Bayesian modelling of repeated cross-sectional epidemic prevalence survey data

Large-scale epidemic prevalence surveys are highly informative but resource-intensive tools for monitoring the spread of infectious diseases. Even in large studies, the generated data are often noisy, presenting challenges in both interpretation and inference. State-of-the-art Bayesian methods for analysing epidemic survey data were constructed independently and under pressure during the COVID-19 pandemic. In this paper, we compare two existing approaches (leveraging Bayesian P-splines and approximate Gaussian processes) and a novel approach using sequential Monte Carlo for smoothing and performing inference on epidemic survey data. We use our simpler approach to investigate the impact of survey design and underlying epidemic dynamics on the quality of estimates. We then incorporate these considerations into the existing methods and compare all three methods on simulated data and on real-world data from the SARS-CoV-2 REACT-1 prevalence study in England. All three methods, once appropriate considerations are made, produce similar estimates of infection prevalence; however, estimates of the growth rate and instantaneous reproduction number are more sensitive to underlying assumptions. Notebooks demonstrating all three methods are also provided alongside recommendations on hyperparameter selection and other practical guidance, with some cases resulting in orders-of-magnitude faster runtime.