A certain blood test for some disease gives \'positive\' result for 90% ofpatien

Question

A certain blood test for some disease gives 'positive' result for 90% ofpatient who are infected with the disease (detection rate Pr(PID)-90%), but also a 'positive' result for 5% of people who are NOT infected (false positive rate Pr(PID) =590). The infection rate among the population is one in ten thousands (prevalence rate of Pr(D) =0.0196). What is the probability that a person who tested ‘positive' is indeed infected with this disease? Define an ‘accuracy, measure as: Pr(DIP) × Pr(DIP), what will be its value for this test? The company can invest X number of dollars into R&D; and to improve either the detection rate to 99% OR to reduce the false positive rate to 4% (but not both), what should the company do to improve the test's accuracy the most? a) b) c)

Explanation / Answer

a)P( disease/positive) = 0.0001*0.90 /[0.0001*0.90+0.9999*0.05]=0.001793

b) Accuracy measure = 0.00179* [ 0.9999*0.95]/[0.999*0.95+0.0001*0.10]=0.001791

c)If detection rate is improved P(D/P)= 0.0001*0.99 /[0.0001*0.99+0.9999*0.05]=0.00197

If false positive is reduced to 4, P(D/P)=0.0001*0.90 /[0.0001*0.90+0.9999*0.04]=0.002245

Hence, False positive should be reduced to 4%

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