Enhanced empirical likelihood estimation of incubation period of COVID-19 by integrating published information

Since the outbreak of the new coronavirus disease (COVID-19), a large number of scientific studies and data analysis reports have been published in the International Journal of Medicine and Statistics. Taking the estimation of the incubation period as an example, we propose a low-cost method to integrate external research results and available internal data together. By using empirical likelihood method, we can effectively incorporate summarized information even if it may be derived from a misspecified model. Taking the possible uncertainty in summarized information into account, we augment a logarithm of the normal density in the log empirical likelihood. We show that the augmented log-empirical likelihood can produce enhanced estimates for the underlying parameters compared with the method without utilizing auxiliary information. Moreover, the Wilks' theorem is proved to be true. We illustrate our methodology by analyzing a COVID-19 incubation period data set retrieved from Zhejiang Province and summarized information from a similar study in Shenzhen, China.