Bayesian hierarchical mixture modelling to derive probabilistic iELISA thresholds for bovine brucellosis in endemic dairy systems

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. Conclusions: Bayesian modelling captures intermediate serological “gray zones” and herd-level variability overlooked by standard binary interpretations. This probabilistic approach supports targeted control strategies in complex endemic environments.