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.

Conditional independence is a foundational concept for understanding probabilistic relationships among variables, with broad applications in fields such as causal inference and machine learning. This study focuses on testing conditional independence, $T\perp X|Z$, where T represents survival data possibly subject to right censoring, Z represents established risk factors for T, and X represents potential novel biomarkers. The goal is to identify novel biomarkers that offer additional merits for further risk assessment and prediction. This can be achieved by using either the partial or parametric likelihood ratio statistic to evaluate whether the coefficient vector of X in the conditional model of T given $(X^{ \mathrm{\scriptscriptstyle \top } }, Z^{ \mathrm{\scriptscriptstyle \top } })^{ \mathrm{\scriptscriptstyle \top } }$ is equal to zero. Traditional tests such as directly comparing likelihood ratios to chi-squared distributions may produce erroneous type-I error rates under model misspecification. As an alternative, we propose a resampling-based method to approximate the distribution of the likelihood ratios. A key advantage of the proposed test is its double robustness: it achieves approximately correct type-I error rates when either the conditional outcome model or the working model of ${\rm pr} (X|Z)$ is correctly specified. Additionally, machine learning techniques can be incorporated to improve test performance. Simulation studies and the application to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) data demonstrate the finite-sample performance of the proposed tests.

Identifying important features associated with right-censored survival time in ultrahigh-dimensional survival data is a challenging task due to the curse of dimensionality and information loss caused by censoring. To address these challenges, we propose a two-stage feature screening framework consisting of an imputation step and a feature screening step. The use of Buckley–James imputation leverages information from censoring and can therefore enhance the overall screening performance, particularly when the censoring rate is relatively high. We establish the sure screening properties of the two screening procedures proposed under this framework and illustrate their advantages through simulations. A real-world example is also provided to demonstrate the practical usefulness of the proposed approach.