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

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. 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.