On the question of proportionality of the count of observed Scrapie cases and the size of holding Dankmar Böhning * 1 and

Background: The present paper investigates the question of a suitable basic model for the number of scrapie cases in a holding and applications of this knowledge to the estimation of scrapieaffected holding population sizes and adequacy of control measures within holding. Is the number of scrapie cases proportional to the size of the holding in which case it should be incorporated into the parameter of the error distribution for the scrapie counts? Or, is there a different – potentially more complex – relationship between case count and holding size in which case the information about the size of the holding should be better incorporated as a covariate in the modeling? Methods: We show that this question can be appropriately addressed via a simple zero-truncated Poisson model in which the hypothesis of proportionality enters as a special offset-model. Model comparisons can be achieved by means of likelihood ratio testing. The procedure is illustrated by means of surveillance data on classical scrapie in Great Britain. Furthermore, the model with the best fit is used to estimate the size of the scrapie-affected holding population in Great Britain by means of two capture-recapture estimators: the Poisson estimator and the generalized Zelterman estimator. Results: No evidence could be found for the hypothesis of proportionality. In fact, there is some evidence that this relationship follows a curved line which increases for small holdings up to a maximum after which it declines again. Furthermore, it is pointed out how crucial the correct model choice is when applied to capture-recapture estimation on the basis of zero-truncated Poisson models as well as on the basis of the generalized Zelterman estimator. Estimators based on the proportionality model return very different and unreasonable estimates for the population sizes. Conclusion: Our results stress the importance of an adequate modelling approach to the association between holding size and the number of cases of classical scrapie within holding. Reporting artefacts and speculative biological effects are hypothesized as the underlying causes of the observed curved relationship. The lack of adjustment for these artefacts might well render ineffective the current strategies for the control of the disease. Published: 6 May 2009 BMC Veterinary Research 2009, 5:17 doi:10.1186/1746-6148-5-17 Received: 27 November 2008 Accepted: 6 May 2009 This article is available from: http://www.biomedcentral. com/1746-6148/5/17 © 2009 Böhning and Del Rio Vilas; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Page 1 of 11 (page number not for citation purposes) BMC Veterinary Research 2009, 5:17 http://www.biomedcentral. com/1746-6148/5/17 Background Surveillance efforts must adjust to the levels of occurrence of disease especially in the face of multiple threats and finite resources. There is a need to consider, among other parameters that would inform the level of priority allocated to a given disease, its prevalence and, ideally, that adjusted for any source of under-ascertainment. We define ascertainment as the definitive and complete determination of individuals with a particular trait of interest, scrapie in our case. Readily available methods for the estimation of the under-ascertainment-adjusted holding prevalence and within holding prevalence are required when planning surveillance strategies and control measures in animal health settings. The occurrence of classical scrapie, a fatal, neurological disease of small ruminants, appears to be decreasing in Great Britain, both in the number of holdings affected and the number of sheep infected within holding [1]. Such a decreasing trend will undoubtedly lead to the reconsideration by policy makers of the overall efforts dedicated to the surveillance of the disease. The importance of the size of the holding in the occurrence of classical scrapie is well described in the literature [2-6]. The results from these studies have been used to parameterize mathematical models describing scrapie transmission between sheep and between flocks [7]. In this particular case, a positive linear relationship was assumed between the occurrence of the disease within holding and the size of the holding. Note that some of the studies above indicated some form of non proportionality between holding size and the occurrence of scrapie [5,6]. There is a need to describe this relationship to direct disease control measures in Great Britain. Sampling and TSEtesting of scrapie-affected flocks is one of the measures in place after the introduction of the Compulsory Scrapie Flocks Scheme (CSFS) in Great Britain in 2004 [8]. The calculation of the sample size is based on the number of adult sheep within the holding and increases proportional to the size of the holding (under the assumption of a perfect test). A non-linear relationship between the occurrence of the disease and the size of the flock might render these sample calculations ineffective for larger holdings at the right end of the size distribution. Furthermore, there is a need to inform this relationship not only when dealing with reported clinical disease, potentially affected by reporting artefacts. The count of scrapie cases arising from the TSE-testing within holding under the CSFS provides the data for the assessment of this relationship free from potential reporting biases and merits study. Previous studies have applied capture-recapture (CRC) techniques to obtain adjusted estimates of the prevalence of scrapie-affected holdings in Great Britain [9]. Recently, two approaches [10,11] were pursued for the incorporation of observed holding-specific variability in their CRC models: via an extension of Zelterman's (1988) estimator either as a covariate in a logistic model [10] or as a proportional term [11]. The form of this relationship influences the estimates of the scrapie-affected holding population and requires further analyses. Hence, our objective in this paper is three-fold: i) To model the relationship between holding size and the occurrence of disease, ii) To study the effects of this relationship in capturerecapture estimates of the size of the scrapie-affected holding population and iii) To discuss the consequences for within-holding sampling schemes for the detection of the disease. Methods Materials Several sets of analysis were conducted and for each we used different datasets. The first analysis used year-specific disease data from the Scrapie Notifications Database (SND) (see [6] for more details). The SND collects all the suspect clinical cases of scrapie reported by farmers to the veterinary authorities. More specifically, we restricted our analyses to the number of confirmed clinical cases for the years 2002, 2003 and 2004. This provided a snapshot of the relationship between the holding characteristic of interest, its size, and the presence of clinical disease. The year-specific datasets were also used to estimate the underascertainment-adjusted population of scrapie-affected holdings, with clinical disease, in Great Britain per year. Note that as a by product of the application of CRC models to the SND dataset, the surveillance's sensitivity, for the detection of scrapie-affected holdings with clinical disease, was estimated at around 40–50% [10]. A second set of analysis used the list of holdings sampled and TSE-tested within the CSFS during 2005 and 2006. More specifically, animals tested and confirmed from the initial cull (IC) route (see [8] for more details). In theory, this route deals only with healthy animals, randomly selected from the eligible cull population within holdings, so if any case arises it is likely to be pre-clinical. This set of analysis would inform the relationship between the number of pre-clinical cases and the size of the holding, free from reporting artefacts potentially affecting the SND results. We extended the analyses on this dataset to estimate the overall population size of scrapie-affected holdings (in the remainder of the paper simply referred to as the population size estimate). The three regular surveillance sources for scrapie in Great Britain, the SND and the Page 2 of 11 (page number not for citation purposes) BMC Veterinary Research 2009, 5:17 http://www.biomedcentral. com/1746-6148/5/17 fallen stock survey targeting clinical disease and the abattoir survey targeting infection (note that the SND is an exhaustive list and the two surveys are sample-based sources), feed cases into the CSFS. As a result, any population size estimate based on the CSFS would be comprehensive and represent the overall burden of the disease, regardless of its manifestation (i.e. clinical disease or infection). The authors showed the limitations of population size estimates based on CSFS data [12]. We have conducted these analyses for illustrative purposes to show the effect of an inadequate parameterisation on the model's results. Note that for the estimation of the relationship between counts of cases and holding size for the CSFS dataset, index cases, those detected through the regular surveillance activities (for further details see [13,14]) that triggered the incorporation of the holdings in the CSFS, were initially included in the analyses. Due to the weight of the holdings detected through the SND in the CSFS dataset [12] we would expect similar results to those obtained from modelling the SND data alone. In a further analysis, we removed the index cases to reduce the impact of potential reporting artefacts. We extended this approach to study the relationship between the number of tested animals within a holding in the CSFS and the count of cases. Here we would expect to see a linear relationship to