Strategies for two-stage sampling designs for estimating herd-level prevalence

We propose a herd-level sample-size formula based on a common adjustment for prevalence estimates when diagnostic tests are imperfect. The formula depends on estimates of herd-level sensitivity and specificity. With Monte Carlo simulations, we explored the effects of different intracluster correlations on herd-level sensitivity and specificity. At low prevalence (e.g. 1% of animals infected), herd-level sensitivity increased with increasing intracluster correlation and many herds were classified as positive based only on false-positive test results. Herd-level sensitivity was less affected at higher prevalence (e.g. 20% of animals infected). A real-life example was developed for estimating ovine progressive pneumonia prevalence in sheep. The approach allows researchers to balance the number of herds and the total number of animals sampled by manipulating herd-level test characteristics (such as the number of animals sampled within a herd).     

Aggregate testing for the evaluation of Johne's disease herd status

This paper examines methods for evaluating herd Johne's disease status that could be used in a survey of the cattle industry. Emphasis is placed on aggregate testing, a process whereby a random sample of cattle from a herd is assessed using an imperfect test, such as an ELISA for detecting antibody in serum. Important aggregate test parameters discussed include: sample size, herd-level sensitivity, herd-level specificity, the number of reactors used for declaring a positive herd result, and the expected within-herd prevalence of disease. Aggregate testing may be useful for several livestock diseases. However, problems arise when it is applied to Johne's disease because of the poor sensitivity of the available diagnostic tests, the low within herd prevalence of infection, and clustering of false positives within a herd.     

A retrospective evaluation of a Bovine Herpesvirus-1 (BHV-1) antibody ELISA on bulk-tank milk samples for classification of the BHV-1 status of Danish dairy herds

Bulk-tank milk samples analysed in a Bovine Herpesvirus-1 (BHV-1) blocking ELISA are still in use in the Danish BHV-1 programme as a tool to classify dairy herds as BHV-1 infected or BHV-1 free herds. In this retrospective study, we used data from the Danish BHV-1 eradication campaign to evaluate performance characteristics of the BHV-1 blocking ELISA in 1039 BHV-1-seropositive and 502 repeatedly BHV-1-negative dairy herds using the results of blood testing of the individual animals as the true infection status. At a cut-off value of 30% blocking reaction, the herd-level relative sensitivity and relative specificity were 82 and 100%, respectively. The herd-level relative sensitivity depended on the within-herd prevalence of seropositive cows and the cut-off value in the assay, but not on the time interval (up to 90 days) between the collection of the bulk-tank milk sample and the individual serum samples. The BHV-1 blocking ELISA on bulk-tank milk could detect seropositive herds (few), with prevalence proportions as low as one seropositive cow out of 70 cows.     

A practical approach to calculate sample size for herd prevalence surveys

When designing a herd-level prevalence study that will use an imperfect diagnostic test, it is necessary to consider the test sensitivity and specificity. A new approach was developed to take into account the imperfections of the test. We present an adapted formula that, when combined with an existing piece of software, allows improved planning. Bovine paratuberculosis is included as an example infection because it originally stimulated the work. Examples are provided of the trade-off between the benefit (low number of herds) and the disadvantage (large number of animals per herd and exclusion of small herds) that are associated with achieving high herd-level sensitivity and specificity. We demonstrate the bias in the estimate of prevalence and the underestimate of the confidence range that would arise if we did not account for test sensitivity and specificity.     

Bulk-tank milk ELISA antibodies for estimating the prevalence of paratuberculosis in Danish dairy herds

Paratuberculosis (Johne's disease) has been widespread in Danish dairy herds for a long time but the herd-level prevalence has never been determined precisely. To evaluate the prevalence of paratuberculosis in Danish dairy herds in various regions, an ELISA based on a commercially available antigen was adapted for testing bulk-tank milk for the presence of antibodies to Mycobacterium avium subsp. paratuberculosis. Bulk-tank milk samples were collected from six milk-collecting centres from six different areas of the country. Samples from 900 herds (about 7.5% of all Danish dairy herds) were examined, and 70% were positive at the statistically optimal cut-off (sensitivity 97.1%; specificity 83.3%). The technical performance of the ELISA was not sufficient to provide a tool for surveillance because even slight changes in optical density for the samples would change the classification of some samples. The infection is more widespread than previous investigations have shown.     

Bayesian modeling of animal- and herd-level prevalences

We reviewed Bayesian approaches for animal-level and herd-level prevalence estimation based on cross-sectional sampling designs and demonstrated fitting of these models using the WinBUGS software. We considered estimation of infection prevalence based on use of a single diagnostic test applied to a single herd with binomial and hypergeometric sampling. We then considered multiple herds under binomial sampling with the primary goal of estimating the prevalence distribution and the proportion of infected herds. A new model is presented that can be used to estimate the herd-level prevalence in a region, including the posterior probability that all herds are non-infected. Using this model, inferences for the distribution of prevalences, mean prevalence in the region, and predicted prevalence of herds in the region (including the predicted probability of zero prevalence) are also available. In the models presented, both animal- and herd-level prevalences are modeled as mixture distributions to allow for zero infection prevalences. (If mixture models for the prevalences were not used, prevalence estimates might be artificially inflated, especially in herds and regions with low or zero prevalence.) Finally, we considered estimation of animal-level prevalence based on pooled samples.     

Simulation model estimates of test accuracy and predictive values for the Danish Salmonella surveillance program in dairy herds

The Danish government and cattle industry instituted a Salmonella surveillance program in October 2002 to help reduce Salmonella enterica subsp. enterica serotype Dublin (S. Dublin) infections. All dairy herds are tested by measuring antibodies in bulk tank milk at 3-month intervals. The program is based on a well-established ELISA, but the overall test program accuracy and misclassification was not previously investigated. We developed a model to simulate repeated bulk tank milk antibody measurements for dairy herds conditional on true infection status. The distributions of bulk tank milk antibody measurements for infected and noninfected herds were determined from field study data. Herd infection was defined as having either >or=1 Salmonella culture-positive fecal sample or >or=5% within-herd prevalence based on antibody measurements in serum or milk from individual animals. No distinction was made between Dublin and other Salmonella serotypes which cross-react in the ELISA. The simulation model was used to estimate the accuracy of herd classification for true herd-level prevalence values ranging from 0.02 to 0.5. Test program sensitivity was 0.95 across the range of prevalence values evaluated. Specificity was inversely related to prevalence and ranged from 0.83 to 0.98. For a true herd-level infection prevalence of 15%, the estimate for specificity (Sp) was 0.96. Also at the 15% herd-level prevalence, approximately 99% of herds classified as negative in the program would be truly noninfected and 80% of herds classified as positive would be infected. The predictive values were consistent with the primary goal of the surveillance program which was to have confidence that herds classified negative would be free of Salmonella infection.     

Simulating the sensitivity of pooled-sample herd tests for fecal Salmonella in cattle

Samples from livestock or food items are often submitted to microbiological analysis to determine whether or not the group (herd, flock or consignment) is shedding or is contaminated with a bacterial pathogen. This process is known as 'herd testing' and has traditionally involved subjecting each sample to a test on an individual basis. Alternatively one or more pools can be formed by combining and mixing samples from individuals (animals or items) and then each pool is subjected to a test for the pathogen. I constructed a model to simulate herd-level sensitivity of the individual-sample approach (HSe) and the herd-level sensitivity of the pooled-sample approach (HPSe) of tests for detecting pathogen. The two approaches are compared by calculating the relative sensitivity (RelHSe = HPSe/HSe). An assumption is that microbiological procedures had 100% specificity. The new model accounts for the potential for HPSe and RelHSe to be reduced by the dilution of pathogen that occurs when contaminated samples are blended with pathogen-free samples. Key inputs include a probability distribution describing the concentration of the pathogen of interest in samples, characteristics of the pooled-test protocol, and a 'test-dose-response curve' that quantifies the relationship between concentration of pathogen in the pool and the probability of detecting the target organism. The model also compares the per-herd cost of the pooled-sample and individual-sample approaches to herd testing. When applied to the example of Salmonella spp. in cattle feces it was shown that a reduction in the assumed prevalence of shedding can cause a substantial fall in HPSe and RelHSe. However, these outputs are much less sensitive to changes in prevalence when the number of samples per pool is high, or when the number of pools per herd-test is high, or both. By manipulating the number of pools per herd and the number of samples per pool HPSe can be optimized to suit the range of values of true prevalence of shedding of Salmonella that are likely to be encountered in the field.     

Evaluation of a bulk-milk ELISA test for the classification of herd-level bovine leukemia virus status

The results of a commercial bulk-milk enzyme-linked immunosorbent assay (ELISA) test for herd-level bovine leukemia virus (BLV) status were compared to results obtained from individual agar-gel immunodiffussion (AGID) testing on sampled cattle. A positive herd was defined as a herd having one or more AGID-positive animals. The estimated true herd status was based on the sensitivity and specificity of the AGID test and the number of cattle sampled per herd. Ninety-seven herds were used, with a mean of 13 cows sampled per herd. The AGID test indicated an apparent herd prevalence of 70.1%. After accounting for the number of cows sampled and the sensitivity and specificity of the AGID test, the estimated true herd prevalence of BLV was 52.3%. The ELISA test identified 79.4% of herds as positive for BLV, and had an apparent sensitivity and specificity of 0.97 and 0.62, respectively. However, after accounting for the sensitivity and specificity of the AGID test in individual animals, the specificity of the ELISA test was 0.44. The ELISA test was useful for identifying BLV-negative herds (i.e., ruling out the presence of BLV infection in test negative herds). With the moderately low specificity, herds identified as positive by the ELISA test would require further testing at the individual or herd level to definitively establish their BLV status.     

Herd-level prevalence of Mycobacterium avium subsp. paratuberculosis infection in United States dairy herds in 2007

Testing of composite fecal (environmental) samples from high traffic areas in dairy herds has been shown to be a cost-effective and sensitive method for classification of herd status for Mycobacterium avium subsp. paratuberculosis (MAP). In the National Animal Health Monitoring System's (NAHMS) Dairy 2007 study, the apparent herd-level prevalence of MAP was 70.4% (369/524 had ≥1 culture-positive composite fecal samples out of 6 tested). Based on these data, the true herd-level prevalence (HP) of MAP infection was estimated using Bayesian methods adjusting for the herd sensitivity (HSe) and herd specificity (HSp) of the test method. The Bayesian prior for HSe of composite fecal cultures was based on data from the NAHMS Dairy 2002 study and the prior for HSp was based on expert opinion. The posterior median HP (base model) was 91.1% (95% probability interval, 81.6 to 99.3%) and estimates were most sensitive to the prior for HSe. The HP was higher than estimated from the NAHMS Dairy 1996 and 2002 studies but estimates are not directly comparable with those of prior NAHMS studies because of the different testing methods and criteria used for herd classification.     

Associations between farm management practices, productivity, and bovine leukemia virus infection in Ontario dairy herds

The objective of this study was to investigate the associations between herd-level bovine leukemia virus (BLV) status and herd-level management and production variables. The study population consisted of 1330 cows sampled from 102 Ontario dairy herds. The individual-cow prevalence of BLV infection in the population (based on AGID testing) was 23%, with 69.6% of herds having one or more positive animals. The herd-level explanatory variables were divided into two datasets containing winter housing variables and all non-seasonal variables, and summer housing variables and all non-seasonal variables. In both datasets, multivariable analyses found a negative association between herd-level milk production and BLV status, and positive associations between weaning age and purchasing animals from outside sources, and BLV status. Housing pre-weaned calves in hutches or separate calf buildings in either season was associated with an increased risk of BLV. The model containing winter housing variables also included positive associations between contact with older animals and BLV status, and between BLV status and the facilities used to house dry cows in the winter.     

The reproductive performance of sows raised by smallholder farmers in the Philippines.

We conducted a cross-sectional study at two sites in the Philippines to obtain baseline information about the reproductive performance of smallholder sows, and to identify important constraints and opportunities for smallholder pig raisers. Using an interview-based questionnaire, we collected data about 99 (with 128 sows) and 123 (144) herds at the northern and southern study sites, respectively. A range of animal- and herd-level measures of sow productivity were assessed, including average interfarrowing interval (9.7 and 6.6 mo in herds at the northern and southern sites, respectively), number of liveborn piglets (8.5 and 8.4) and preweaning mortality (19.0% and 12.8%). We have identified a number of animal- and herd-level factors associated with the productivity of smallholder sows in the Philippines, including aspects of breeding and piglet management and nutrition.     

Cut-off points for aggreate herd testing in the presence of disease clustering and correlation of test errors

In order to test if disease is present in a large herd, an investigator will often subject only a small sample of animals to a fallible diagnostic test. The herd is declared positive for disease if the number of test-positive animals is greater than or equal to a previously chosen cut-off value. Such a test, called an aggregate test, has a sensitivity and specificity that depends on the sample size, the cut-off point and the sensitivity and specificity of the individual test. It also depends on the distribution of the disease among the herds being tested and on the fact that factors such as herd-level seropositivity may cause some herds to be more prone to testing errors than others. In this paper, we use the beta-binomial distribution to model all these factors and thereby calculate and tabulate aggregate test sensitivities and specificities under a variety of conditions. Receiver operating characteristic (ROC) curve methodology permits the choice of optimum sample sizes and cut-off values. We also investigate the situation in which an investigator may be willing to miss detecting the disease if the prevalence in the herd is low. A compiled FORTRAN program for the calculation of aggregate test cut-off point properties, including positive and negative predictive values, is available from the authors.     

Frequentist and Bayesian approaches to prevalence estimation using examples from Johne's disease

Although frequentist approaches to prevalence estimation are simple to apply, there are circumstances where it is difficult to satisfy assumptions of asymptotic normality and nonsensical point estimates (greater than 1 or less than 0) may result. This is particularly true when sample sizes are small, test prevalences are low and imperfect sensitivity and specificity of diagnostic tests need to be incorporated into calculations of true prevalence. Bayesian approaches offer several advantages including direct computation of range-respecting interval estimates (e.g. intervals between 0 and 1 for prevalence) without the requirement of transformations or large-sample approximations, direct probabilistic interpretation, and the flexibility to model in a straightforward manner the probability of zero prevalence. In this review, we present frequentist and Bayesian methods for animal- and herd-level true prevalence estimation based on individual and pooled samples. We provide statistical methods for detecting differences between population prevalence and frequentist methods for sample size and power calculations. All examples are motivated using Mycobacterium avium subspecies paratuberculosis infection and we provide WinBUGS code for all examples of Bayesian estimation.     

Aspects of bovine herpesvirus 1 and bovine viral diarrhoea virus herd-level seroprevalence and vaccination in dairy and beef herds in Northern Ireland

Background

Infections with bovine herpesvirus 1 (BoHV-1) and bovine viral diarrhoea (BVD) virus cause diseases of cattle with a worldwide distribution. The primary objective of the present study was to describe aspects of herd-level BoHV-1 and BVDV seroprevalence (based on testing of pooled sera) and control on farms in Northern Ireland, including vaccine usage.An indirect antibody ELISA test (SVANOVA, Biotech AB, Uppsala, Sweden) was applied to serum pools which were constructed from serum samples taken for a cross-sectional study of a convenience sample of 500 Northern Irish dairy and beef cow herds in 2010, for which vaccination status was determined by telephone survey. The herd-level seroprevalence of BoHV-1 and BVDV in Northern Ireland was estimated in non-vaccinating herds and associations between possible risk factors (herd type and herd size (quartiles)) and herd-level prevalence were determined using chi-squared analysis.

Results

The herd-level seroprevalence (of BoHV-1 and BVDV) in non-vaccinating herds was 77.3% (95% CI: 73.6–80.9%) and 98.4% (95% CI: 97.3–99.5%) respectively in the cross-sectional study. A significant difference existed in BoHV-1 herd-level seroprevalence between dairy and beef herds (74.7% vs 86.5% respectively; p < 0.02) though not for BVDV seroprevalence (98.5% vs 98.3% respectively; p > 0.91). A significant association was found between herd size (quartiles) and herd-level classification for BoHV-1 herd-level seroprevalence based on cut-off percentage positivity (COPP) (p < 0.01) while no such association was found for BVDV (p = 0.22).15.5% and 23.8% of farmers used BoHV-1 and BVDV vaccines, respectively. BoHV-1 vaccine was used in 30% of dairy herds and in 11% of beef herds, while BVDV vaccine was used in 46% and 16% of dairy and beef herds, respectively.

Conclusions

The results from this study indicate that the true herd-level seroprevalences to bovine herpesvirus 1 and bovine virus diarrhoea virus in non-vaccinating herds in Northern Northern Ireland are 77.3% (95% CI: 73.6–80.9%) and 98.4% (95% CI: 97.3–99.5%), respectively. The present study will assist in guiding regional policy development and establish a baseline against which the progress of current and future control and eradication programmes can be measured.     

Bovine viral diarrhoea virus seroprevalence and vaccination usage in dairy and beef herds in the Republic of Ireland

Background

Bovine viral diarrhoea (BVD) is an infectious disease of cattle with a worldwide distribution. Herd-level prevalence varies among European Union (EU) member states, and prevalence information facilitates decision-making and monitoring of progress in control and eradication programmes. The primary objective of the present study was to address significant knowledge gaps regarding herd BVD seroprevalence (based on pooled sera) and control on Irish farms, including vaccine usage.

Methods

Preliminary validation of an indirect BVD antibody ELISA test (Svanova, Biotech AB, Uppsala, Sweden) using pooled sera was a novel and important aspect of the present study. Serum pools were constructed from serum samples of known seropositivity and pools were analysed using the same test in laboratory replicates. The output from this indirect ELISA was expressed as a percentage positivity (PP) value. Results were used to guide selection of a proposed cut-off (PCO) PP. This indirect ELISA was applied to randomly constructed within-herd serum pools, in a cross-sectional study of a stratified random sample of 1,171 Irish dairy and beef cow herds in 2009, for which vaccination status was determined by telephone survey. The herd-level prevalence of BVD in Ireland (percentage positive herds) was estimated in non-vaccinating herds, where herds were classified positive when herd pool result exceeded PCO PP. Vaccinated herds were excluded because of the potential impact of vaccination on herd classification status. Comparison of herd-level classification was conducted in a subset of 111 non-vaccinating dairy herds using the same ELISA on bulk milk tank (BMT) samples. Associations between possible risk factors (herd size (quartiles)) and herd-level prevalence were determined using chi-squared analysis.

Results

Receiver Operating Characteristics Analysis of replicate results in the preliminary validation study yielded an optimal cut-off PP (Proposed Cut-off percentage positivity - PCO PP) of 7.58%. This PCO PP gave a relative sensitivity (Se) and specificity (Sp) of 98.57% and 100% respectively, relative to the use of the ELISA on individual sera, and was chosen as the optimal cut-off since it resulted in maximization of the prevalence independent Youden’s Index.The herd-level BVD prevalence in non-vaccinating herds was 98.7% (95% CI - 98.3-99.5%) in the cross-sectional study with no significant difference between dairy and beef herds (98.3% vs 98.8%, respectively, p = 0.595).An agreement of 95.4% was found on Kappa analysis of herd serological classification when bulk milk and serum pool results were compared in non-vaccinating herds. 19.2 percent of farmers used BVDV vaccine; 81% of vaccinated herds were dairy. A significant association was found between seroprevalence (quartiles) and herd size (quartiles) (p < 0.01), though no association was found between herd size (quartiles) and herd-level classification based on PCO (p = 0.548).

Conclusions

The results from this study indicate that the true herd-level seroprevalence to Bovine Virus Diarrhoea (BVD) virus in Ireland is approaching 100%. The results of the present study will assist with national policy development, particularly with respect to the national BVD eradication programme which commenced recently.     

Prevalence of paratuberculosis infection in dairy cattle in Northern Italy

Paratuberculosis is a chronic granulomatous infection caused by Mycobacterium avium subsp. paratuberculosis (MAP) that affects multiple ruminant species causing important economic losses. Therefore, control programmes at herd and regional levels have been established worldwide and prevalence estimates are needed for their implementation. Although different herd-level prevalence estimations for paratuberculosis have been reported in Europe, very few studies provided comparable and interpretable values, due to poor study designs and lack of knowledge about the accuracy of the diagnostic tests used. To overcome these problems we applied a latent class analysis to the results of two prevalence studies carried out in two neighbouring Northern Italian regions (Lombardy and Veneto) that account for over 50% of the Italian dairy cattle population. Serum samples from a randomly selected number of farms in the two regions were analyzed by different ELISA tests. The herd-level Apparent Prevalences (AP) were 48% (190/391) for Lombardy and 65% (272/419) for Veneto. Median within-herd APs were 2.6% and 4.0% for Lombardy and Veneto, respectively. Posterior estimates for the herd-level True Prevalences (TP) based on a Bayesian model were very similar between the two regions (70% for Lombardy and 71% for Veneto) and close to previous estimates of infected herds in Europe. The two 95% credibility intervals overlap each other, virtually showing only one distribution of the herd-level true prevalence for both regions. On the contrary, estimates of the within-herd TP distributions differed between the two regions (mean values: 6.7% for Lombardy and 14.3% for Veneto), possibly due to the different age distribution within the herds from the two regions.     

Evaluation of an iscom ELISA used for detection of antibodies to Neospora caninum in bulk milk

The intracellular parasite Neospora caninum is increasingly recognized as an important cause of abortion and stillbirth in cattle. Presence of specific antibodies indicates infection, and the immunostimulating complex (iscom) enzyme-linked immunoassay (ELISA) has previously been evaluated for use on individual milk and sera. In the present study, this test is investigated for use on bulk milk. In this study, 124 herds were used to analyse the relationship between within-herd prevalences based on individual sera and bulk milk optical densities. The individual test results were translated into a herd-level result, which enabled comparison of the bulk milk test result to the aggregate of individual serum results. The relative contribution of milk from cows with different milk yield and antibody status to the tank, i.e. its composition, was expected to influence the outcome of the bulk milk test. Therefore, sensitivity and specificity were calculated at different cut-off levels, not only using a standard cross-tabulation technique, but also a logistic regression model. By using the latter method, the sensitivity and specificity could be estimated adjusting for milk yield covariates. Specificity was estimated to be high ( approximately 98%) at the 0.20 cut-off, which can be used as a decision threshold to rule in infection. With more equal emphasis on sensitivity and specificity, a lower cut-off should be used. Although infection cannot be completely ruled out, herds with test results below 0.05 are highly likely to be non-infected. The within-herd prevalence of false negative herds is probably less than 10-15% at this level. From what is known about test performance at the individual level and the prevalence of infection, the estimate of the specificity of the bulk milk test should be quite accurate while the sensitivity is likely to be underestimated. We confirmed that the performance of the bulk milk test depends on the milk tank composition. In particular the milk yield of cows with high antibody levels affects the probability of a positive outcome of the bulk milk test.     

Novel insights into the pathogenic importance,diagnosis and treatment of the rumen fluke (Calicophoron daubneyi) in cattle

Recently, sharp increases in the prevalence of rumen fluke infections have been recorded throughout Western Europe. However, scarce information is available on the diagnosis, pathogenic importance and control of this parasite. We undertook 3 pilot studies to gain more insights into these aspects of rumen fluke biology in cattle. First, we evaluated the diagnostic performance of mini-FLOTAC to detect adult rumen fluke infections based on faecal egg count in an abattoir survey and found high sensitivity (0.94) and specificity (0.98). Moreover, there was an association between ruminal fluke burden (assessed by visual scoring) and faecal egg count and a cut-off of 200 eggs per gram is proposed to detect highly infected animals (>200 flukes present in the rumen and/or reticulum). There was also a significant association between ruminal fluke burden and faecal consistency. However, in a second study, we performed a case-control field survey to investigate the association between rumen fluke infection and herd-level problems with diarrhoea and no association was found. Finally, we evaluated the use of closantel (Flukiver^®, Elanco Animal Health, subcutaneous administration at 10 mg/kg) to treat rumen fluke infection on 3 herds, but no significant reduction in egg output post-treatment was found. Because this result is in contrast with a previous study using an oral dose of closantel, more research is required into the effect of administration route on the efficacy of closantel on rumen fluke.     

Prevalence estimates for paratuberculosis adjusted for test variability using Bayesian analysis

The ELISA tests that are available to detect an infection with Mycobacterium avium subsp. paratuberculosis (MAP) have a limited validity expressed as the sensitivity (Se) and specificity (Sp). In many studies, the Se and Sp of the tests are treated as constants and this will result in an underestimation of the variability of the true prevalence (TP). Bayesian inference provided a natural framework for using information on the test variability (i.e., the uncertainty) in the estimates of test Se and Sp when estimating the TP.

Data from two prevalence studies for MAP using an ELISA in several regions in two locations were available for the analyses. In location 1, all cattle of at least 3 years of age were sampled in approximately 90 randomly sampled herds in each of the four regions of the country. In location 2, in 30 randomly sampled herds in each of three regions, approximately 30 randomly selected cows were sampled. Information about the unknown test Se and Sp and MAP prevalence was incorporated into a Bayesian model by joint prior probability distributions. Posterior estimates were obtained by combining the actual likelihood with the prior distributions using Bayes’ formula.

The corrected cow-level TP (proportion of infected cows in a herd) was low, 5.8 and 3.6% in locations 1 and 2, respectively. Certain regions within a location differed significantly in herd-level TP (proportion of infected herds). The herd-level TP was 54.3% in location 1 (95% credible interval (CI) 46.1, 63.3%) and 32.9% in location 2 (95% CI: 14.4, 73.3%). The variation in the herd-level TP estimate for location 2 was more than three times as large as the variation in location 1 mainly because of the relatively small number of investigated herds in location 2. In future prevalence studies for MAP, sample size calculations should be based on a very low cow-level prevalence. Approximately 50 and 90% of the herds in the current study had an estimated cow-level TP below 4 and 10%, respectively.