When a test is conducted to determine whether someone is infected with a particu

Question

When a test is conducted to determine whether someone is infected with a particular virus, an incorrect result can occur in two ways: an infected person may test negative, or a noninfected person may test positive. The latter is called a false positive test. For this problem, assume that the test always correctly identifies all persons who are really infected with the AIDS virus. Assume that 5% of a population to be tested for the AIDS virus really is infected and that the test has a false positive rate of .5%. Find the probability that a person who tests positive really is infected. Would your answer to part (a) be higher or lower if more than 5% of the population to be tested were actually infected? Answer the question by referring to the formula for conditional probability without performing any calculations. Assume now that a low-risk population is to be tested. Specifically, assume that .01 % of the population to be tested is actually infected with the AIDS virus and that the test has a false positive rate of .005% (which is unusually low). Find the probability that a person who tests positive is really infected. What would your answer to part (c) be if you assumed a false positive rate of .5%? Summarize the implications of your findings in parts (a) through (d).

Explanation / Answer

B If prevalence is higher than 5%, true positive is alsohigher C .01% is infected, gives true positive .01%, and.005%x99.99%=.00499% false positive,  TP/ TP+FN=66.6% D then the probability of the person with a positive testactually having the disease would be much lower than 66% E for a disease with low prevalence, a screening test evenwith a very low false positive rate yields a very low positivepredictive value
The positive predictivevalue, or post-test probability ofdisease, is the proportion of patients with positive testresults who are correctly diagnosed, it reflects theprobability that a positive test means the disease is present, andby Bayes Theorem the value depends on the prevalence of the diseasein the population

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