During an epidemic outbreak of a new disease, the probability of dying once infected is considered an important though difficult task to be computed. Since it is very hard to know the true number of infected people, the focus is placed on estimating the case fatality rate, which is defined as the probability of dying once tested and confirmed as infected. The estimation of this rate at the beginning of an epidemic remains challenging for several reasons, including the time gap between diagnosis and death, and the rapid growth in the number of confirmed cases. In this work, an unbiased estimator of the case fatality rate of a virus is presented. The consistency of the estimator is demonstrated, and its asymptotic distribution is derived, enabling the corresponding confidence intervals (C.I.) to be established. The proposed method is based on the distribution F of the time between confirmation and death of individuals who die because of the virus. The estimator's performance is analyzed in both simulation scenarios and the real-world context of Argentina in 2020 for the COVID-19 pandemic, consistently achieving excellent results when compared to an existing proposal as well as to the conventional \naive" estimator that was employed to report the case fatality rates during the last COVID-19 pandemic. In the simulated scenarios, the empirical coverage of our C.I. is studied, both using the F employed to generate the data and an estimated F, and it is observed that the desired level of confidence is reached quickly when using real F and in a reasonable period of time when estimating F.

翻译：在新发疾病暴发期间，感染后死亡的概率被视为一项重要但难以计算的任务。由于难以获知真实感染人数，研究重点转向估计病死率——即经检测确诊为感染者后死亡的概率。疫情初期该比率的估计面临多重挑战，包括诊断与死亡之间的时间差，以及确诊病例数的快速增长。本研究提出一种病毒病死率的无偏估计量，论证了该估计量的一致性，并推导了其渐近分布，从而可构建相应的置信区间。所提方法基于感染者从确诊到死亡这一时间间隔的分布F。我们在模拟场景和2020年阿根廷COVID-19疫情的真实背景下分析了该估计量的性能，与现有方法及上次COVID-19疫情期间用于报告病死率的传统“朴素”估计量相比，该估计量始终表现优异。在模拟场景中，我们分别利用生成数据的真实分布F和估计的F研究置信区间的经验覆盖率，观察到使用真实F时能快速达到期望置信水平，而使用估计F时亦可在合理时间内达到该水平。