Spatial sampling design to improve the efficiency of the estimation of the critical parameters of the SARS-CoV-2 epidemic
The pandemic linked to COVID-19 infection represents an unprecedented clinical and healthcare challenge for many medical researchers attempting to prevent its worldwide spread. This pandemic also represents a major challenge for statisticians involved in quantifying the phenomenon and in offering timely tools for the monitoring and surveillance of critical pandemic parameters. In a recent paper, Alleva et al. (2020) proposed a two-stage sample design to build a continuous-time surveillance system designed to correctly quantify the number of infected people through an indirect sampling mechanism that could be repeated in several waves over time to capture different target variables in the different stages of epidemic development. The proposed method exploits the indirect sampling (Lavalle, 2007; Kiesl, 2016) method employed in the estimation of rare and elusive populations (Borchers, 2009; Lavall\'ee and Rivest, 2012) and a capture/recapture mechanism (Sudman, 1988; Thompson and Seber, 1996). In this paper, we extend the proposal of Alleva et al. (2020) to include a spatial sampling mechanism (M\"uller, 1998; Grafstr\"om et al., 2012, Jauslin and Till\`e, 2020) in the process of data collection to achieve the same level of precision with fewer sample units, thereby facilitating the process of data collection in a situation where timeliness and costs are crucial elements. We present the basic idea of the new sample design, analytically prove the theoretical properties of the associated estimators and show the relative advantages through a systematic simulation study where all the typical elements of an epidemic are accounted for.