Estimating the hidden number of scrapie affected holdings in Great Britain using a simple,truncated count model allowing for heterogeneity |
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Authors: | Dankmar Böhning Victor Javier Del Rio Vilas |
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Institution: | (1) Quantitative Biology and Applied Statistics, School of Biological Sciences, University of Reading, RG6 6FN Reading, UK;(2) Veterinary Laboratories Agency (VLA), New Haw, Weybridge, Surrey, KT15 3NB, UK;(3) Department for Environment, Food and Rural Affairs (Defra), Nobel House, 17 Smith Square, London, SW1P 3JR, UK |
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Abstract: | None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased
estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted
prevalence of scrapie in Great Britain applied multiple-list capture-recapture methods. The enforcement of new control measures
on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application
of multiple-list capture-recapture models. Alternative methods, still under the capture-recapture methodology, relying on
repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture-recapture
approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings
with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool
for indication of heterogeneity as well as a new understanding of the Zelterman and Chao’s lower bound estimators to account
for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood
estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows
the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates—in
case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity
supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around
300 holdings per year. None of the covariates appear to inform the model significantly. |
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