A spatio-temporal block aggregation model for latent log Gaussian outcomes: application on modelling wastewater virus concentration in Wales

Wastewater-based epidemiology has emerged as a valuable tool for monitoring community-level infectious disease dynamics, providing population-wide signals that complement clinical surveillance. However, wastewater measurements are often observed as aggregated values over irregular spatial units. This work develops an approach to link an underlying spatially continuous processes and an aggregated outcome. We propose a spatio-temporal model for latent log-Gaussian outcomes that provides a coherent framework for inference and prediction, allowing the process to be integrated over arbitrary spatial configurations. This framework can also be used for subsequent analyses, such as linking wastewater signal to health outcomes at administrative areas. We use a Bayesian framework for inference via the linearised integrated nested Laplace approximation (INLA) approach. We apply the proposed methodology to model SARS-CoV-2 N1 gene copies in wastewater across 47 catchment areas in Wales from the beginning of August 2022 to the end of July 2023. The results demonstrate that the model captures spatial and temporal patterns and has good predictive performance. Results also show that estimated viral gene copies are strongly linked to positivity rates from COVID-19 PCR tests at the local authority level. Our findings highlight the importance of explicitly modelling block aggregation when analysing wastewater surveillance data. The proposed framework provides a flexible and principled approach for integrating environmental surveillance data into public health monitoring systems.