Removing weekly administrative noise in the daily count of COVID-19 new cases. Application to the computation of Rt

The way each country counts and reports the incident cases of SARS-CoV-2 infections is strongly affected by the "weekend effect". During the weekend, fewer tests are carried out and there is a delay in the registration of cases. This introduces an "administrative noise" that can strongly disturb the calculation of trend estimators such as the effective reproduction number R(t). In this work we propose a procedure to correct the incidence curve and obtain a better fit between the number of infected and the one expected using the renewal equation. The classic way to deal with the administrative noise is to invoke its weekly period and therefore to filter the incidence curve by a seven days sliding mean. Yet this has three drawbacks: the first one is a loss of resolution. The second one is that a 7-day mean filter hinders the estimate of the effective reproduction number R(t) in the last three days before present. The third drawback of a mean filter is that it implicitly assumes the administrative noise to be additive and time invariant. The present study supports the idea that the administrative is better dealt with as being both periodic and multiplicative. The simple method that derives from these assumptions amount to multiplying the number of infected by a correcting factor which depends on the day of the week. This correcting factor is estimated from the incidence curve itself. The validity of the method is demonstrated by its positive impact on the accuracy of an the estimates of R(t). To exemplify the advantages of the multiplicative periodic correction, we apply it to Sweden, Germany, France and Spain. We observe that the estimated administrative noise is country dependent, and that the proposed strategy manages to reduce it noise considerably. An implementation of this technique is available at www.ipol.im/ern, where it can be tested on the daily incidence curves of an extensive list of states and geographic areas provided by the European Centre for Disease Prevention and Control.