 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2001/iii/paper-29/3/b/ii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

Two reasons are selection bias and unequal ascertainment.

The slaughter cohort need not be representative of the adult dairy herd. Culling can select animals with poor health, while its age distribution may also differ. Eligibility from 24 months includes many cattle below the usual age at clinical onset, and cases before 30 months are rare; differing age composition can strongly alter the underlying risk. These effects can work in different directions, so age and reason for slaughter should be examined rather than assuming a direction.
A focused veterinary examination at slaughter and repeated routine observations by farmers have different opportunities to detect subtle clinical signs. Early disease can remain unreported in the field, while inspection can reveal previously accumulated undetected cases. Thus one is a single-time screen for existing disease and the other a stream of newly recognized cases; even after converting denominators to comparable time units, prevalence, incidence and detection sensitivity are not identical quantities.

Standardize the sampled population and the ascertainment process before interpreting the numerical detection-rate ratio causally.

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