key: cord-0852739-7qyp829c authors: Maruotti, Antonello; Ciccozzi, Massimo; Divino, Fabio title: On the misuse of the reproduction number in the COVID‐19 surveillance system in Italy date: 2021-02-19 journal: J Med Virol DOI: 10.1002/jmv.26881 sha: 0508bc6c9e87b241d2a45fa64cbbf8885efd769a doc_id: 852739 cord_uid: 7qyp829c We discuss the statistical method used in Italy to estimate the reproduction number Rt at the regional level. In Italy, Rt is not only used to provide a picture of the epidemic spread, but rather as a decision tool to plan and organize non-pharmaceutical interventions by imposing a-priori thresholds to define different levels of risks. We comment on methodological limitations of the statistical approach which lead to a misuse of Rt. Though remarking the importance of the reproduction number to evaluate the severity of the COVID-19 spread, we must be cautious to use Rt over its real meaning, and avoid its use to impose constraints to the dailylife activities as these would be based on an unreliable estimate of the reproduction number. This article is protected by copyright. All rights reserved. We believe this is a misuse of R t , which is dangerous and widely uncertain. For this reason, it is important that this parameter as an indicator for restriction measures must be managed by an expert in the field. Some practical and statistically relevant considerations are given in Gostic et al. 1 Nature (https://www.nature.com/articles/ d41586-020-02009-w), in July, already discussed the potential bias in using R t over its real meaning. Here, we discuss the main limits of the Italian approach to estimate and use R t , showing that the restrictions imposed on the population are based on an unreliable estimate of the reproduction number. The reference model is proposed by Cori et al. 2 The reproduction number is estimated in a Bayesian framework and requires the a priori definition/estimation of some fundamental quantities needed to estimate R t . The authors correctly discussed the limitations of their approach, but it seems that the Italian authorities neglect them. The main issues are related to • the time window defined to estimate R t ; • the distributions assumed to model the number of new cases and the generation time. The first risk is clearly stated in the Introduction, "When the data aggregation time step is small (e.g., daily data), estimates of R t can vary considerably over short time periods, producing substantial negative autocorrelation." In other words, the obtained estimates of Moreover, Cori et al. 2 assumed that the distribution of infectiousness through time after infection is independent of calendar time and follows a Poisson process, that is, overdispersion is not accounted for. This is a rather restrictive assumption that must be carefully checked on the real data. It is well-known that Poissonbased estimates are biased if overdispersion arises in the data. We believe these points are already enough to conclude that the estimates of R t should be used with caution, but the most relevant assumptions strongly affecting the estimates of R t are not still discussed. Indeed, in Cori et al. 2 where transmission can reliably be ascertained (e.g., households) can be used to estimate the distribution of the serial interval (time between symptoms onset of a case and symptoms onset of his/her secondary cases)." In other words, different estimates of the serial interval lead to different estimates of R t , that is, a reliable estimate of the serial interval is mandatory because it drives the estimate of R t , and its misspecification is the major source of bias. In Italy, the reference serial interval to estimate the official R t is taken from Cerada et al., 3 In addition, the delay between the date in which the result of the test was received and the date of the recording in the data set also plays a crucial role. Cori et al. 2 uses the instantaneous reproductive number and considers incidence cases observed before time point t; therefore, data may be affected by underreporting due to the delay between tests and reports: larger the delay, less accurate the estimation of R t due to missing information concerning incidence cases that are not yet recorded. Furthermore, the underreporting rate is not constant; it mostly affects the cases observed at the previous time points and closer to t, introducing a bias effect in the estimation. As a critical consequence, when the delay between test and report is large, the estimates of R t may be biased and in significant delay with respect to the current evolution of the epidemic process. Available epidemiological data are not ideal, and this reinforces, even more, the idea that statistical adjustments are needed to obtain accurate estimates of R t . As a result of neglecting all these issues, uncertain estimates of R t are obtained. Just to provide an example, we focus on the R t estimates reported in the ISS weekly report (see e.g., figure 8 at https://www.epicentro.iss.it/coronavirus/bollettino/ Bollettino-sorveglianza-integrata-COVID-19_20-gennaio-2021.pdf). All credible intervals are rather wide, and even huge for some regions. The high uncertainty surrounding these estimates is a clear indication that the use of R t must be limited to provide a trend in the epidemic spread, but it must be avoided any further use. Annunziato and Asikainen 5 compare different methods to estimate R t and show that point estimates vary across methods, though they share a similar trend. In Italy, instead, through a priori specified levels of the reproductive number, R t estimates are used to label the administrative regions in classes of risks (called scenario in the main ISS report, see e.g., http://www.salute.gov.it/imgs/C_17_monitoraggi_13_ 0_fileNazionale.pdf), with the respective restrictions. For estimating R t no golden standard methods exist. The work by Cori et al. 2 is a milestone in epidemiology research. Nevertheless, like many other models, it is based on assumptions that must be checked and fulfilled to avoid misleading inference. In Italy, not only are these assumptions neglected but the estimates of R t are used widely over their reliable interpretation. At the end of the games the R t seems a dancer, dancing music depending on the actual director of the orchestra who performs it. Practical considerations for measuring the effective reproductive number, Rt A new framework and software to estimate time-varying reproduction numbers during epidemics The early phase of the COVID-19 outbreak in Lombardy, Italy Estimating the generation interval for coronavirus disease (COVID-19) based on symptom onset data Effective reproduction number estimation from data series, EUR 30300 EN, Publications Office of the European Union Luxembourg On the misuse of the reproduction number in the COVID-19 surveillance system in Italy We express our deep thanks to Alessio Farcomeni, Giovanna Jona-Lasinio, and Gianfranco Lovison for valuable discussions.