1. A. A disease aflicts 1 person in 1,000 in a population. A test for this disea
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1. A. A disease aflicts 1 person in 1,000 in a population. A test for this disease results in 5% false not selected for the test because there are other symptoms indicating the presence of the disease nor are there any special signs of being disease free). Assume that there are no false negatives from this test. A person tests positive. What is the probability that the person truly has the disease? positives. Assume that a random person is tested for the disease (this person is B. Now assume that false negatives are 1 person in 100 in a population. What is the probability that the person truly has the disease? C. The following paragraph is taken from the National Cancer Institute's web site on the PSA test for prostate cancer. The paragraph is the complete discussion of false positive PSA results offered on the web site. What are your thoughts about this paragraph? What are some of the limitations of the PSA test? False-positive tests: False-positive test results (also called false positives) occur when the PSA level is elevated but no cancer is actually present. False positives may lead to additional medical procedures that have potential risks and significant financial costs and can create anxiety for the patient and his family. Most men with an elevated PSA test result turn out not to have cancer; only 25 to 35 percent of men who have a biopsy due to an elevated PSA level actually have prostate cancerExplanation / Answer
P(D)=0.001 P(ND)=0.999
FPR = 0.05
FP/(FP+TP) = 0.05
FP=0.05, TP =0.95
P( actually has the disease) = 0.95
Probability that person truly has the disease =0.95
b)P( Actual disease/Positive) = 0.95*0.001/ [ 0.95*0.001 + 0.01*0.999]= 0.0863
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