Hu Jie, Liang Wei, Dai Hongsheng, Bao Yanchun
School of Mathematical Science, Xiamen University, China.
Department of Mathematical Sciences, University of Essex, UK.
J Stat Plan Inference. 2022 Dec;221:172-187. doi: 10.1016/j.jspi.2022.04.005. Epub 2022 May 7.
Doubly censored data are very common in epidemiology studies. Ignoring censorship in the analysis may lead to biased parameter estimation. In this paper, we highlight that the publicly available COVID19 data may involve high percentage of double-censoring and point out the importance of dealing with such missing information in order to achieve better forecasting results. Existing statistical methods for doubly censored data may suffer from the convergence problems of the EM algorithms or may not be good enough for small sample sizes. This paper develops a new empirical likelihood method to analyze the recovery rate of COVID19 based on a doubly censored dataset. The efficient influence function of the parameter of interest is used to define the empirical likelihood (EL) ratio. We prove that (EL-ratio) asymptotically follows a standard distribution. This new method does not require any scale parameter adjustment for the log-likelihood ratio and thus does not suffer from the convergence problems involved in traditional EM-type algorithms. Finite sample simulation results show that this method provides much less biased estimate than existing methods, when censoring percentage is large. The application to COVID19 data will help researchers in other field to achieve better estimates and forecasting results.
双删失数据在流行病学研究中非常常见。在分析中忽略删失可能导致参数估计有偏差。在本文中，我们强调公开可用的新冠病毒数据可能包含高比例的双删失情况，并指出处理此类缺失信息对于获得更好预测结果的重要性。现有的双删失数据统计方法可能会遇到期望最大化（EM）算法的收敛问题，或者对于小样本量来说不够理想。本文基于双删失数据集开发了一种新的经验似然方法来分析新冠病毒的康复率。使用感兴趣参数的有效影响函数来定义经验似然（EL）比。我们证明（EL比）渐近服从标准分布。这种新方法不需要对对数似然比进行任何尺度参数调整，因此不会遇到传统EM类算法中涉及的收敛问题。有限样本模拟结果表明，当删失百分比很大时，该方法提供的估计偏差比现有方法小得多。将其应用于新冠病毒数据将有助于其他领域的研究人员获得更好的估计和预测结果。
