https://orcid.org/0009-0005-4701-0569
Figures
Abstract
Background
In endemic dairy systems, the interpretation of serological tests for bovine brucellosis is compromised using fixed diagnostic cut-offs, which fail to account for continuous antibody distributions and population heterogeneity. This study aimed to apply a Bayesian hierarchical Gaussian mixture model (BHGMM) to resolve diagnostic uncertainty by deriving probabilistic, biologically informed thresholds for indirect ELISA (iELISA).
Methods
A cross-sectional dataset comprising 2,696 milk samples from large-scale dairy herds was analysed. Log-transformed and standardised antibody values were modelled using a three-component hierarchical mixture representing healthy, latent, and diseased populations. Posterior class distributions, herd-specific cut-offs, and prevalence were estimated, and model performance was evaluated using convergence diagnostics, posterior predictive checks, and ROC analysis.
Results
Three distinct serological populations were identified. Mean antibody levels (S/P%) were 5.29 in healthy, 17.07 in latent, and 299.84 in diseased animals. Dual diagnostic thresholds were estimated at 10.7 S/P% and 82.2 S/P%. Estimated class proportions were 23.5% healthy, 43.6% latent, and 32.9% diseased. Substantial between-herd heterogeneity was observed, with confirmatory cut-offs ranging from approximately 68–133 S/P% and herd-level true prevalence varying from about 1% to 67%. The model demonstrated high diagnostic accuracy (AUC = 84.5%) and stability across prior specifications.
Citation: Alam MS, Islam MN, Adhikari BJ, Islam S, Mahmud Hasan R, Rahman MS, et al. (2026) Bayesian hierarchical mixture modelling to derive probabilistic iELISA thresholds for bovine brucellosis in endemic dairy systems. PLoS One 21(7): e0347719. https://doi.org/10.1371/journal.pone.0347719
Editor: Saurabh Gupta, GLA University, INDIA
Received: April 2, 2026; Accepted: July 14, 2026; Published: July 30, 2026
Copyright: © 2026 Alam et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The datasets, model code, and analysis scripts supporting the conclusions of this article are available as Supplementary Material.
Funding: This research was funded by the Livestock and Dairy Development Project (LDDP), grant number RP-C-01-10. The funder had no role in study design, data collection, analysis, interpretation of the results, manuscript preparation, or the decision to submit the work for publication.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Bovine brucellosis, caused primarily by Brucella abortus, remains a major zoonosis and a leading cause of reproductive failure in cattle worldwide. In endemic regions, the disease imposes a substantial economic burden on the dairy industry through abortion, infertility, and reduced milk yield, while simultaneously posing a serious public health threat to farmers, veterinary personnel, and consumers of unpasteurized dairy products [1–5]. The intensification of dairy sectors in these regions—characterized by high stocking densities and increased animal movement—creates favorable environments for the persistence and rapid transmission of Brucella spp [6]. Despite this, control programs in many endemic countries often lack strategic policies such as mass vaccination or systematic test-and-cull programs, leaving the growing commercial sector vulnerable.
Accurate diagnosis is central to effective control, particularly in intensive systems. The indirect enzyme-linked immunosorbent assay (iELISA) is commonly used for large-scale screening due to its high throughput and objectivity. However, standard interpretation typically applies a single manufacturer-recommended cut-off (e.g., S/P% 50%) to dichotomize results into positive or negative. This binary classification neglects the continuous and biologically complex nature of antibody responses. In endemic settings, many animals occupy a “gray zone” of intermediate antibody levels—representing latent or subclinical infections—that may fall below fixed positivity thresholds yet still contribute to transmission. Conversely, rigid cut-offs can lead to the unnecessary culling of productive animals due to false positives. While standard ELISA protocols often include a ‘doubtful’ category to reflect uncertainty near the cut-off, traditional epidemiological analyses frequently collapse this data into binary outcomes, discarding valuable nuance [7].
To address these limitations, statistical methods that treat serological outcomes as continuous distributions offer a superior fit to biological reality. Finite mixture models allow continuous serological measurements to be decomposed into latent biological subpopulations without requiring a perfect reference test. Embedding these models within a Bayesian hierarchical framework further enables estimation of herd-specific parameters while accounting for between-herd variability [8,9]. This approach is particularly relevant for large commercial herds in endemic areas, where infection pressure and background immunity differ substantially from settings where standard cut-offs were originally validated [10,11].
This study applied a Bayesian hierarchical Gaussian mixture modelling framework to: (1) identify serological subpopulations corresponding to healthy, latent, and diseased states; (2) derive herd-specific diagnostic thresholds; and (3) estimate true prevalence at both the animal and herd levels under diagnostic uncertainty.
Materials and methods
Study design, target and study population
A cross-sectional study was conducted between January 2023 and December 2024. The target population consisted of dairy cattle within large-scale farming systems. The study population included a selection of institutional and private commercial dairy herds. None of the sampled herds practiced brucellosis vaccination, consistent with the national situation in Bangladesh, where systematic mass vaccination with strain 19 (S19) or RB51 vaccines is not implemented and is generally restricted at the national level. Consequently, the antibody (S/P%) distributions analyzed here reflect natural infection kinetics rather than vaccine-induced seroreactivity, allowing the intermediate (latent) subpopulation to be interpreted as genuinely infected animals rather than vaccine responders.
Ethics statement
This study involved sampling of dairy cattle and did not include human participants. All procedures were conducted in accordance with internationally accepted standards for the ethical use of animals in research and with reporting guidelines for diagnostic accuracy studies using Bayesian latent class models (STARD-BLCM). Ethical approval was obtained from the Animal Welfare and Experimentation Ethical Committee of Bangladesh Agricultural University (approval no. AWEEC/BAU/2022/07).
Sample size calculation and sampling protocol
Sample size calculations were performed using a one-stage cluster sampling approach via the ‘epi.ssclus1estb’ function in the epiR package [12] for R statistical environment (v4.5.1) [13]. The calculations were based on an expected true prevalence () of 20.4% [14] and a desired absolute precision (
) of 5% with 95% confidence. To account for the clustering effect of animals within herds, an intra-cluster correlation coefficient (
) of 0.09 [15] was applied. Assuming 100 animals per herd, the analysis initially indicated that 25 herds (totaling 2,473 animals) would be required to achieve the desired precision. In practice, however, the participating commercial herds were larger than expected. As a result, the target sample size at the animal level was not only met but exceeded, with 2,696 milk samples collected from 17 herds. This higher density of observations per herd provides robust data for characterizing the continuous serological distributions and ensures that the study remains adequately powered for the hierarchical mixture model, despite having fewer herds than originally planned [10].
Sample collection and iELISA testing
A total of 2,696 individual milk samples were collected from lactating cows across all participating herds. Samples were aseptically collected and stored at –20 °C until analysis. Antibodies against Brucella spp. were quantified using a commercially available antibody indirect ELISA (iELISA) assay (ID Screen® Brucellosis Indirect ELISA kit, Innovative Diagnostics, Grabels, France). Milk samples were centrifuged to separate lactoserum. The assay was performed according to manufacturer instructions. The results were interpreted by calculating the S/P% for each sample; samples with an S/P% less than or equal to 45% were classified as negative, those between 45% and 50% as doubtful, and those greater than 50% as positive [16].
Diagnostic and analytical workflow
To improve transparency and accessibility for non-specialist readers, the end-to-end diagnostic and analytical pipeline is summarized below as a step-by-step workflow in Fig 1.
The BHGMM framework was chosen over fixed binary cut-offs because a single manufacturer threshold forces a continuous, biologically graded antibody response into two artificial categories, discarding the intermediate “gray-zone” signal and ignoring the substantial differences in infection pressure between herds. By instead modelling the S/P% distribution as a mixture of three latent subpopulations with herd-specific random effects, the framework recovers the healthy, latent, and diseased components directly from the data, derives dual probabilistic thresholds adapted to each herd, and propagates diagnostic uncertainty into every estimate—none of which is achievable with a fixed cut-off.
Data processing and transformation
To address the positive skewness typical of serological data and to facilitate model convergence, the raw S/P ratio (SP%) values were log-transformed. A small constant c was added prior to transformation to handle zero or negative values, defined as
The transformed variable was defined as:
where represents the serological value for animal i in herd j.
To place observations on a common scale and improve Markov Chain Monte Carlo (MCMC) mixing, these log-transformed values were standardized to have a mean of 0 and a standard deviation of 1:
Where and
denote the sample mean and standard deviation of the log-transformed SP% values, respectively. All subsequent Bayesian analyses were conducted on the standardized variable
.
Exploratory component selection
Prior to fitting the Bayesian model, the number of underlying biological populations was assessed using an unsupervised Gaussian Mixture Model (GMM) via the Expectation-Maximization algorithm (mclust package in R). Models ranging from 1 to 9 components were compared, with the optimal number selected based on the Bayesian Information Criterion (BIC). This analysis provided empirical evidence for a three-population structure:
- Healthy (low titers)
- Latent (intermediate titers)
- Diseased (high titers)
Bayesian Hierarchical Gaussian Mixture Model (BHGMM)
Likelihood specification.
The likelihood of the observed standardized value or animal i in herd j is defined as a mixture of three density components [7]:
Where:
is the herd-specific prevalence (mixing proportion) of component k in herd j.
represents the probability density function for populationk k, defined as follows:
- Healthy (
) and Latent (
) populations: Modeled as Normal distributions:
- Healthy (
- Diseased Population
: To account for heavy tails and high-titer outliers, the density for the diseased population is modeled using a Student-t distribution with 4 degrees of freedom [10]:
Ordered population means and non-centered parameterization.
To enforce biological consistency (Healthy < Latent < Diseased), we applied an ordering constraint using positive offset parameters (δ):
To account for the hierarchical clustering of animals within herds and to improve the efficiency of MCMC sampling, we applied a non-centered parameterization for the herd-specific means. This is mathematically expressed as: :
Where: is the estimated mean antibody level for component k in herd j.
represents the global, population-level mean for component k.
is the between-herd standard deviation, quantifying the expected heterogeneity in mean antibody levels across herds for component k.
represents the latent herd-effect offset for herd j, drawn from a standard normal distribution with a mean of 0 and a variance of 1.
Herd-specific parameters and cutoff determination.
Herd-specific prevalence estimation: The distribution of animals across the three classes within each herd was modeled using a Dirichlet prior:
This allows the model to estimate herd-specific prevalence while sharing information across the entire population (shrinkage estimation).
Localized cutoff logic: Rather than a single global cutoff, our model allows for herd-specific thresholds. The cutoff between class k and class for herd j is the point C where the weighted densities intersect [8]:
This ensures that the diagnostic threshold adapts to the specific disease pressure and titer distribution of the local environment.
Model implementation and convergence diagnostics: We implemented the model in Stan [17] using the ‘cmdstanr’ interface [18] within the R statistical environment (v4.5.1) [13]. Posterior samples were drawn using the No-U-Turn Sampler (NUTS) across four parallel chains, each consisting of 2,000 warmup and 6,000 sampling iterations (totaling 24,000 post-warmup samples). Convergence was assessed through visual inspection of trace plots to confirm stationarity and mixing. Additionally, we monitored Effective Sample Size (ESS) to ensure sufficient posterior exploration, requiring both Bulk-ESS and Tail-ESS to exceed 400. All parameters met current best practices for MCMC convergence, with a potential scale reduction factor R-hat maintained below 1.01 [19].
Performance evaluation: Posterior predictive checks (PPC). The model’s generative fit was validated by simulating replicated datasets () from the posterior predictive distribution [10]:
The observed Log-SP% distribution was compared against the 95% credible intervals of the replicated data to ensure the model accurately captured the data structure.
Diagnostic accuracy (AUC). Diagnostic accuracy was evaluated empirically to quantify the separability of the three identified subpopulations. Pairwise Area Under the Curve (AUC) values were calculated for three distinct comparisons: Healthy () versus Subclinical (
), Subclinical (
) versus Diseased (
), and Healthy (
) versus Diseased (
). Because the diseased component was modeled using a heavy-tailed Student-t distribution, closed-form analytical calculation of the AUC is intractable; therefore, accuracy was estimated computationally. Using the posterior predictive distributions, random draws from the estimated densities of each class pair were compared across all possible classification thresholds to compute the empirical AUC. This pairwise evaluation was implemented via the pROC package in R [20].
Prior specification and sensitivity analysis
Data standardization and parameterization.
Standardization is standard practice in hierarchical mixture modeling to improve the geometry of the posterior distribution, thereby increasing the efficiency of the MCMC sampling [10]. To resolve the “label switching” non-identifiability problem inherent in finite mixture models, we imposed an ordering constraint on the component means (Healthy < Latent < Diseased) by defining the means of the Latent and Diseased classes as positive offsets () from the preceding class.
Prior selection.
The manufacturer’s interpretation for iELISA defines distinct zones (Negative 45%, Doubtful 45–50%, Positive > 50%), implying a biologically plausible separation between the antibody distributions of healthy and infected populations [21]. Consistent with this biological knowledge and statistical guidance for regularization, the separation parameter (δ) was assigned a weakly informative Normal prior centered on moderate class separation (μ = 0.6, σ = 0.3). Variance parameters were assigned bounded Half-Normal hyperpriors, and class prevalences were modeled using a Dirichlet distribution.
Sensitivity analysis.
To ensure that our results were driven by the data rather than subjective prior choices, we performed a global sensitivity analysis comparing three distinct prior scenarios [22]. The Primary Model utilized the priors described above, including a Dirichlet concentration parameter of to favor non-zero prevalence across all classes. This was contrasted with a Weakly Informative Scenario, which employed broad, flat priors (e.g.,
for means) and a uniform Dirichlet prior (
) to minimize the influence of regularization. Finally, we evaluated a Strong Informative Scenario characterized by highly concentrated priors (small
) for the separation parameter (
) to test model stability under restrictive assumptions. We monitored the stability of the posterior distributions for prevalence and the Area Under the Curve (AUC) across these scenarios. Consistency in estimates across these diverse prior specifications was interpreted as evidence that the likelihood (the data) dominated the statistical inference. All data, model, code and diagnostic plots are provided in Supplementary Materials S1–S4 Files.
Results
Descriptive statistics
The age of the sampled cows ranged from 2.4 to 17.5 years, with a mean age of 6.33 years and a median of 6.0 years. The interquartile range (IQR) spanned from 4.0 to 8.0 years. The breed composition of the study population (N = 2,696) was predominantly Local x Friesian, comprising 2,436 animals (90.4%). The remaining herds consisted of Local x Sahiwal (n = 150; 5.6%) and Local x Jersey (n = 110; 4.1%).
Exploratory analysis and model convergence
Unsupervised Gaussian mixture modelling using the Bayesian Information Criterion supported a three-component solution. The components corresponded to distributions consistent with Healthy, Latent, and Diseased subpopulations. The hierarchical Bayesian model achieved convergence across all monitored parameters, with potential scale reduction factors and effective sample sizes exceeding 1000.
Diagnostic performance and model validation
The estimated population-level area under the receiver operating characteristic curve was 84.5% (95% credible interval: 79.9–88.6) (Table 1; Fig 2). Posterior predictive checks showed that the observed log-transformed S/P% distribution lay within the 95% credible intervals of replicated datasets generated from the posterior distribution (Fig 3).
The curve demonstrates the trade-off between sensitivity and specificity for distinguishing healthy, latent, and diseased animals, with the area under the curve (AUC) quantifying overall model accuracy.
The estimated lower cutoff separating Healthy from Latent animals was 10.64 S/P% (95% CrI: 8.82–12.71), and the upper cutoff separating Latent from Diseased animals was 82.00 S/P% (95% CrI: 67.76–102.16).
A dual-cutoff classification framework was estimated. At the lower cutoff (C1), specificity for identifying healthy animals was 98.12% (95% CrI: 86.30–100.00). At the upper cutoff (C2), sensitivity for identifying diseased animals was 95.10% (95% CrI: 92.70–97.10) (Table 1). Within the intermediate range (C1 < test value < C2), 62.00% of latent animals were classified in the gray zone (95% CrI: 58.00–65.50). Posterior estimates of AUC and component means were similar across informative, weakly informative, and vague prior specifications (Table 2).
Population-level parameter estimates
Posterior component means on the original S/P% scale differed across the three classes (Table 3). The mean S/P% was 5.21 (95% CrI: 2.71–8.31) for the Healthy class, 17.04 (95% CrI: 14.63–19.56) for the Latent class, and 299.47 (95% CrI: 262.81–344.08) for the Diseased class. Estimated weighted class prevalences were 23.47% (95% CrI: 21.7–25.3) for Healthy, 43.61% (95% CrI: 41.2–46.0) for Latent, and 32.91% (95% CrI: 30.7–35.1) for Diseased animals (Table 4).
Herd-specific analysis
Herd-level variation was observed in confirmatory cutoff estimates and true milk antibody prevalence.
Herd-specific upper cutoffs (C2) ranged from 67.62 in Herd 1 to 132.76 in Herd 3 (Fig 4; Table 5). Estimated true milk antibody prevalence also varied across herds, from 1.05% (95% CrI: 0.13–2.86) in Herd 14 to 67.12% (95% CrI: 62.49–71.62) in Herd 17 (Fig 5; Table 6).
Points represent posterior mean cutoffs for each herd, and the horizontal dashed line indicates the overall population-level cutoff (82.00 S/P%).
Each point represents the posterior mean prevalence for a herd, with 95% credible intervals reflecting uncertainty in the estimates.
Discussion
This study demonstrates the utility of Bayesian hierarchical mixture modelling for characterizing heterogeneous serological responses to bovine brucellosis in intensive dairy herds. By deriving probabilistic diagnostic thresholds, this approach overcomes the limitations of conventional fixed cut-offs, which often fail in endemic settings.
A key finding was the identification of a substantial “latent” subpopulation, comprising approximately 44% of sampled animals. These individuals exhibited antibody titres elevated above the healthy baseline yet lower than the diseased cluster. This pattern aligns with the intracellular pathogenesis of Brucella abortus, where persistence within macrophages drives fluctuating humoral responses and prolonged subclinical infection phases [23,24]. In traditional binary testing, these intermediate animals are forced into a dichotomous classification, resulting in “false negatives” that sustain transmission or “false positives” that cause economic waste [25].
The high proportion of animals in non-negative categories (Latent + Diseased) suggests a state of “endemic stability” [26]. In high-transmission environments, constant re-exposure likely acts as a natural booster, maintaining high antibody prevalence with muted clinical signs. However, the identification of this latent class challenges the assumption that low or borderline titers represent merely “background noise.” Animals in this “grey zone” may harbor persistent infections, acting as cryptic reservoirs that shed bacteria and could contribute to public health risks [27,28]. The BHGMM’s dual-cutoff framework is therefore an epidemiological necessity, identifying silent carriers that standard binary approaches overlook [29].
Methodologically, the model demonstrated high diagnostic discrimination. The use of a Student-t distribution for the diseased component was critical to accommodate biological outliers without distorting estimates [8,10,11,30]. Furthermore, sensitivity analyses confirmed that classification was driven by observed data rather than prior specifications, satisfying key criteria for robust Bayesian inference [31].
A major strength of the hierarchical framework was its ability to quantify herd-level heterogeneity. Confirmatory cut-offs varied substantially between herds, proving that universal thresholds generate systematic misclassification in endemic settings [21]. This variability supports the move toward risk-based surveillance strategies tailored to specific herd epidemiology [32].
These findings have direct implications for brucellosis control globally. First, binary serological interpretation weakens control programs by allowing subclinically infected animals to evade detection [23]. Second, the heterogeneity in herd-specific thresholds supports international recommendations to adapt decision thresholds to the local context [33]. Finally, the large latent population suggests that testing alone is insufficient; effective control requires integrated programs combining vaccination, movement control, and strategic testing [34,35]. From a One Health perspective, detecting subclinical infection is critical to reducing zoonotic transmission [36]. Incorporating Bayesian modelling into routine surveillance is a practical step toward aligning analytics with the complex ecological reality of zoonotic disease [37].
An important next step is the external validation of the BHGMM framework beyond the present setting. Because the model derives herd-specific, probabilistic thresholds rather than a single fixed cut-off, its parameters should be re-estimated and validated in independent populations that differ in infection pressure, breed composition, and husbandry—for example, other South Asian and endemic dairy systems where brucellosis epidemiology and background seroreactivity may diverge from intensive Bangladeshi herds. Such multi-region validation would establish the transportability of the dual-cutoff structure and clarify how much of the between-herd heterogeneity is generalizable rather than context-specific. Methodologically, the BHGMM should also be benchmarked against established alternatives, including conventional latent class analysis (LCA) that dichotomizes results against an imperfect reference test, multi-test Bayesian latent class models, and traditional fixed manufacturer cut-offs. Unlike binary latent class approaches, the mixture formulation preserves the continuous antibody signal and explicitly recovers the intermediate (latent) component, while comparison against fixed cut-offs allows the operational gains in sensitivity and specificity to be quantified directly. Prospective head-to-head evaluation against these methods, ideally with partial bacteriological or molecular confirmation, would further strengthen confidence in the derived thresholds.
The pronounced between-herd variation in true prevalence (from approximately 1% to 67%) and in confirmatory cut-offs points to farm-level factors shaping the continuous antibody distribution. Herd size, stocking density, introduction and movement of replacement animals, biosecurity, calving and abortion management, and trade practices are plausible determinants of within-herd transmission intensity; greater infection pressure shifts the mixture weights toward the latent and diseased components and raises herd-specific thresholds. Within the hierarchical structure, these farm-level influences are absorbed by the herd random effects, so that herds with intensive trade and weak biosecurity express higher latent and diseased proportions and right-shifted S/P% distributions, whereas closed, lower-density herds concentrate near the healthy mode. Explicitly incorporating such covariates as herd-level predictors of the mixing proportions in future models would allow the framework to move from describing heterogeneity to explaining it, linking the probabilistic thresholds to actionable, risk-based management at the farm level.
Several limitations should be noted. Serological results were analyzed without concurrent bacteriological confirmation. The cross-sectional design precludes tracking temporal progression between states. In particular, paired milk samples collected 21 days apart were not tested; such repeated sampling, which could capture short-term fluctuations in antibody titers, was logistically and financially unfeasible across the 2,696 samples in this field-based study. Importantly, the BHGMM is designed to accommodate this constraint: by modelling the full continuous antibody distribution as a mixture of latent subpopulations, it characterizes population heterogeneity and diagnostic uncertainty from a single cross-sectional measurement, without requiring longitudinal re-testing of individual animals. While the study focused on intensive herds, the methodological framework is applicable to other production systems.
Conclusion
Bayesian hierarchical mixture modelling of iELISA data revealed substantial serological heterogeneity and a large intermediate antibody population that is obscured by fixed cut-offs. The identification of herd-specific diagnostic thresholds provides a robust framework for improving surveillance accuracy. Probabilistic, herd-adapted diagnostic frameworks are recommended to support targeted brucellosis control within integrated One-Health programs in endemic regions.
Supporting information
S1 File. Raw dataset containing iELISA S/P values and herd ID used for the Bayesian Hierarchical Gaussian Mixture Model analysis.
https://doi.org/10.1371/journal.pone.0347719.s001
(CSV)
S2 File. Stan code for the Bayesian Hierarchical Gaussian Mixture Model (BHGMM) including likelihood definitions, priors, and non-centered parameterizations.
https://doi.org/10.1371/journal.pone.0347719.s002
(DOC)
S3 File. R script for data preprocessing, model execution via ‘cmdstanr’, and posterior predictive checks.
https://doi.org/10.1371/journal.pone.0347719.s003
(DOC)
S4 File. Trace, autocorrelation, and posterior predictive check plots for model evaluation.
https://doi.org/10.1371/journal.pone.0347719.s004
(DOC)
Acknowledgments
We are grateful to the farmers for dedicating their time and providing samples from their animals.
References
- 1. Rasmussen P, Barkema HW, Osei PP, Taylor J, Shaw AP, Conrady B, et al. Global losses due to dairy cattle diseases: a comorbidity-adjusted economic analysis. J Dairy Sci. 2024;107(9):6945–70. pmid:38788837
- 2. Pal M, Gizaw F, Fekadu G, Alemayehu G, Kandi V. Public health and economic importance of bovine brucellosis: an overview. AJEID. 2017;5:27–34.
- 3. Mitiku W, Desa G. Review of bovine brucellosis and its public health significance. HR. 2020;1(2):16–33.
- 4. Khurana SK, Sehrawat A, Tiwari R, Prasad M, Gulati B, Shabbir MZ, et al. Bovine brucellosis - a comprehensive review. Vet Q. 2021;41(1):61–88. pmid:33353489
- 5. Santos RL, Martins TM, Borges ÁM, Paixão TA. Economic losses due to bovine brucellosis in Brazil. Pesq Vet Bras. 2013;33:759–64.
- 6. Samad MA. A six-decade review: Research on cattle production, management and dairy products in Bangladesh. JVMOHR. 2020;2.
- 7. Yang DA, Xiao X, Jiang P, Pfeiffer DU, Laven RA. Keeping continuous diagnostic data continuous: application of Bayesian latent class models in veterinary research. Prev Vet Med. 2022;201:105596. pmid:35220040
- 8. McLachlan GJ, Lee SX, Rathnayake SI. Finite mixture models. Annu Rev Stat Appl. 2019;6:355–78.
- 9. Mathevon Y, Foucras G, Falguières R, Corbiere F. Estimation of the sensitivity and specificity of two serum ELISAs and one fecal qPCR for diagnosis of paratuberculosis in sub-clinically infected young-adult French sheep using latent class Bayesian modeling. BMC Vet Res. 2017;13(1):230. pmid:28774299
- 10.
Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis. 3 ed. CRC Press; 2013.
- 11. Branscum AJ, Gardner IA, Johnson WO. Bayesian modeling of animal- and herd-level prevalences. Prev Vet Med. 2004;66(1–4):101–12. pmid:15579338
- 12.
Stevenson M, Nunes T, Heuer C, Marshall J, Sanchez J, Thornton R. epiR: tools for the analysis of epidemiological data. R package version. Vol 2. 2018. pp. 26.
- 13.
R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2025. http://wwwR-projectorg/
- 14. Rahman AKMA, Smit S, Devleesschauwer B, Kostoulas P, Abatih E, Saegerman C, et al. Bayesian evaluation of three serological tests for the diagnosis of bovine brucellosis in Bangladesh. Epidemiol Infect. 2019;147:e73. pmid:30869026
- 15. Otte M, Gumm I. Intra-cluster. Prev Vet Med. 1997;3:147–50.
- 16. Gall D, Nielsen K. Serological diagnosis of bovine brucellosis: a review of test performance and cost comparison. Rev Sci Tech. 2004;23(3):989–1002. pmid:15861895
- 17. Carpenter B, Gelman A, Hoffman MD, Lee D, Goodrich B, Betancourt M, et al. Stan: a probabilistic programming language. J Stat Softw. 2017;76:1. pmid:36568334
- 18.
Gabry J. cmdstanr: R Interface to’CmdStan’. 2021.
- 19. Vehtari A, Gelman A, Simpson D, Carpenter B, Bürkner P-C. Rank-normalization, folding, and localization: an improved Rˆ for assessing convergence of MCMC (with discussion). Bayesian Anal. 2021;16(2).
- 20.
Robin X, Turck N, Hainard A, Tiberti N, Lisacek F, Sanchez JC, et al. Package ‘pROC’. 2021.
- 21. World Organisation for Animal Health. Principles and methods of validation of diagnostic assays for infectious diseases. Paris. 2024. Available from: https://www.woah.org/en/what-we-do/standards/codes-and-manuals/terrestrial-manual-online-access/
- 22. Berkvens D, Speybroeck N, Praet N, Adel A, Lesaffre E. Estimating disease prevalence in a Bayesian framework using probabilistic constraints. Epidemiology. 2006;17(2):145–53. pmid:16477254
- 23. Godfroid J, Scholz HC, Barbier T, Nicolas C, Wattiau P, Fretin D, et al. Brucellosis at the animal/ecosystem/human interface at the beginning of the 21st century. Prev Vet Med. 2011;102(2):118–31. pmid:21571380
- 24. Nielsen K. Diagnosis of brucellosis by serology. Vet Microbiol. 2002;90(1–4):447–59. pmid:12414164
- 25. Greiner M, Sohr D, Göbel P. A modified ROC analysis for the selection of cut-off values and the definition of intermediate results of serodiagnostic tests. J Immunol Methods. 1995;185(1):123–32. pmid:7665894
- 26. Coleman PG, Perry BD, Woolhouse ME. Endemic stability--a veterinary idea applied to human public health. Lancet. 2001;357(9264):1284–6. pmid:11418173
- 27. Islam MS, Islam MA, Khatun MM, Saha S, Basir MS, Hasan M-M. Molecular detection of Brucella spp. from milk of seronegative cows from some selected area in Bangladesh. J Pathog. 2018;2018:9378976. pmid:29568653
- 28. Gwida M, El-Ashker M, Melzer F, El-Diasty M, El-Beskawy M, Neubauer H. Use of serology and real time PCR to control an outbreak of bovine brucellosis at a dairy cattle farm in the Nile Delta region, Egypt. Ir Vet J. 2016;69:3. pmid:26913182
- 29. Ozsvari L, Harnos A, Lang Z, Monostori A, Strain S, Fodor I. The impact of paratuberculosis on milk production, fertility, and culling in large commercial hungarian dairy herds. Front Vet Sci. 2020;7:565324. pmid:33195541
- 30.
Bonfini B, Chiarenza G, Paci V, Sacchini F, Salini R, Vesco G, et al. Cross-reactivity in serological tests for brucellosis: a comparison of immune response of Escherichia coli O157: H7 and Yersinia enterocolitica O: 9 vs Brucella spp. 2018.
- 31. Hamra G, MacLehose R, Richardson D. Markov chain Monte Carlo: an introduction for epidemiologists. Int J Epidemiol. 2013;42(2):627–34. pmid:23569196
- 32. Stärk KD, Regula G, Hernandez J, Knopf L, Fuchs K, Morris RS. Concepts for risk-based surveillance in the field of veterinary medicine and veterinary public health: Review of current approaches. Vet Res. 2007;38(1):1–12.
- 33. Ghanbari MK, Gorji HA, Behzadifar M, Sanee N, Mehedi N, Bragazzi NL. One health approach to tackle brucellosis: a systematic review. Trop Med Health. 2020;48:86. pmid:33093792
- 34. Abd El-Wahab EW. A scoping review of the national strategy for brucellosis control in Egypt: logic framework, challenges, and prospects. One Health Outlook. 2025;7(1):42. pmid:40931356
- 35. Al Hamada A, Bruce M, Barnes A, Habib I, D Robertson I. Cost-benefit analysis of a mass vaccination strategy to control brucellosis in sheep and goats in Northern Iraq. Vaccines (Basel). 2021;9(8):878. pmid:34452003
- 36. McDermott J, Grace D, Zinsstag J. Economics of brucellosis impact and control in low-income countries. Rev Sci Tech. 2013;32(1):249–61. pmid:23837382
- 37. Zhou K, Wu B, Pan H, Paudyal N, Jiang J, Zhang L, et al. ONE health approach to address zoonotic brucellosis: a spatiotemporal associations study between animals and humans. Front Vet Sci. 2020;7:521. pmid:32984409