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Bayesian estimation of the true prevalence of Mycobacterium avium subsp. paratuberculosis infection in Cypriot dairy sheep and goat flocks
Small Ruminant Research 95 (2011) 174–178
Contents lists available at ScienceDirect
Small Ruminant Research journal homepage: www.elsevier.com/locate/smallrumres
Bayesian estimation of the true prevalence of Mycobacterium avium subsp. paratuberculosis infection in Cypriot dairy sheep and goat flocks M. Liapi a , L. Leontides b,∗ , P. Kostoulas b , G. Botsaris c , Y. Iacovou a , C. Rees c , K. Georgiou a , G.C. Smith d , D.C. Naseby e a b c d e
Cyprus Veterinary Services, 1417 Athalassas Av, Nicosia, Cyprus Laboratory of Epidemiology, Biostatistics and Animal Health Economics, University of Thessaly, Trikalon 224, GR-43100 Karditsa, Greece Division of Food Sciences, School of Biosciences, University of Nottingham, Leicestershire LE12 5RD, United Kingdom Food and Environment Research Agency, Sand Hutton, York YO41 1LZ, UK School of Life Sciences, Faculty of Health and Human Sciences, University of Hertfordshire, Herts AL10 9AB, Hatfield, UK
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Article history: Received 8 February 2010 Received in revised form 20 September 2010 Accepted 23 September 2010 Available online 18 November 2010 Keywords: Mycobacterium avium paratuberculosis ELISA Seroprevalence Bayesian estimation True prevalence
a b s t r a c t We estimated the prevalence of Mycobacterium avium subsp. paratuberculosis (MAP) infected sheep and goats, older than 2 years, reared in the region effectively controlled by the Government of the Republic of Cyprus, in September 2005. The sera collected from 8011 animals (3429 sheep and 4582 goats) from 83 flocks, non-vaccinated against MAP, were examined for antibodies with a commercially available enzyme linked immunosorbent assay (Pourquier® paratuberculosis antibody screening ELISA). The true prevalence of MAP infection was calculated, in a Bayesian framework, separately in sheep and goats, with models that adjusted for the misclassification of animals because of the imperfect accuracy of the ELISA. The within-flock mean seroprevalence in sheep and goats was 9.9% (95% CI: 8.9; 10.9%) and 7.9% (7.2; 8.7%), respectively. There was at least one seropositive sheep in 52% (38; 66%) of flocks with sheep and one seropositive goat in 50% (39; 62%) of flocks with goats. Within the seropositive flocks the mean seroprevalence was 12.1% (10.9; 13.4%) and 10.3% (9.3; 11.4%) in sheep and goats, respectively. The calculated mean true prevalence of infected sheep and goats was 15.0 and 11.1%, respectively. There was at least one infected sheep in 60.8% (95% credible interval: 42.3; 78.8%) and at least an infected goat in 48.6% (30.4; 68.5%) of the flocks. In the infected flocks, the mean within flock true prevalence of infection in sheep and goats was estimated at 24.6% (16.3; 33.3%) and 23.1% (15.5; 33.6%), respectively. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Paratuberculosis is a chronic infection, mainly of ruminants, which is caused by Mycobacterium avium subsp. paratuberculosis (MAP). The infection is responsible for major economic losses in the primary industry and adversely affects international and national animal trade; therefore, there is increasing interest in control programs
∗ Corresponding author. Tel.: +30 24410 66002; fax: +30 24410 66047. E-mail address: [email protected] (L. Leontides). 0921-4488/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.smallrumres.2010.09.010
(Kennedy and Benedictus, 2001; Nielsen, 2009). In Cyprus, paratuberculosis was first diagnosed in sheep in 1965 (Crowther et al., 1976). From 1979 onwards, an average of 19 outbreaks of paratuberculosis per year, usually with severe clinical symptoms, is officially reported in sheep or goat flocks [Diagnostic Veterinary Agency (DVA) 1979–2008]. Valid estimation of the true prevalence of MAP infection in sheep and goats, both at the flock- and at the animallevel, is the starting point for decision makers to determine whether the infection should be considered important or not, and which measures to apply. Such measures
M. Liapi et al. / Small Ruminant Research 95 (2011) 174–178
could pertain to eradication in case of low prevalence, control in case of high prevalence, and surveillance in case of the likely absence of the infection. The latency and slow progression of MAP infection makes diagnosis a challenge and tests with high sensitivity (Se) are lacking, therefore, seriously impeding successful control efforts for paratuberculosis. Due to the serious misclassification rate, particularly in sub-clinically infected animals, lack of knowledge of or disregard for test errors could lead to bias in prevalence estimation surveys. Thus, it is imperative that studies aiming to estimate the true herd prevalence and within herd prevalence of MAP infection should adjust for the imperfect Se and Sp of the diagnostic procedure. Importantly, Se and Sp estimates to be incorporated in the estimation procedure should originate from studies relevant to the study population because the Se of the available tests depends on the distribution of the infection stages in the test population (Collins and Sockett, 1993), whilst Sps are likely to differ between areas with different environmental mycobacteria (Nielsen et al., 2002). Recently, Nielsen and Toft (2009) conducted a critical comparative review of the reported within- and betweenherd prevalence estimates of MAP infection among farmed animals in Europe. They found no interpretable animallevel and only very scarce flock-level estimates for sheep and goats due to the variability in the (a) study design, (b) target population, (c) target disorder detected by the diagnostic procedure and (d) the variability or absence of Se and Sp estimates. In this study we aimed to estimate the true prevalence of MAP infection in Cypriot sheep and goat flocks. The true prevalence was estimated, in a Bayesian framework, separately in sheep and goats with models that adjusted for the misclassification of animals because of the imperfect accuracy of the ELISA. 2. Materials and methods 2.1. Management of sheep and goats in Cyprus The majority of Cypriot sheep and goats are cross-breeds. Sheep belong mostly to crosses between the Chios and the local breed, whereas goats are crosses between the Damascus and the local breed. The animals are kept, under intensive or semi-intensive management, for milk production, which is the primary production goal. There is no seasonal movement between pastures. Semi-intensively managed flocks graze for some hours in private pastures but their diet is mainly based on in-house feeding and watering. Approximately half of the flocks are located in 57 farming areas defined with wire strand fences. Sheep-only and goat-only flocks comprise 15 and 46%, respectively, and the remaining (39%) are mixed flocks with, on average, half sheep and half goats. Purchase of females between flocks is limited and very few animals are imported into the island. The farmers usually select replacements among the daughters of high-yielding ewes and goats, whilst males bought into the flocks usually originate from high yielding animals from other flocks. In 2008, 36629 animals were recorded as moving between flocks and, in the past 4 years, only 500 animals have been imported. These were from UK, Germany and Bulgaria. The overall number of sheep and goats are fairly constant, with a turnover rate of 20–30%.
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Fig. 1. Age distribution of sheep and goats in the region effectively controlled by the Government of the Republic of Cyprus in September 2005.
of Cyprus covers an area of 5828 km2 and is administratively divided into 5 Districts namely, Lefkosia, Lemesos, Larnaka, Paphos and Ammochostos. The sampling unit was the flock and the design was a combination of stratified and cluster sampling. The District and herd size (categorized in 3 groups, flocks with ≤100 animals, with 101–300 animals and with >300 animals) were the strata variants for stratification (15 strata). Sampled flocks were randomly selected proportionally to the District-specific herd-size distribution. Within these flocks, all sheep and goats older than 2 years were blood sampled, to increase the Se of the diagnostic procedure (Kostoulas et al., 2006a). The minimum number of flocks in order to estimate a prevalence of 65% (estimate based on DVA data) of infected flocks with a 95% level of confidence and 10% absolute precision was 83. Blood sampling was done from September 2005 until September 2006. Collected samples were centrifuged (1000 × g for 10 min) and the separated sera were stored at −20 ◦ C until examination. 2.3. Serological testing Sera were examined with a commercial indirect absorbed ELISA kit (Pourquier® Elisa paratuberculosis antibody screening) according to the manufacturer’s instructions. Samples were considered positive at a sample to positive value ≥70% and negative otherwise. 2.4. Bayesian estimation of true prevalence of infection To estimate the true prevalence of MAP infection separately in sheep and goats we applied models that adjusted for the misclassification of animals because of the imperfect accuracy of the ELISA. We chose a Bayesian approach that allowed for the incorporation of prior information in terms of probability space rather than single values (Branscum et al., 2005). 2.4.1. Definition of MAP infection Bayesian models for prevalence estimation create their own probabilistic definition of infection, which, however, implicitly assumes a biological definition based on the fact that true prevalence estimates are obtained after adjusting for the imperfect Se and Sp of the diagnostic procedure (Enøe, 2003). For defining MAP infection in biological terms, we used the approach described by Nielsen et al. (2002) and Kostoulas et al. (2006a). Hence, by ‘infection’ we mean that sheep or goats carry MAP intracellularly; substantial replication need not take place because the infection can be latent. Entrance and persistence of MAP have lasted long enough to give an immune response at any time during their life; we assumed that once an animal has an established infection, the infection persists for life.
2.2. Target population and sampling In total, there were 339,371 sheep and goats reared in 3878 flocks. Their age-distributions are given in Fig. 1. The target population included all sheep and goats over 24 months old (according to the records of the DVA, these animals comprised an estimated 55 and 65% of the population of sheep or goats, respectively), with no history of vaccination against MAP. The region effectively controlled by the Government of the Republic
2.4.2. The model We apply a model that has been extensively described by Branscum et al. (2005). Briefly, let y1 , y2 , . . ., yk , be the numbers of test-positive animals out of n sampled animals in each of k flocks. The data yk are assumed to be independent and follow binomial distributions: yk ∼Binomial(n, k Se + (1 − k )(1 − Sp))
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where k denotes the true prevalence of MAP infection in the kth flock, and Se and Sp the sensitivity and specificity of the test, respectively (Rogan and Gladen, 1978). Se and Sp are assumed to be constant across the k flocks. Further, we allowed for the possibility of flocks being entirely free of MAP infection by modeling k as: k = k∗ , k = 0,
with probability with probability 1 −
where denotes the proportion of infected flocks and k the prevalence of MAP infection in the kth flock assuming this flock is infected. Further, the prevalences among the diseased flocks were modeled using a beta distribution: k∗ |,
functions that serves as a processor of WinBUGS output (Best et al., 2003). To calculate the parameters a and b of the beta prior distributions for Se and Sp we utilized the Betabuster software, which is a public domain software also available at the aforementioned web address.
∼Beta( ,
(1 − ))
where is the mean true prevalence among all diseased flocks in the region and is related to the variability of these prevalences that flexibly allows for disperse or homogeneous infection prevalences among flocks; larger values of correspond to less variable prevalences (Hanson et al., 2003). 2.4.3. Prior information Independent beta prior distributions, beta(˛,ˇ) were used to model uncertainty about, Se, Sp, , and . A gamma prior distribution was used to model , Gamma(a ,b ). For Se and Sp, prior derivation was based on relevant published estimates (Kostoulas et al., 2006a,b; Nielsen and Toft, 2009) and expert opinion. The most likely value of ELISA Se for sheep and goats was thought to be 37 and 63%, while we were 95% confident that it was not less than 10 and 42%, respectively. The corresponding distributions were beta(1.68,2.46) and beta(10.65,6.67). For ELISA Sp the most likely values were set to 97 and 95% and we were 95% confident that they were not less than 93 and 90%, beta(115.8,4.5) and beta(99.7,6.2), respectively. For , in either sheep or goats, we expected that, most likely, 65% of the flocks were infected and were 95% confident that not less than 40% of them were infected, beta(7.98,4.76). For , in an infected flock, the mean prevalence of MAP infection was thought to be 30% and we were 95% confident that it was not more than 40%, beta(19.06,44.04). Finally, for , we specified prior information about our prior belief for the variability of within flock prevalence in infected flocks: we were confident that 90% of all infected flocks had prevalence less or equal to 50% and 95% certain that it did not exceed 60%, Gamma(5.4,0.55). Computation of a and b was done as described in Hanson et al. (2003).
3. Results In total 8011 animals (3429 sheep and 4582 goats) from 83 flocks (11 sheep-only, 33 goat-only and 39 mixed flocks) were tested. Three hundred and forty of 3429 [9.9% (95% CI: 8.9; 10.9%)] sheep and 362/4582 [7.9% (7.2; 8.7%)] goats tested positive. There was at least one test-positive sheep in 26/49 [53% (39; 67%)] flocks with sheep and one test-positive goat in 36/72 [50% (39; 62%)] flocks with goats. Within the test-positive flocks the mean apparent prevalence was 340/2812 [12.1% (10.9; 13.4%)] and 362/3513 [10.3% (9.3; 11.4%)] in sheep and goats, respectively. Overall, in the target population, the estimated mean true prevalence of infected sheep and goats was 15 and 11.1%, respectively. We estimated that there was at least one infected sheep in 60.8% (95% credible interval: 42.3; 78.8%) and at least an infected goat in 48.6% (30.4; 68.5%) of the flocks. In those flocks, with ≥1 infected sheep or goat, the estimated mean within flock true prevalence of infection were 24.6% (16.3; 33.3%) and 23.1% (15.5; 33.6%), respectively. The probability that a randomly chosen flock had no infected sheep or goat was 39.2 and 51.4%, respectively. The probability that a randomly chosen flock in the region had true prevalence of infected sheep or goats <5% was 47.7 and 57.8%, respectively. The estimated posterior cumulative distributions of the true flock prevalence in sheep and goats are in Fig. 2. Furthermore, sensitivity analysis revealed that under the considered alternative sets of priors our results were qualitatively and quantitatively the same.
2.4.4. Sensitivity analysis To assess the influence of prior information on the estimates of the model parameters we repeated our analysis considering alternative prior information. The current model lacks identifiability if non-informative priors are used for all model parameters, therefore informative priors had to be incorporated in the model to mitigate lack of identifiability. We chose to retain the Se and Sp priors used in the primary analysis because they were based on recent, relevant and scientifically justifiable information (Kostoulas et al., 2006a) and adopted non-informative priors either on the prevalence of infected flocks () or the within flock prevalence () in infected flocks, which were the primary parameters of interest and original prior derivation was only based on expert opinion. 2.4.5. Convergence diagnostics Convergence diagnostics of the Markov Chain Monte Carlo (MCMC) chain are not foolproof. Therefore, a combination of diagnostics plus visual inspection of the trace plots and summary statistics is recommended. Standard diagnostic procedures of the MCMC chain (Heidelberger and Welch, 1983; Raftery and Lewis, 1992), plus visual inspection of the autocorrelation plots and the posterior distributions of the parameters, revealed no convergence problems. 2.4.6. Statistical software All models were run in the freeware program WinBUGS (Spiegelhalter et al., 2003). Example WinBUGS codes for the Bayesian model we have used can be found at http://www.epi.ucdavis.edu/diagnostictests. For convergence diagnostics we used the Convergence Diagnostic and Output Analysis (CODA) package, which is a menu-driven set of R-Plus
Fig. 2. Estimated cumulative posterior probability for the prevalence of Mycobacterium avium subsp. paratuberculosis-infected sheep (grey line) and goat (black line) Cypriot flocks. A flock was considered infected when at least one, older than two years, animal was infected. The vertical line corresponds to flock prevalence of 5%.
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4. Discussion In this study we estimated the true animal- and flocklevel prevalence of infected sheep and goats from a large random sample, representative of all older than two-years old, non-vaccinated against MAP, small ruminants reared in the region effectively controlled by the Government of the Republic of Cyprus in 2005. In the Cypriot population of small ruminants, a higher percentage of sheep than goats were <2 years old and was excluded from sampling (Fig. 1, statistical comparison not shown). Thus, our prevalence estimates may refer to different proportions of sheep and goats in the target population. Sampled animals were serologically tested with a commercial ELISA. Subsequently, we incorporated the observed seroprevalence data in statistical models, which adjusted, in a Bayesian framework, for the misclassification of animals because of the imperfect accuracy of the ELISA, and estimated the true prevalence of infection, separately in sheep and goats. In a recent review of prevalences of paratuberculosis in farmed animals in Europe, Nielsen and Toft (2009), found no studies that provided accurate and unbiased country-specific animal-level prevalence estimates and estimated that flock level prevalences should be higher than 20%. Therefore, it is difficult to validly compare our results with similar results from other European countries. Furthermore, because this was the first countrywide study of the prevalence of MAP infection in sheep and goats in Cyprus we cannot compare our findings with previous ones and discuss possible longitudinal trends. We used a Bayesian framework to adjust for the imperfect accuracy of the ELISA (Kostoulas et al., 2006a) and estimated the true prevalence of MAP infection because it allowed for the incorporation of prior information on the Se and Sp of the ELISA in terms of probability space rather than single values. A primary practical advantage of Bayesian estimation is the combination of the observed data with available scientific information in a coherent way. The latter was crucial in our case because the proposed model is not identifiable and would not have converged in the total absence of informative priors. Such models cannot be treated under frequentist analysis (Messam et al., 2008). Although, incorporation of prior information has received historical criticism because of its impact on parameter estimation it has also been viewed as a great strength of Bayesian methodology (Gardner, 2002). Prior elicitation must be – and was in our case – based on available, relevant and scientifically justifiable information (Kostoulas et al., 2006a,b; Nielsen and Toft, 2008) and the role of priors needs to be – and was – critically assessed through a sensitivity analysis. Further, in contrast to traditional frequentist methods, the Bayesian approach allowed for the flexible handling – both conceptually and computationally – of the employed model that simultaneously estimated the herd-level and within herd prevalence of MAP infection. Bayesian estimation resulted in posterior distributions for animal- and flock-level prevalence rather than point estimates and confidence intervals, which can be used to directly calculate probability intervals. Hence, the flocks that were free of MAP infection at a desired level could be readily evaluated from the posterior cumulative flock
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prevalence distributions (Fig. 2). Last but not least, under standard frequentist analysis we would have obtained a single true prevalence estimate (Rogan and Gladen, 1978) for each herd. This would have resulted in many instances to nonsensical point estimates (greater than 1 or less than 0) for herds of high or low seroprevalence, respectively. Such issues usually arise in frequentist analysis particularly when sample sizes are small, test prevalences are low and diagnostics are seriously lacking in Se or Sp (Messam et al., 2008). These issues have been resolved under Bayesian analysis that offers direct computation of range respecting interval estimates for prevalence (between 0 and 1) without the requirement of transformations or large-sample approximations. We separately calculated the prevalence of MAP infection in sheep and goats by incorporating relevant Se and Sp estimates because we have recently demonstrated the need of a species-specific approach in the diagnostic accuracy and prevalence estimation between sheep and goats because of the significantly different Se of the ELISA between sub-clinically infected Greek dairy sheep and goats (Kostoulas et al., 2006a). In line with this, Corpa et al. (2000) argued that the scarcity of goats with focal lesions along with the higher number of goats with diffuse lesions when compared with studies carried out in sheep (Perez et al., 1996) may indicate that goats have only limited ability to control infection. Diffuse lesions are associated with failure of effective immune mechanisms and subsequent humoral response development (Sergeant et al., 2003; Perez et al., 1997; Clarke et al., 1996). The Se of tests detecting humoral response to paratuberculosis is inversely related to the extent of lesions and therefore depends on the age- and disease-stage distribution in the tested population (Perez et al., 1997; Sergeant et al., 2003; Nielsen and Toft, 2008). Nevertheless, it is believed that ovine paratuberculosis predominantly results from infection with sheep strains of MAP, while caprine paratuberculosis may result from infection of goat-adapted cattle strains of MAP (Cousins et al., 2000). Saxegaard (1990) reported a strain of MAP that was pathogenic for goats and non-pathogenic for cattle and sheep suggesting that certain strains may have a host preference for goats. We isolated both sheep and cattle strains of MAP from either sheep or goats (Florou et al., 2009). Likely, not only immunological but also differences in strain virulence along with host preference may also account for the different Se of the ELISA between sheep and goats. Hence, true prevalence estimation must be performed separately for sheep and goats adjusting for the different target population – specific and strain distribution – specific accuracy of the diagnostic process. Our estimates indicate that paratuberculosis is today endemic and widely spread among the small ruminants on the island. Two out of three sheep flocks and one every two goat flocks have at least a MAP infected animal. Within these infected flocks the prevalence is, on average, close to 25%. Cypriot husbandry features, such as farming areas where animals live in close proximity, likely favoured MAP transmission between flocks. Simple wire strand fences such as used to separate flocks in farming areas do not prevent the spread of infection (Whittington and McGregor,
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2005). Additionally, the intensive management and lack of pastures leading to high stocking density can affect the within herd prevalence due to higher exposure of susceptible animals to contaminated faeces. From a control point of view, our finding that one of three sheep flocks and one of two goat flocks may not have infected animals is encouraging. Though herd certification is complicated and might involve testing and re-testing of animals and long term follow-up of herds, the likely existence of a noninfected population is essential for the design of regional or nationwide control programs (Nielsen, 2009). Experience from the control of ovine paratuberculosis in Australia shows that vaccination together with risk based control strategies – such as replacement of animals from MAP free flocks – is a practical way to limit the spread of the infection. Acknowledgement This study was partially financed by the Research Promotion Foundation of Cyprus, under the code AEIFO 1104/02 References Best, N., Cowles, M.K., Vines, K., 2003. CODA: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output. Version 0. 6-1. MRC Biostatistics Unit, Cambridge, UK. Branscum, A.J., Gardner, I.A., Johnson, W.O., 2005. Estimation of diagnostic-test sensitivity and specificity through Bayesian modelling. Prev. Vet. Med. 68, 145–163. Clarke, C.J., Patterson, I.A., Armstrong, K.E., Low, J.C., 1996. Comparison of the absorbed ELISA and agar gel immunodiffusion test with clinicopathological findings in ovine clinical paratuberculosis. Vet. Rec. 139, 618–621. Collins, M.T., Sockett, D.C., 1993. Accuracy and economics of the USDA-licensed enzyme-linked immunosorbent assay for bovine paratuberculosis. J. Am. Vet. Med. Assoc. 203, 1456–1463. Corpa, J.M., Garrido, J., Garcia Marin, J.F., Perez, V., 2000. Classification of lesions observed in natural cases of paratuberculosis in goats. J. Comp. Pathol. 122, 255–265. Cousins, D.V., Williams, S.N., Hope, A., Eamens, G.J., 2000. DNA fingerprinting of Australian isolates of Mycobacterium avium subsp. paratuberculosis using IS900 RFLP. Aus. Vet. 78, 184–190. Crowther, R.W., Polydorou, K., Nitti, S., Phyrilla, A., 1976. Johnes disease in sheep in Cyprus. Vet. Rec. 98, 463. Enøe, C., 2003. Measures of disease in pigs: validation and inference. Ph.D. Thesis. The Royal Veterinary and Agricultural University, Copenhagen, p. 62. Florou, M., Leontides, L., Kostoulas, P., Billinis, C., Sofia, M., 2009. Strain-specific sensitivity estimates of Mycobacterium avium subsp.
paratuberculosis culture in Greek sheep and goats. Zoonoses Public Health 56, 49–52. Gardner, I.A., 2002. The utility of Bayes’ theorem and Bayesian inference in veterinary clinical practice and research. Aust. Vet. J. 80, 758–761. Hanson, T., Johnson, W.O., Gardner, I.A., 2003. Hierarchical models for estimating herd prevalence and test accuracy in the absence of a gold standard. J. Agric. Biol. Environ. Stat. 8, 223–239. Heidelberger, P., Welch, P.D., 1983. Simulation run length control in the presence of an initial transient. Oper. Res., 1109–1144. Kennedy, D.J., Benedictus, G., 2001. Control of Mycobacterium avium subsp. paratuberculosis infection in agricultural species. Rev. Sci. Tech. Off. Int. Epiz. 20, 151–179. Kostoulas, P., Leontides, L., Enøe, C., Billinis, C., Florou, M., Sofia, M., 2006a. Bayesian estimation of sensitivity and specificity of serum ELISA and faecal culture for diagnosis of paratuberculosis in Greek dairy sheep and goats. Prev. Vet. Med. 76, 56–73. Kostoulas, P., Leontides, L., Billinis, C., Florou, M., 2006b. Application of a semi-dependent latent model in the Bayesian estimation of the sensitivity and specificity of two faecal culture methods for diagnosis of paratuberculosis in subclinically infected Greek dairy sheep and goats. Prev. Vet. Med. 76, 121–134. Messam, V., Branscum, A.J., Collins, M.T., Gardner, I.A., 2008. Frequentist and Bayesian approaches to prevalence estimation using examples from Johne’s disease. Anim. Health Res. Rev. 9, 1–23. Nielsen, S.S., 2009. Paratuberculosis in dairy cattle: epidemiological studies used for design of a control programme in Denmark. Dr. Med. Vet. Thesis. ISBN 978-87-7611-320-9. Nielsen, S.S., Grønbæk, C., Agger, J.F., Houe, H., 2002. Maximum-likelihood estimation of sensitivity and specificity of ELISAs and faecal culture for diagnosis of paratuberculosis. Prev. Vet. Med. 53, 191–204. Nielsen, S.S., Toft, N., 2008. Ante mortem diagnosis of paratuberculosis: a review of accuracies of ELISA, interferon-␥ assay and faecal culture techniques. Vet. Microbiol. 129, 217–235. Nielsen, S.S., Toft, N., 2009. A review of prevalences of paratuberculosis in farmed animals in Europe. Prev. Vet. Med. 88, 1–14. Perez, V., Garcia Marin, J.F., Badiola, J.J., 1996. Description and classification of different types of lesion associated with natural paratuberculosis infection in sheep. J. Comp. Pathol. 114, 107–122. Perez, V., Tellechea, J., Badiola, J.J., Gutierrez, M., Garcia Marin, J.F., 1997. Relation between serologic response and pathologic findings in sheep with naturally acquired paratuberculosis. Am. J. Vet. Res. 58, 799–803. Raftery, A.E., Lewis, S.M., 1992. [Practical Markov Chain Monte Carlo]: Comment: one long run with diagnostics: implementation strategies for Markov Chain Monte Carlo. Stat. Sci. 7, 493–497. Rogan, W.J., Gladen, B., 1978. Estimating prevalence from the results of a screening test. Am. J. Epidemiol. 107, 71. Saxegaard, F., 1990. Experimental infection of calves with an apparently specific goat-pathogenic strain of Mycobacterium paratuberculosis. J. Comp. Pathol. 102, 149–156. Sergeant, E.S., Marshall, D.J., Eamens, G.J., Kearns, C., Whittington, R.J., 2003. Evaluation of an absorbed ELISA and an agar-gel immunodiffusion test for ovine paratuberculosis in sheep in Australia. Prev. Vet. Med. 61, 235–248. Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., 2003. WinBUGS User Manual, version 1.4. MRC Biostatistics Unit, Cambridge. Whittington, R.J., McGregor, H., 2005. Epidemiology of Ovine Johne’s Disease 2 – Pasture Contamination Level and Age Susceptibility. Project OJD 028. Meat and Livestock Australia, North Sydney, pp. 1–49.
Contents lists available at ScienceDirect
Small Ruminant Research journal homepage: www.elsevier.com/locate/smallrumres
Bayesian estimation of the true prevalence of Mycobacterium avium subsp. paratuberculosis infection in Cypriot dairy sheep and goat flocks M. Liapi a , L. Leontides b,∗ , P. Kostoulas b , G. Botsaris c , Y. Iacovou a , C. Rees c , K. Georgiou a , G.C. Smith d , D.C. Naseby e a b c d e
Cyprus Veterinary Services, 1417 Athalassas Av, Nicosia, Cyprus Laboratory of Epidemiology, Biostatistics and Animal Health Economics, University of Thessaly, Trikalon 224, GR-43100 Karditsa, Greece Division of Food Sciences, School of Biosciences, University of Nottingham, Leicestershire LE12 5RD, United Kingdom Food and Environment Research Agency, Sand Hutton, York YO41 1LZ, UK School of Life Sciences, Faculty of Health and Human Sciences, University of Hertfordshire, Herts AL10 9AB, Hatfield, UK
a r t i c l e
i n f o
Article history: Received 8 February 2010 Received in revised form 20 September 2010 Accepted 23 September 2010 Available online 18 November 2010 Keywords: Mycobacterium avium paratuberculosis ELISA Seroprevalence Bayesian estimation True prevalence
a b s t r a c t We estimated the prevalence of Mycobacterium avium subsp. paratuberculosis (MAP) infected sheep and goats, older than 2 years, reared in the region effectively controlled by the Government of the Republic of Cyprus, in September 2005. The sera collected from 8011 animals (3429 sheep and 4582 goats) from 83 flocks, non-vaccinated against MAP, were examined for antibodies with a commercially available enzyme linked immunosorbent assay (Pourquier® paratuberculosis antibody screening ELISA). The true prevalence of MAP infection was calculated, in a Bayesian framework, separately in sheep and goats, with models that adjusted for the misclassification of animals because of the imperfect accuracy of the ELISA. The within-flock mean seroprevalence in sheep and goats was 9.9% (95% CI: 8.9; 10.9%) and 7.9% (7.2; 8.7%), respectively. There was at least one seropositive sheep in 52% (38; 66%) of flocks with sheep and one seropositive goat in 50% (39; 62%) of flocks with goats. Within the seropositive flocks the mean seroprevalence was 12.1% (10.9; 13.4%) and 10.3% (9.3; 11.4%) in sheep and goats, respectively. The calculated mean true prevalence of infected sheep and goats was 15.0 and 11.1%, respectively. There was at least one infected sheep in 60.8% (95% credible interval: 42.3; 78.8%) and at least an infected goat in 48.6% (30.4; 68.5%) of the flocks. In the infected flocks, the mean within flock true prevalence of infection in sheep and goats was estimated at 24.6% (16.3; 33.3%) and 23.1% (15.5; 33.6%), respectively. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Paratuberculosis is a chronic infection, mainly of ruminants, which is caused by Mycobacterium avium subsp. paratuberculosis (MAP). The infection is responsible for major economic losses in the primary industry and adversely affects international and national animal trade; therefore, there is increasing interest in control programs
∗ Corresponding author. Tel.: +30 24410 66002; fax: +30 24410 66047. E-mail address: [email protected] (L. Leontides). 0921-4488/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.smallrumres.2010.09.010
(Kennedy and Benedictus, 2001; Nielsen, 2009). In Cyprus, paratuberculosis was first diagnosed in sheep in 1965 (Crowther et al., 1976). From 1979 onwards, an average of 19 outbreaks of paratuberculosis per year, usually with severe clinical symptoms, is officially reported in sheep or goat flocks [Diagnostic Veterinary Agency (DVA) 1979–2008]. Valid estimation of the true prevalence of MAP infection in sheep and goats, both at the flock- and at the animallevel, is the starting point for decision makers to determine whether the infection should be considered important or not, and which measures to apply. Such measures
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could pertain to eradication in case of low prevalence, control in case of high prevalence, and surveillance in case of the likely absence of the infection. The latency and slow progression of MAP infection makes diagnosis a challenge and tests with high sensitivity (Se) are lacking, therefore, seriously impeding successful control efforts for paratuberculosis. Due to the serious misclassification rate, particularly in sub-clinically infected animals, lack of knowledge of or disregard for test errors could lead to bias in prevalence estimation surveys. Thus, it is imperative that studies aiming to estimate the true herd prevalence and within herd prevalence of MAP infection should adjust for the imperfect Se and Sp of the diagnostic procedure. Importantly, Se and Sp estimates to be incorporated in the estimation procedure should originate from studies relevant to the study population because the Se of the available tests depends on the distribution of the infection stages in the test population (Collins and Sockett, 1993), whilst Sps are likely to differ between areas with different environmental mycobacteria (Nielsen et al., 2002). Recently, Nielsen and Toft (2009) conducted a critical comparative review of the reported within- and betweenherd prevalence estimates of MAP infection among farmed animals in Europe. They found no interpretable animallevel and only very scarce flock-level estimates for sheep and goats due to the variability in the (a) study design, (b) target population, (c) target disorder detected by the diagnostic procedure and (d) the variability or absence of Se and Sp estimates. In this study we aimed to estimate the true prevalence of MAP infection in Cypriot sheep and goat flocks. The true prevalence was estimated, in a Bayesian framework, separately in sheep and goats with models that adjusted for the misclassification of animals because of the imperfect accuracy of the ELISA. 2. Materials and methods 2.1. Management of sheep and goats in Cyprus The majority of Cypriot sheep and goats are cross-breeds. Sheep belong mostly to crosses between the Chios and the local breed, whereas goats are crosses between the Damascus and the local breed. The animals are kept, under intensive or semi-intensive management, for milk production, which is the primary production goal. There is no seasonal movement between pastures. Semi-intensively managed flocks graze for some hours in private pastures but their diet is mainly based on in-house feeding and watering. Approximately half of the flocks are located in 57 farming areas defined with wire strand fences. Sheep-only and goat-only flocks comprise 15 and 46%, respectively, and the remaining (39%) are mixed flocks with, on average, half sheep and half goats. Purchase of females between flocks is limited and very few animals are imported into the island. The farmers usually select replacements among the daughters of high-yielding ewes and goats, whilst males bought into the flocks usually originate from high yielding animals from other flocks. In 2008, 36629 animals were recorded as moving between flocks and, in the past 4 years, only 500 animals have been imported. These were from UK, Germany and Bulgaria. The overall number of sheep and goats are fairly constant, with a turnover rate of 20–30%.
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Fig. 1. Age distribution of sheep and goats in the region effectively controlled by the Government of the Republic of Cyprus in September 2005.
of Cyprus covers an area of 5828 km2 and is administratively divided into 5 Districts namely, Lefkosia, Lemesos, Larnaka, Paphos and Ammochostos. The sampling unit was the flock and the design was a combination of stratified and cluster sampling. The District and herd size (categorized in 3 groups, flocks with ≤100 animals, with 101–300 animals and with >300 animals) were the strata variants for stratification (15 strata). Sampled flocks were randomly selected proportionally to the District-specific herd-size distribution. Within these flocks, all sheep and goats older than 2 years were blood sampled, to increase the Se of the diagnostic procedure (Kostoulas et al., 2006a). The minimum number of flocks in order to estimate a prevalence of 65% (estimate based on DVA data) of infected flocks with a 95% level of confidence and 10% absolute precision was 83. Blood sampling was done from September 2005 until September 2006. Collected samples were centrifuged (1000 × g for 10 min) and the separated sera were stored at −20 ◦ C until examination. 2.3. Serological testing Sera were examined with a commercial indirect absorbed ELISA kit (Pourquier® Elisa paratuberculosis antibody screening) according to the manufacturer’s instructions. Samples were considered positive at a sample to positive value ≥70% and negative otherwise. 2.4. Bayesian estimation of true prevalence of infection To estimate the true prevalence of MAP infection separately in sheep and goats we applied models that adjusted for the misclassification of animals because of the imperfect accuracy of the ELISA. We chose a Bayesian approach that allowed for the incorporation of prior information in terms of probability space rather than single values (Branscum et al., 2005). 2.4.1. Definition of MAP infection Bayesian models for prevalence estimation create their own probabilistic definition of infection, which, however, implicitly assumes a biological definition based on the fact that true prevalence estimates are obtained after adjusting for the imperfect Se and Sp of the diagnostic procedure (Enøe, 2003). For defining MAP infection in biological terms, we used the approach described by Nielsen et al. (2002) and Kostoulas et al. (2006a). Hence, by ‘infection’ we mean that sheep or goats carry MAP intracellularly; substantial replication need not take place because the infection can be latent. Entrance and persistence of MAP have lasted long enough to give an immune response at any time during their life; we assumed that once an animal has an established infection, the infection persists for life.
2.2. Target population and sampling In total, there were 339,371 sheep and goats reared in 3878 flocks. Their age-distributions are given in Fig. 1. The target population included all sheep and goats over 24 months old (according to the records of the DVA, these animals comprised an estimated 55 and 65% of the population of sheep or goats, respectively), with no history of vaccination against MAP. The region effectively controlled by the Government of the Republic
2.4.2. The model We apply a model that has been extensively described by Branscum et al. (2005). Briefly, let y1 , y2 , . . ., yk , be the numbers of test-positive animals out of n sampled animals in each of k flocks. The data yk are assumed to be independent and follow binomial distributions: yk ∼Binomial(n, k Se + (1 − k )(1 − Sp))
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where k denotes the true prevalence of MAP infection in the kth flock, and Se and Sp the sensitivity and specificity of the test, respectively (Rogan and Gladen, 1978). Se and Sp are assumed to be constant across the k flocks. Further, we allowed for the possibility of flocks being entirely free of MAP infection by modeling k as: k = k∗ , k = 0,
with probability with probability 1 −
where denotes the proportion of infected flocks and k the prevalence of MAP infection in the kth flock assuming this flock is infected. Further, the prevalences among the diseased flocks were modeled using a beta distribution: k∗ |,
functions that serves as a processor of WinBUGS output (Best et al., 2003). To calculate the parameters a and b of the beta prior distributions for Se and Sp we utilized the Betabuster software, which is a public domain software also available at the aforementioned web address.
∼Beta( ,
(1 − ))
where is the mean true prevalence among all diseased flocks in the region and is related to the variability of these prevalences that flexibly allows for disperse or homogeneous infection prevalences among flocks; larger values of correspond to less variable prevalences (Hanson et al., 2003). 2.4.3. Prior information Independent beta prior distributions, beta(˛,ˇ) were used to model uncertainty about, Se, Sp, , and . A gamma prior distribution was used to model , Gamma(a ,b ). For Se and Sp, prior derivation was based on relevant published estimates (Kostoulas et al., 2006a,b; Nielsen and Toft, 2009) and expert opinion. The most likely value of ELISA Se for sheep and goats was thought to be 37 and 63%, while we were 95% confident that it was not less than 10 and 42%, respectively. The corresponding distributions were beta(1.68,2.46) and beta(10.65,6.67). For ELISA Sp the most likely values were set to 97 and 95% and we were 95% confident that they were not less than 93 and 90%, beta(115.8,4.5) and beta(99.7,6.2), respectively. For , in either sheep or goats, we expected that, most likely, 65% of the flocks were infected and were 95% confident that not less than 40% of them were infected, beta(7.98,4.76). For , in an infected flock, the mean prevalence of MAP infection was thought to be 30% and we were 95% confident that it was not more than 40%, beta(19.06,44.04). Finally, for , we specified prior information about our prior belief for the variability of within flock prevalence in infected flocks: we were confident that 90% of all infected flocks had prevalence less or equal to 50% and 95% certain that it did not exceed 60%, Gamma(5.4,0.55). Computation of a and b was done as described in Hanson et al. (2003).
3. Results In total 8011 animals (3429 sheep and 4582 goats) from 83 flocks (11 sheep-only, 33 goat-only and 39 mixed flocks) were tested. Three hundred and forty of 3429 [9.9% (95% CI: 8.9; 10.9%)] sheep and 362/4582 [7.9% (7.2; 8.7%)] goats tested positive. There was at least one test-positive sheep in 26/49 [53% (39; 67%)] flocks with sheep and one test-positive goat in 36/72 [50% (39; 62%)] flocks with goats. Within the test-positive flocks the mean apparent prevalence was 340/2812 [12.1% (10.9; 13.4%)] and 362/3513 [10.3% (9.3; 11.4%)] in sheep and goats, respectively. Overall, in the target population, the estimated mean true prevalence of infected sheep and goats was 15 and 11.1%, respectively. We estimated that there was at least one infected sheep in 60.8% (95% credible interval: 42.3; 78.8%) and at least an infected goat in 48.6% (30.4; 68.5%) of the flocks. In those flocks, with ≥1 infected sheep or goat, the estimated mean within flock true prevalence of infection were 24.6% (16.3; 33.3%) and 23.1% (15.5; 33.6%), respectively. The probability that a randomly chosen flock had no infected sheep or goat was 39.2 and 51.4%, respectively. The probability that a randomly chosen flock in the region had true prevalence of infected sheep or goats <5% was 47.7 and 57.8%, respectively. The estimated posterior cumulative distributions of the true flock prevalence in sheep and goats are in Fig. 2. Furthermore, sensitivity analysis revealed that under the considered alternative sets of priors our results were qualitatively and quantitatively the same.
2.4.4. Sensitivity analysis To assess the influence of prior information on the estimates of the model parameters we repeated our analysis considering alternative prior information. The current model lacks identifiability if non-informative priors are used for all model parameters, therefore informative priors had to be incorporated in the model to mitigate lack of identifiability. We chose to retain the Se and Sp priors used in the primary analysis because they were based on recent, relevant and scientifically justifiable information (Kostoulas et al., 2006a) and adopted non-informative priors either on the prevalence of infected flocks () or the within flock prevalence () in infected flocks, which were the primary parameters of interest and original prior derivation was only based on expert opinion. 2.4.5. Convergence diagnostics Convergence diagnostics of the Markov Chain Monte Carlo (MCMC) chain are not foolproof. Therefore, a combination of diagnostics plus visual inspection of the trace plots and summary statistics is recommended. Standard diagnostic procedures of the MCMC chain (Heidelberger and Welch, 1983; Raftery and Lewis, 1992), plus visual inspection of the autocorrelation plots and the posterior distributions of the parameters, revealed no convergence problems. 2.4.6. Statistical software All models were run in the freeware program WinBUGS (Spiegelhalter et al., 2003). Example WinBUGS codes for the Bayesian model we have used can be found at http://www.epi.ucdavis.edu/diagnostictests. For convergence diagnostics we used the Convergence Diagnostic and Output Analysis (CODA) package, which is a menu-driven set of R-Plus
Fig. 2. Estimated cumulative posterior probability for the prevalence of Mycobacterium avium subsp. paratuberculosis-infected sheep (grey line) and goat (black line) Cypriot flocks. A flock was considered infected when at least one, older than two years, animal was infected. The vertical line corresponds to flock prevalence of 5%.
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4. Discussion In this study we estimated the true animal- and flocklevel prevalence of infected sheep and goats from a large random sample, representative of all older than two-years old, non-vaccinated against MAP, small ruminants reared in the region effectively controlled by the Government of the Republic of Cyprus in 2005. In the Cypriot population of small ruminants, a higher percentage of sheep than goats were <2 years old and was excluded from sampling (Fig. 1, statistical comparison not shown). Thus, our prevalence estimates may refer to different proportions of sheep and goats in the target population. Sampled animals were serologically tested with a commercial ELISA. Subsequently, we incorporated the observed seroprevalence data in statistical models, which adjusted, in a Bayesian framework, for the misclassification of animals because of the imperfect accuracy of the ELISA, and estimated the true prevalence of infection, separately in sheep and goats. In a recent review of prevalences of paratuberculosis in farmed animals in Europe, Nielsen and Toft (2009), found no studies that provided accurate and unbiased country-specific animal-level prevalence estimates and estimated that flock level prevalences should be higher than 20%. Therefore, it is difficult to validly compare our results with similar results from other European countries. Furthermore, because this was the first countrywide study of the prevalence of MAP infection in sheep and goats in Cyprus we cannot compare our findings with previous ones and discuss possible longitudinal trends. We used a Bayesian framework to adjust for the imperfect accuracy of the ELISA (Kostoulas et al., 2006a) and estimated the true prevalence of MAP infection because it allowed for the incorporation of prior information on the Se and Sp of the ELISA in terms of probability space rather than single values. A primary practical advantage of Bayesian estimation is the combination of the observed data with available scientific information in a coherent way. The latter was crucial in our case because the proposed model is not identifiable and would not have converged in the total absence of informative priors. Such models cannot be treated under frequentist analysis (Messam et al., 2008). Although, incorporation of prior information has received historical criticism because of its impact on parameter estimation it has also been viewed as a great strength of Bayesian methodology (Gardner, 2002). Prior elicitation must be – and was in our case – based on available, relevant and scientifically justifiable information (Kostoulas et al., 2006a,b; Nielsen and Toft, 2008) and the role of priors needs to be – and was – critically assessed through a sensitivity analysis. Further, in contrast to traditional frequentist methods, the Bayesian approach allowed for the flexible handling – both conceptually and computationally – of the employed model that simultaneously estimated the herd-level and within herd prevalence of MAP infection. Bayesian estimation resulted in posterior distributions for animal- and flock-level prevalence rather than point estimates and confidence intervals, which can be used to directly calculate probability intervals. Hence, the flocks that were free of MAP infection at a desired level could be readily evaluated from the posterior cumulative flock
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prevalence distributions (Fig. 2). Last but not least, under standard frequentist analysis we would have obtained a single true prevalence estimate (Rogan and Gladen, 1978) for each herd. This would have resulted in many instances to nonsensical point estimates (greater than 1 or less than 0) for herds of high or low seroprevalence, respectively. Such issues usually arise in frequentist analysis particularly when sample sizes are small, test prevalences are low and diagnostics are seriously lacking in Se or Sp (Messam et al., 2008). These issues have been resolved under Bayesian analysis that offers direct computation of range respecting interval estimates for prevalence (between 0 and 1) without the requirement of transformations or large-sample approximations. We separately calculated the prevalence of MAP infection in sheep and goats by incorporating relevant Se and Sp estimates because we have recently demonstrated the need of a species-specific approach in the diagnostic accuracy and prevalence estimation between sheep and goats because of the significantly different Se of the ELISA between sub-clinically infected Greek dairy sheep and goats (Kostoulas et al., 2006a). In line with this, Corpa et al. (2000) argued that the scarcity of goats with focal lesions along with the higher number of goats with diffuse lesions when compared with studies carried out in sheep (Perez et al., 1996) may indicate that goats have only limited ability to control infection. Diffuse lesions are associated with failure of effective immune mechanisms and subsequent humoral response development (Sergeant et al., 2003; Perez et al., 1997; Clarke et al., 1996). The Se of tests detecting humoral response to paratuberculosis is inversely related to the extent of lesions and therefore depends on the age- and disease-stage distribution in the tested population (Perez et al., 1997; Sergeant et al., 2003; Nielsen and Toft, 2008). Nevertheless, it is believed that ovine paratuberculosis predominantly results from infection with sheep strains of MAP, while caprine paratuberculosis may result from infection of goat-adapted cattle strains of MAP (Cousins et al., 2000). Saxegaard (1990) reported a strain of MAP that was pathogenic for goats and non-pathogenic for cattle and sheep suggesting that certain strains may have a host preference for goats. We isolated both sheep and cattle strains of MAP from either sheep or goats (Florou et al., 2009). Likely, not only immunological but also differences in strain virulence along with host preference may also account for the different Se of the ELISA between sheep and goats. Hence, true prevalence estimation must be performed separately for sheep and goats adjusting for the different target population – specific and strain distribution – specific accuracy of the diagnostic process. Our estimates indicate that paratuberculosis is today endemic and widely spread among the small ruminants on the island. Two out of three sheep flocks and one every two goat flocks have at least a MAP infected animal. Within these infected flocks the prevalence is, on average, close to 25%. Cypriot husbandry features, such as farming areas where animals live in close proximity, likely favoured MAP transmission between flocks. Simple wire strand fences such as used to separate flocks in farming areas do not prevent the spread of infection (Whittington and McGregor,
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2005). Additionally, the intensive management and lack of pastures leading to high stocking density can affect the within herd prevalence due to higher exposure of susceptible animals to contaminated faeces. From a control point of view, our finding that one of three sheep flocks and one of two goat flocks may not have infected animals is encouraging. Though herd certification is complicated and might involve testing and re-testing of animals and long term follow-up of herds, the likely existence of a noninfected population is essential for the design of regional or nationwide control programs (Nielsen, 2009). Experience from the control of ovine paratuberculosis in Australia shows that vaccination together with risk based control strategies – such as replacement of animals from MAP free flocks – is a practical way to limit the spread of the infection. Acknowledgement This study was partially financed by the Research Promotion Foundation of Cyprus, under the code AEIFO 1104/02 References Best, N., Cowles, M.K., Vines, K., 2003. CODA: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output. Version 0. 6-1. MRC Biostatistics Unit, Cambridge, UK. Branscum, A.J., Gardner, I.A., Johnson, W.O., 2005. Estimation of diagnostic-test sensitivity and specificity through Bayesian modelling. Prev. Vet. Med. 68, 145–163. Clarke, C.J., Patterson, I.A., Armstrong, K.E., Low, J.C., 1996. Comparison of the absorbed ELISA and agar gel immunodiffusion test with clinicopathological findings in ovine clinical paratuberculosis. Vet. Rec. 139, 618–621. Collins, M.T., Sockett, D.C., 1993. Accuracy and economics of the USDA-licensed enzyme-linked immunosorbent assay for bovine paratuberculosis. J. Am. Vet. Med. Assoc. 203, 1456–1463. Corpa, J.M., Garrido, J., Garcia Marin, J.F., Perez, V., 2000. Classification of lesions observed in natural cases of paratuberculosis in goats. J. Comp. Pathol. 122, 255–265. Cousins, D.V., Williams, S.N., Hope, A., Eamens, G.J., 2000. DNA fingerprinting of Australian isolates of Mycobacterium avium subsp. paratuberculosis using IS900 RFLP. Aus. Vet. 78, 184–190. Crowther, R.W., Polydorou, K., Nitti, S., Phyrilla, A., 1976. Johnes disease in sheep in Cyprus. Vet. Rec. 98, 463. Enøe, C., 2003. Measures of disease in pigs: validation and inference. Ph.D. Thesis. The Royal Veterinary and Agricultural University, Copenhagen, p. 62. Florou, M., Leontides, L., Kostoulas, P., Billinis, C., Sofia, M., 2009. Strain-specific sensitivity estimates of Mycobacterium avium subsp.
paratuberculosis culture in Greek sheep and goats. Zoonoses Public Health 56, 49–52. Gardner, I.A., 2002. The utility of Bayes’ theorem and Bayesian inference in veterinary clinical practice and research. Aust. Vet. J. 80, 758–761. Hanson, T., Johnson, W.O., Gardner, I.A., 2003. Hierarchical models for estimating herd prevalence and test accuracy in the absence of a gold standard. J. Agric. Biol. Environ. Stat. 8, 223–239. Heidelberger, P., Welch, P.D., 1983. Simulation run length control in the presence of an initial transient. Oper. Res., 1109–1144. Kennedy, D.J., Benedictus, G., 2001. Control of Mycobacterium avium subsp. paratuberculosis infection in agricultural species. Rev. Sci. Tech. Off. Int. Epiz. 20, 151–179. Kostoulas, P., Leontides, L., Enøe, C., Billinis, C., Florou, M., Sofia, M., 2006a. Bayesian estimation of sensitivity and specificity of serum ELISA and faecal culture for diagnosis of paratuberculosis in Greek dairy sheep and goats. Prev. Vet. Med. 76, 56–73. Kostoulas, P., Leontides, L., Billinis, C., Florou, M., 2006b. Application of a semi-dependent latent model in the Bayesian estimation of the sensitivity and specificity of two faecal culture methods for diagnosis of paratuberculosis in subclinically infected Greek dairy sheep and goats. Prev. Vet. Med. 76, 121–134. Messam, V., Branscum, A.J., Collins, M.T., Gardner, I.A., 2008. Frequentist and Bayesian approaches to prevalence estimation using examples from Johne’s disease. Anim. Health Res. Rev. 9, 1–23. Nielsen, S.S., 2009. Paratuberculosis in dairy cattle: epidemiological studies used for design of a control programme in Denmark. Dr. Med. Vet. Thesis. ISBN 978-87-7611-320-9. Nielsen, S.S., Grønbæk, C., Agger, J.F., Houe, H., 2002. Maximum-likelihood estimation of sensitivity and specificity of ELISAs and faecal culture for diagnosis of paratuberculosis. Prev. Vet. Med. 53, 191–204. Nielsen, S.S., Toft, N., 2008. Ante mortem diagnosis of paratuberculosis: a review of accuracies of ELISA, interferon-␥ assay and faecal culture techniques. Vet. Microbiol. 129, 217–235. Nielsen, S.S., Toft, N., 2009. A review of prevalences of paratuberculosis in farmed animals in Europe. Prev. Vet. Med. 88, 1–14. Perez, V., Garcia Marin, J.F., Badiola, J.J., 1996. Description and classification of different types of lesion associated with natural paratuberculosis infection in sheep. J. Comp. Pathol. 114, 107–122. Perez, V., Tellechea, J., Badiola, J.J., Gutierrez, M., Garcia Marin, J.F., 1997. Relation between serologic response and pathologic findings in sheep with naturally acquired paratuberculosis. Am. J. Vet. Res. 58, 799–803. Raftery, A.E., Lewis, S.M., 1992. [Practical Markov Chain Monte Carlo]: Comment: one long run with diagnostics: implementation strategies for Markov Chain Monte Carlo. Stat. Sci. 7, 493–497. Rogan, W.J., Gladen, B., 1978. Estimating prevalence from the results of a screening test. Am. J. Epidemiol. 107, 71. Saxegaard, F., 1990. Experimental infection of calves with an apparently specific goat-pathogenic strain of Mycobacterium paratuberculosis. J. Comp. Pathol. 102, 149–156. Sergeant, E.S., Marshall, D.J., Eamens, G.J., Kearns, C., Whittington, R.J., 2003. Evaluation of an absorbed ELISA and an agar-gel immunodiffusion test for ovine paratuberculosis in sheep in Australia. Prev. Vet. Med. 61, 235–248. Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., 2003. WinBUGS User Manual, version 1.4. MRC Biostatistics Unit, Cambridge. Whittington, R.J., McGregor, H., 2005. Epidemiology of Ovine Johne’s Disease 2 – Pasture Contamination Level and Age Susceptibility. Project OJD 028. Meat and Livestock Australia, North Sydney, pp. 1–49.