Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 37 / 3 / iv

Surveillance should be calibrated to the prevalence of concern, $q_{\ast }=1/200000=5\times 10^{-6}$, rather than only to the higher rate used in the preceding calculation. With $50000$ representative independent tests,Thus 50,000 tests give only about 22% detection probability at the concerning rate; a negative survey is quite likely, with probability about $78\%$. It costs $50000\times \pounds 40=\pounds 2$ million. Even $500000$ tests, costing $\pounds 20$ million, give about $91.8\%$ detection probability at $q_{\ast }$.

For a target $95\%$ detection probability, solveThe cost is about $\pounds 24$ million. The zero-event binomial upper confidence bound gives the same perspective: after zero positives in $50000$ tests, the one-sided $95\%$ upper bound isroughly one in $16700$, well above the concerning rate. A 50,000-animal survey is insufficient to rule out that prevalence with high confidence. A practical design should specify its desired detection probability, diagnostic sensitivity, representativeness and dependence between sampled animals. Targeting the higher-risk scrapie-positive stratum may improve efficiency if testing that stratum is feasible and its contribution to the slaughter population is estimated; its result then needs the appropriate population weighting. A cost alone does not establish adequate surveillance.