Dynamic Linear Models for Wastewater-Based Epidemiology with Missing Values: an Application to Covid-19 Surveillance

We argue for the usage of dynamic linear models (DLMs) for pre-processing and modeling of wastewater data used for surveillance of population infectious disease levels. Unlike other existing models widely implemented in the literature and in practice, DLMs can naturally impute missing values (useful for data aggregation) and model multiple types of observation noise. Simple DLMs are useful for pre-processing wastewater data since they naturally denoise and impute missing values. The output is useful for visualization and also improves performance in downstream analyses as we show on data from Minnesota. DLMs can also be used as statistical models that are flexible, yet interpretable, and more parsimonious than machine learning methods, which can be too data hungry for many wastewater infectious disease settings. We demonstrate the usage of DLMs on wastewater and clinical COVID-19 data collected across the US state of Minnesota from March, 2022 to May, 2024. We see improved prediction performance over machine learning methods. Minnesota has seven public health regions each of which has many wastewater treatment plants; we demonstrate the usage of DLMs for principled aggregation of wastewater data within regions. We also implement more sophisticated “regime-switching” DLMs for detection of disease surges. Code implementing our framework is available in the R package dlmwwbe.