5% of the population have the disease (D). A test is available that has a 10% false positive and a 10% false negative rate.part (B) of the question asks what is the probability of having the disease given that you test positive. I'm quite confident the answer to this is ~ 32%Part (D) - Suppose that there is no cost or benefit from testing negative but a benefit B from true positives which detect the disease and a cost C to false positives.i) What is the expected value of the testing programme?ii) What benefit-cost ratio would you require to proceed with the testing programme?I'm not quite sure to how to answer either of part D. My somewhat educated guesses arethe expected value = 0.045B - 0.095Cand the benefit to cost ratio required to proceed with the testing programme is 2.11 (or greater)

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5% of the population have the disease (D). A test is available that has a 10% false positive and a 10% false negative rate.part (B) of the question asks what is the probability of having the disease given that you test positive. I&#039;m quite confident the answer to this is ~ 32%Part (D) - Suppose that there is no cost or benefit from testing negative but a benefit B from true positives which detect the disease and a cost C to false positives.i) What is the expected value of the testing programme?ii) What benefit-cost ratio would you require to proceed with the testing programme?I&#039;m not quite sure to how to answer either of part D. My somewhat educated guesses arethe expected value = 0.045B - 0.095Cand the benefit to cost ratio required to proceed with the testing programme is 2.11 (or greater)

Cristian Hamilton · Accepted Answer

Your answers are not only educated but also correct.The expected value per person is                          P        (        T        P        ∩        D        )        B        −              P        (        T        P        ∩        N        D        )        C                            =                          P        (        T        P        ∣        D        )              P        (        D        )        B        −              P        (        T        P        ∣        N        D        )              P        (        N        D        )        C                                          =                    0.9        ⋅        0.05        ⋅        B        −        0.1        ⋅        0.95        ⋅        C                                          =                    0.045        B        −        0.095        C                .

5% of the population have the disease (D). A test is available that has a 10% false positive and a 1

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