143/1/55.full a. How many false positives were there? Explain the consequence of a false positive for the person tested. b. How many false negatives were there? Explain the consequence of a false negative for the person tested. c. What is the sensitivity of this test? Explain the meaning of this statistic, in the context of this test. d. What is the specificity of this test? Explain the meaning of this statistic, in the context of this test. e. What is the positive predictive value (PPV)? Use this value in a sentence explaining to a person what his or her positive test might indicate. f. What is the negative predictive value (NPV)? Use this value in a sentence explaining to a person what his or her negative test might indicate. g. Based on your results, explain why people are reluctant to recommend universal screening for HIV.

4 When the prevalence of a disease in the population is very low, such as HIV infection or certain cancers, there is controversy about the benefits of screening everyone for the disease. In this problem, you will see why this is the case. The table below shows what is likely to happen if all roughly 300,000,000 Americans each were given an inexpensive enzyme immunoassay screening test for HIV infection. Test Positive 1,339,370 4,479,849 5,819,219 Test Negative 4,030 Total Have HIV 1,343,400 Do Not Have HIV 294,176,751 298,656,600 Total 294,180,781 300,000,000 Sources: www.cdc.gov, R. Chou et al. (July 2005). "Screening for HIV: A Review of the Evidence for the U.S. Preventive Services Task Force," Annals of Internal Medicine, Vol. 143, July 2005, pp. 55-73, www.annals.org/content/143/1/55.full a. How many false positives were there? Explain the consequence of a false positive for the person tested. b. How many false negatives were there? Explain the consequence of a false negative for the person tested. c. What is the sensitivity of this test? Explain the meaning of this statistic, in the context of this test. d. What is the specificity of this test? Explain the meaning of this statistic, in the context of this test. e. What is the positive predictive value (PPV)? Use this value in a sentence explaining to a person what his or her positive test might indicate. f. What is the negative predictive value (NPV)? Use this value in a sentence explaining to a person what his or her negative test might indicate. g. Based on your results, explain why people are reluctant to recommend universal screening for HIV.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Table Explanation:** The table represents the outcomes of an enzyme immunoassay screening test for HIV applied to a hypothetical population of 300 million Americans. **Table Data:** - **Have HIV:** - Test Positive: 1,339,370 - Test Negative: 4,030 - Total: 1,343,400 - **Do Not Have HIV:** - Test Positive: 4,479,849 - Test Negative: 294,176,751 - Total: 298,656,600 - **Overall Totals:** - Test Positive: 5,819,219 - Test Negative: 294,180,781 - Total: 300,000,000 **Questions and Analysis:** a. **False Positives:** - There are 4,479,849 false positives (people who do not have HIV but tested positive). False positives can lead to anxiety, unnecessary further testing, and psychological distress for the person tested. b. **False Negatives:** - There are 4,030 false negatives (people who have HIV but tested negative). False negatives can result in a lack of necessary treatment and care, potentially leading to the spread of the virus. c. **Sensitivity:** - Sensitivity is calculated as the proportion of true positives (1,339,370) out of the total who have HIV (1,343,400). It measures the test's ability to correctly identify those with the disease. d. **Specificity:** - Specificity is the proportion of true negatives (294,176,751) out of all those who do not have HIV (298,656,600). It measures the test's ability to correctly identify those without the disease. e. **Positive Predictive Value (PPV):** - PPV is the probability that a person truly has HIV given that they tested positive. Use the formula: PPV = True Positives / Total Test Positives. f. **Negative Predictive Value (NPV):** - NPV is the probability that a person truly does not have HIV given that they tested negative. Use the formula: NPV = True Negatives / Total Test Negatives. g. **Reluctance for Universal Screening:** - Reluctance to recommend universal screening may be due to the high number of false positives,
Transcribed Image Text:**Table Explanation:** The table represents the outcomes of an enzyme immunoassay screening test for HIV applied to a hypothetical population of 300 million Americans. **Table Data:** - **Have HIV:** - Test Positive: 1,339,370 - Test Negative: 4,030 - Total: 1,343,400 - **Do Not Have HIV:** - Test Positive: 4,479,849 - Test Negative: 294,176,751 - Total: 298,656,600 - **Overall Totals:** - Test Positive: 5,819,219 - Test Negative: 294,180,781 - Total: 300,000,000 **Questions and Analysis:** a. **False Positives:** - There are 4,479,849 false positives (people who do not have HIV but tested positive). False positives can lead to anxiety, unnecessary further testing, and psychological distress for the person tested. b. **False Negatives:** - There are 4,030 false negatives (people who have HIV but tested negative). False negatives can result in a lack of necessary treatment and care, potentially leading to the spread of the virus. c. **Sensitivity:** - Sensitivity is calculated as the proportion of true positives (1,339,370) out of the total who have HIV (1,343,400). It measures the test's ability to correctly identify those with the disease. d. **Specificity:** - Specificity is the proportion of true negatives (294,176,751) out of all those who do not have HIV (298,656,600). It measures the test's ability to correctly identify those without the disease. e. **Positive Predictive Value (PPV):** - PPV is the probability that a person truly has HIV given that they tested positive. Use the formula: PPV = True Positives / Total Test Positives. f. **Negative Predictive Value (NPV):** - NPV is the probability that a person truly does not have HIV given that they tested negative. Use the formula: NPV = True Negatives / Total Test Negatives. g. **Reluctance for Universal Screening:** - Reluctance to recommend universal screening may be due to the high number of false positives,
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