Bayesian Modeling of Bovine Tuberculosis Prevalence for Enhanced Estimation and Control in Intensive Dairy Farms: A...

Accurate prevalence estimation is crucial for effective bovine tuberculosis (bTB) control, as unreliable data often gives rise to strategic failures, misallocation of resources, and loss of stakeholder trust. In an epidemiological study, obtaining true prevalence (Tp) requires accounting for misclassification and measurement errors inherent in diagnostic testing. Given the imperfect specificity and sensitivity of single intradermal comparative tuberculin tests (SICCTT), Bayesian methods present a natural way to propagate these uncertainties. This study uses a Bayesian approach to improve bTB prevalence estimates from imperfect diagnostic tests. It transforms raw screening data from a dairy farm case study into reliable evidence for better veterinary decisions and targeted disease control policies. Prior sensitivity estimates of SICCTT under standard and severe interpretations were 70.0% (BPI: 52.0%-84.6%) and 78.68% (BPI: 62.1%-90.5%), with corresponding specificities of 96.4% (BPI: 92.2%-98.8%) and 94.7% (BPI: 91.4%-97.1%). Posterior estimates showed a slight reduction in sensitivity under standard interpretation (68.3%, BPI: 50.4-83.7), while other estimates remained comparable to prior distributions. Bayesian modeling revealed notable variation in Tp across testing rounds. Rounds 1 and 3 had the highest prevalence, 27.6% (BPI: 18.5-40.6) and 30.9% (BPI: 23.3-47.5) under standard interpretation, respectively. In contrast, test round 4 yielded the lowest prevalence estimate at 4.1% (BPI: 0.6-8.6). The posterior probability of Tp being below 1%, the threshold for herd freedom from M. bovis infection, was 0% for the first three test rounds, but increased to 5.8% in test round 4. Comparative analysis of estimation methods showed that Bayesian estimators with informative priors produced slightly higher point estimates for Tp than the Rogan-Gladen estimator and Bayesian models with uninformative priors, except in test round 3. However, Bayesian estimation with informative priors exhibited wider credible intervals and strong coverage, reflecting the added uncertainty from not fixing test sensitivity and specificity. Convergence diagnostics, including trace plots, autocorrelation function (ACF) plots, and Gelman-Rubin statistics, confirmed adequate mixing and stationarity of the Markov chains, indicating satisfactory performance of the Markov Chain Monte Carlo (MCMC) algorithms. Rapid autocorrelation decay and the stabilization of Gelman-Rubin statistics near 1.0 provide evidence that the posterior samples adequately represent the target distributions. In conclusion, classic apparent prevalence estimates are overly precise when uncertainty around test performance is high. These Bayesian approaches provide a more accurate estimate of bTB prevalence in the study herd and provide baseline data for future Tp estimates using linked combined data.