AUTHOR=Courbariaux Marie , Cluzel Nicolas , Wang Siyun , Maréchal Vincent , Moulin Laurent , Wurtzer Sébastien ,  Obépine Consortium , Mouchel Jean-Marie , Maday Yvon , Nuel Grégory , Bertrand Isabelle , Boni Mickaēl , Gantzer Christophe , Le Guyader Soizick F. , Maday Yvon , Maréchal Vincent , Mouchel Jean-Marie , Moulin Laurent , Teyssou Rémy , Wurtzer Sébastien 

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

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=8

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.836349

DOI=10.3389/fams.2022.836349

ISSN=2297-4687

ABSTRACT=<p>A sentinel network, <italic>Obépine</italic>, 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 <italic>via</italic> a discretized smoother which makes it a very flexible tool. This method is both validated on simulations and real data from <italic>Obépine</italic>. The resulting smoothed signal shows a good correlation with other epidemiological indicators and is currently used by <italic>Obépine</italic> to provide an estimate of virus circulation over the watersheds corresponding to about 200 WWTPs.</p>