Hierarchical modelling of risk factors with and without prior information – the process of regression model evaluation for an example of respiratory diseases in piglet production from daily practice data

Timur Tug^1*Fiona Mers¹Franziska Schäkel²Doris Höltig³Katja Ickstadt¹Lothar Kreienbrock^4*

• ¹Department of Statistics, TU Dortmund university, Dortmund, Germany
• ²Institute for Biometry, Epidemiology and Information Processing, University of Veterinary Medicine Hannover, Hannover, Germany
• ³Clinical Centre for Farm Animals, University of Veterinary Medicine, Hannover, Germany
• ⁴Institute of Biometry,Epidemiology and Information Processing,WHO Collaborating Centre for Research and Training for Health at the Human-Animal-Environment Interface, University of Veterinary Medicine, Hannover, Germany

In veterinary epidemiology, regression models are commonly used to describe animal health and related risk factors. However, model selection and evaluation present ongoing challenges - especially when many potential predictors, complex interactions, and limited sample sizes are involved. The VASIB project serves as a representative example, focusing on piglet-producing farms with persistent respiratory disease problems. Across 30 farms, a wide array of variables was collected at the farm, barn, compartment, pen, and individual animal levels, aiming to support optimized treatment and management strategies to improve respiratory health. This study investigates the occurrence of coughing in pigs using various epidemiological models, including hierarchical frequentist logistic regression, non-hierarchical Bayesian logistic regression (with full and partial pooling), and hierarchical Bayesian models with informative and non-informative priors. These approaches are evaluated and compared using statistical measures such as the corrected Akaike Information Criterion (AICc), marginal and conditional R², and intra-class correlation coefficients (ICCc /ICCadj). In the frequentist models, convergence issues arose due to limited observations within clusters, which did not occur in the Bayesian framework. While the choice of priors had limited influence on Bayesian model results, differences between models suggest that prior specification can still be relevant. Thus, it is important to assess and compare various model structures—including both hierarchical and non-hierarchical, and Bayesian versus frequentist approaches - to capture the data's complexity and ensure robust inference. Here, the Bayesian hierarchical models outperform frequentist models, especially in handling complex data structures and providing robust estimates. Across all models, stocking density and floor condition emerged as consistently significant factors influencing the likelihood of coughing. Overall, this work emphasizes that there is no universal rule for model selection in veterinary data analysis. Instead, a balanced, context-sensitive modeling strategy that considers both statistical and epidemiological perspectives is essential to derive meaningful and actionable conclusions for improving animal health.