Revises Problem In an article posted in May 2016 by Fivethirtyeight.com, \"Thera

Question

Revises Problem In an article posted in May 2016 by Fivethirtyeight.com, "Theranos Is Wrong: We Don't Need More Blood Tests," the following argument was made: "The wider the pool of people being tested, the greater the chance of false positives. Estima Founder Elizab Matthew Herper, " Consider a diagnostic test with a sensitivity % (test will indicate "disease among those with the disease) and a specificinof 90% (the fraction of those without disease who will have a negative test result). THERANOS VALUE INVESTORS PREFE WOULD GET PAD HOLMES COMMON THEREFORE, HER ST ESSENTIALLY WOR Use the following data to construct the logic table shown below where the total number of subjects is 1,000 Diagnostic Test Results ITOTAL NUMBER OF SUBJECTS- Positive Test Result disease is indicated Negative Test Results disease is not indicated Subject has disease true false negative Subject does not have with a true inci ate of 6%. How many persons in 1,000 would be expected to have the disease? 4.02 | The test in question has a positive predictive value of 85%. That is, P(+test | disease)-.85, what is the tabular value A (i.e, the number of true positives)? .03 What is the tabular value B (e.g., the number of false negatives)? .04 The test in question has a negative predictive value of 90%. That is, P(neg.test no disease) 90. What is the tabular value D (i.e., the number of true negatives)? 4.05 What is the tabular value C (e.g., the number of false positives)? 4.06 What percentage of the positive tests are actually corect? 4.07 In the event of receiving a positive test, what is the probability the person in reality does not have the disease?

Explanation / Answer

4.01) If the disease has true incident rate of 6% then the persons expected to have disease

= incidence rate * Total Pool/100

=6*1000/100 =60

so., 60 people are expected to have the disease

4.02) P(+test|disease) = A/(A+B) = 0.85 and sensitivity given and from the above question we get A+B=60

so., substituting the same in the previous equation we get

A/60 = 0.85 ,

so., A= 51

4.03) As we know that A+B=60 and A =51 we get B= 9

4.04 & 4.05)As we know that A+B=60 then C+D must be 1000-60 =940

now P(-ve|No disease) =D/(C+D) = 0.9 and C+D 940 is given so

D= 0.9*940 =846 and C=940-846=94

4.06) %OF CORRECT pOSITIVE TESTS = A/(A+C) =51/(51+94) = 35.17%

4.07) i.e. C/(A+C) =94/(51+94) = 64.83%

Hope the above explaination has helped you in understanding the problem Pls upvote the ans if it has really helped you. Good Luck!!

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