Efficient Empirical Likelihood Inference for recovery rate of COVID-19 under Double-Censoring

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 analyse 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 $-2\log$(EL-ratio) asymptotically follows a standard $\chi^2$ 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 method application to the COVID19 data will help researchers in other field to achieve better estimates and forecasting results.