• Center for Applied Statistics, Renmin University of China, Beijing, 100872, China
• Xia Junwen & Zhang Jingxiao
• School of Statistics, Renmin University of China, Beijing, 100872, China
• School of Public Health, Southern Medical University, Guangzhou, 510515, China
• Zhan Zishu

The authors would like to express their gratitude to the editor and anonymous referee for their careful reading and useful comments, which led to an improved presentation of the paper. The authors thank the National Cancer Institute (NCI) for access to NCl’s data collected by the prostate, lung, colorectal, and ovarian cancer screening trial. The statements contained herein are solely those of the authors and do not represent or imply concurrence or endorsement by NCI. This work was supported by Public Health & Disease Control and Prevention, Fund for Building World-Class Universities (Disciplines) of Renmin University of China (to J.Z.) and the MOE Project of Key Research Institute of Humanities and Social Sciences (22JJD910001).