A sample approach to the estimation of the critical parameters of the SARS-CoV-2 epidemics: an operational design

Given the urgent informational needs connected with the diffusion of infection with regard to the COVID-19 pandemic, in this paper, we propose a sampling design for building a continuous-time surveillance system. Compared with other observational strategies, the proposed method has three important elements of strength and originality: (i) it aims to provide a snapshot of the phenomenon at a single moment in time, and it is designed to be a continuous survey that is repeated in several waves over time, taking different target variables during different stages of the development of the epidemic into account; (ii) the statistical optimality properties of the proposed estimators are formally derived and tested with a Monte Carlo experiment; and (iii) it is rapidly operational as this property is required by the emergency connected with the diffusion of the virus. The sampling design is thought to be designed with the diffusion of SAR-CoV-2 in Italy during the spring of 2020 in mind. However, it is very general, and we are confident that it can be easily extended to other geographical areas and to possible future epidemic outbreaks. Formal proofs and a Monte Carlo exercise highlight that the estimators are unbiased and have higher efficiency than the simple random sampling scheme.