Comparing statistical learning models in wastewater-based epidemiology: An application to norovirus
Wastewater-based epidemiology (WBE) is an increasingly important tool for infectious disease surveillance, but there has been limited direct comparison of modelling approaches for predicting pathogen concentrations across space and time. We compare the predictive performance of six modelling approaches using norovirus in England as a case study, considering 3,232 wastewater samples from 152 sewage treatment works collected between May 2021 and March 2022 as part of the UK Environmental Monitoring for Health Protection programme. The benchmark was a Bayesian spatio-temporal model using Integrated Nested Laplace Approximation (INLA) with the Stochastic Partial Differential Equation approach (SPDE), compared with Lasso regression, Generalised Additive Models (GAM), Bayesian GAM, Extreme Gradient Boosting (XGBoost), and Random Forest. Models were evaluated using 10-fold spatial-block cross-validation with metrics including mean squared error, bias, correlation, empirical coverage of 95% prediction intervals, interval score, and computational cost. Random Forest was the best overall performing model, achieving the best interval score and nearest to nominal empirical coverage (95.3%), while maintaining point prediction accuracy comparable to XGBoost. The INLA-SPDE model also performed well, with near-nominal empirical coverage, the third best interval score, and consistently low bias across all evaluated metrics. Comparing predicted spatio-temporal trends, both models yielded similar spatial patterns but notable differences in uncertainty estimation. Our findings highlight a trade-off between predictive accuracy, uncertainty quantification, and computational efficiency. Ensemble machine learning methods are well suited to rapid prediction, whereas Bayesian geostatistical models remain valuable when probabilistic decision support is a priority for public health surveillance