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

A sentinel network, Obepine, 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 Obepine. The resulting smoothed signal shows a good correlation with other epidemiological indicators and is currently used by Obepine to provide an estimate of virus circulation over the watersheds corresponding to about 200 WWTPs.