An autoregressive model for a censored data denoising method robust to outliers with application to the Obépine SARS-Cov-2 monitoring

A sentinel network, Ob\'epine, has been designed to monitor SARS-CoV-2 viral load in wastewaters arriving at several tens of wastewater treatment plants in France as an indirect macro-epidemiological parameter. The sources of uncertainty in such monitoring system are numerous and the concentration measurements it provides are left-censored and contain numerous 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 virus arriving to 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 discretised smoother which makes it a very flexible tool. This method is both validated on simulations and on real data from Ob\'epine. The resulting smoothed signal shows a good correlation with other epidemiological indicators and currently contributes to the construction of the wastewater indicators provided each week by Ob\'epine.