A sampling scheme for estimating the prevalence of a pandemic

The spread of COVID-19 makes it essential to investigate its prevalence. In such investigation research, as far as we know, the widely-used sampling methods didn’t use the information sufficiently about the numbers of the previously diagnosed cases, which provides a priori information about the true numbers of infections. This motivates us to develop a new, two-stage sampling method in this paper, which utilizes the information about the distributions of both population and diagnosed cases, to investigate the prevalence more efficiently. The global likelihood sampling, a robust and efficient sampler to draw samples from any probability density function, is used in our sampling strategy, and thus, our new method can automatically adapt to the complicated distributions of population and diagnosed cases. Moreover, the corresponding estimating method is simple, which facilitates the practical implementation. Some recommendations for practical implementation are given. Finally, several simulations and a practical example verify its efficiency.

新冠病毒（COVID-19）的全球传播使得对其感染流行率开展调查成为必要之举。据我们所知，在这类调查研究中，当前广泛应用的抽样方法未能充分利用既往确诊病例数所蕴含的感染真实规模先验信息（a priori information）。基于此，本文提出一种全新的两阶段抽样方法，该方法充分利用人群分布与确诊病例分布的相关信息，以更高效地开展感染流行率调查。全局似然抽样（global likelihood sampling）作为一种可从任意概率密度函数（probability density function）中高效抽取样本的稳健抽样方法，被应用于本文的抽样策略中，因此该新方法可自动适配人群与确诊病例的复杂分布特征。此外，配套的估计方法简洁易用，便于实际落地实施。本文还针对实际应用给出了相关建议。最后，通过多组仿真实验与一则实际案例验证了该方法的有效性。