Robust smoothing of left-censored time series data with a dynamic linear model to infer SARS-CoV-2 RNA concentrations in wastewater

Wastewater sampling for the detection and monitoring of SARS-CoV-2 has been developed and applied at an unprecedented pace, however uncertainty remains when interpreting the measured viral RNA signals and their spatiotemporal variation. The proliferation of measurements that are below a quantifiable threshold, usually during non-endemic periods, poses a further challenge to interpretation and time-series analysis of the data. Inspired by research in the use of a custom Kalman smoother model to estimate the true level of SARS-CoV-2 RNA concentrations in wastewater, we propose an alternative left-censored dynamic linear model. Cross-validation of both models alongside a simple moving average, using data from 286 sewage treatment works across England, allows for a comprehensive validation of the proposed approach. The presented dynamic linear model is more parsimonious, has a faster computational time and is represented by a more flexible modelling framework than the equivalent Kalman smoother. Furthermore we show how the use of wastewater data, transformed by such models, correlates more closely with regional case rate positivity as published by the Office for National Statistics (ONS) Coronavirus (COVID-19) Infection Survey. The modelled output is more robust and is therefore capable of better complementing traditional surveillance than untransformed data or a simple moving average, providing additional confidence and utility for public health decision making. © 2023, American Institute of Mathematical Sciences. All rights reserved.

A Flexible Smoother Adapted to Censored Data With Outliers and Its Application to SARS-CoV-2 Monitoring in Wastewater

A sentinel network, Obépine, has been designed to monitor SARS-CoV-2 viral load in wastewaters arriving at wastewater treatment plants (WWTPs) in France as an indirect macro-epidemiological parameter. The sources of uncertainty in such a monitoring system are numerous, and the concentration measurements it provides are left-censored and contain outliers, which biases the results of usual smoothing methods. Hence, the need for an adapted pre-processing in order to evaluate the real daily amount of viruses arriving at each WWTP. We propose a method based on an auto-regressive model adapted to censored data with outliers. Inference and prediction are produced via a discretized smoother which makes it a very flexible tool. This method is both validated on simulations and real data from Obépine. The resulting smoothed signal shows a good correlation with other epidemiological indicators and is currently used by Obépine to provide an estimate of virus circulation over the watersheds corresponding to about 200 WWTPs. Copyright © 2022 Courbariaux, Cluzel, Wang, Maréchal, Moulin, Wurtzer, Obépine Consortium, Mouchel, Maday and Nuel.