Question

1. (ii) The Centers for Disease Control and Prevention (CDC, not CDCP, for some reason)

estimated in 2016 that the U.S. prevalence of HIV in 1985 was based on about 500,000

cases, for a prevalence rate in the 18+ subpopulation of 500000 = α∗ =. 0.00286, about175000000

0.3% (roughly the same as the U.S. prevalence rate today). The RC would not have been privy to this information in 1985, but assuming that HIV status and the blood- donation choice mechanism are independent, which is almost certainly upper-bounding for α, would give α∗ as the RC prevalence. Use this value for α and the (β,γ) values for E1 to compute the PPV, NPV, FPR and FNR values defining the blood-screening real-world environment facing the RC in 1985. Would You say that E1 was highly successful at keeping HIV out of the RC blood supply in 1985? Explain briefly. [25 points]

(iii) Holding (β, γ) at the E1 values and varying α from 0 to (say) 10 α∗, plot the PPV and NPV as functions of α. How sensitive were each of these quantities to prevalence in the 1985 RC environment? Explain briefly. [15 points]

Answer 1