Bayesian modelling in practice. Estimation of within-herd paratuberculosis prevalence in dairy cattle herds

Background: Bayesian methodology is widely used in veterinary science to model the prevalence of infectious diseases. The main reason for the rapid spread of this methodology is that the Bayesian approach allows the incorporation of both prior knowledge and new data into the estimates. Objectives: The objective of this paper is to give an overview of how the Bayesian methodology works and to present its key concepts. We illustrate the concept, the method, and the interpretation of the outcome by modelling the within-herd prevalence of paratuberculosis (PTBC) infection of individual dairy cattle farms. Materials and Methods: In our study, Bayesian hierarchical modelling was used to estimate the probability of PTBC infection among primi- and multiparous cows. The model incorporates historical priors based on a nationwide voluntary screening data. Linear regression was fitted to the outcome values obtained from the model to provide thumb rules for prevalence estimation. Simulation was used to evaluate the accuracy of the estimates. In addition, based on the results of the model, we proposed fast and straightforward methods for estimating these quantities. Results and Discussion: Based on the regression fitted to all individual results, a simple multiplication of 1.6 for primiparous and 1.5 for multiparous cows is sufficient to get an approximate estimate of the true PTBC prevalence. The simulation study showed that the true prevalence was covered by the 95% credible interval in approximately 90% of the simulated herds, both for primi- and multiparous cows. Testing only a given proportion of the cows in the herds did not change the coverage level but decreased the precision providing wider credible intervals. Understanding the difference between apparent and true prevalence is essential in the quantitative analysis of infectious diseases. Bayesian methods can be used to estimate the true prevalence, helping the herd management to assess the damage caused by infection and develop appropriate preventive measures.