Although Western countries typ
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Although Western countries typically have low HIV prevalencerates (e.g., about 0.2% of the Australian population has HIV),clinics offering free HIV testing usually attract at-risk groupsamong whom the prevalence rate is much higher. Managers of such aclinic believe that 12% of their patients have HIV. The clinic usesa diagnostic test which returns a positive result in 98% of caseswhere the patient actually has HIV. Among patients without HIV, 96%of test results are negative. The following questions concerndiagnostic outcomes at this clinic.
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Use a contingency table to structure the above information aboutdiagnostic outcomes at this clinic. Complete all marginal totals aswell as the body of the table.
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What proportion of patients diagnosed as having HIV actuallyhave it?
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A randomly-selected patient has received a negative diagnosis.What is the chance that this patient does not have HIV?
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Among patients attending this clinic, what does the diagnostictest do better: show who has HIV, or show who doesn’t have it?Justify your answer.
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Answer:
A contigency table will be formed as below:
True Condition | |||
Person has HIV | Person does not has HIV | ||
Test Results |
HIV + | True Positive | False Positive |
HIV – | False Negative | True Negative |
Suppose there are 10000 people coming to the clinic. Hence,people having HIV = 12% * 1000 = 1200.
Now, 98% of the people are diagnosed positive from the test fromthese 1200 people = 1176.
In this manner, the information is collected and gathered intothe following table:
True Condition | ||||
Person has HIV | Person does not has HIV | Total | ||
Test Results | HIV + | 1176 | 352 | 1528 |
HIV – | 24 | 8448 | 8472 | |
Total | 1200 | 8800 | 10000 |
(i) Proportion of people who are diagnosed as having HIVactually having it = 1176/1528 = 76.96%
(ii) The chance that a randomly selected patient who hasreceived a negative diagnosis does not has HIV = 8448/8472 =0.997
(iii) Let’s calculate each statistic:
Let’s say a person who has HIV. The chance that test will showhim HIV + is: 98%
Let’s say a person who does not have HIV. The chance that thetest will show him HIV – = 96%
Hence, the diagnostic test does better in showing who has HIVrather than showing who doesn’t as it is a better predictor in it(98%>96%)
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