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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.

Zero observed events do not mean that the underlying event probability cannot be estimated. For independent observations having a common Bernoulli distribution, the binomial likelihood with no events is $(1-p{)}^{1515}$, maximized at $\hat{p}=0$. A zero-event binomial upper confidence bound shows the remaining uncertainty: the one-sided 95% upper bound solves $(1-p_U{)}^{1515}=0.05$, givingThus the point estimate is zero, but a nonzero mortality risk is compatible with the observations. This bound is an illustration under independent equal-risk sampling; clustered data or unequal risks require their own uncertainty calculation.

The empirical unadjusted odds ratio is also defined:Its log odds ratio is $-\infty$, so the ordinary normal approximation for a log-odds confidence interval is unavailable. Exact likelihood-based limits can still describe uncertainty; a specified continuity correction would instead yield a finite, method-dependent point estimate.

In an unpenalized logistic regression with a separate coefficient for elective exposure, every exposed death outcome is zero. Decreasing that coefficient toward $-\infty$ increases the exposed observations' likelihood contributions and leaves the reference observations unchanged. This is quasi-complete separation: there is no finite ordinary maximum-likelihood estimate of the exposure coefficient, even after adding background predictors. It is reasonable to say that the usual finite adjusted coefficient could not be fitted; it is too strong to say that no risk estimate or statistical information is possible. A specified penalized likelihood or Bayesian inference with proper coefficient priors can provide a finite adjusted estimate, whose dependence on the regularization must be reported.