1. Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI 48109, USA
2. Department of Economics, University of California, San Diego, La Jolla, CA 92161, USA
3. Geely Automobile Holdings Limited, Hangzhou 310051, China
4. National Research Institute for Health and Family Planning, Beijing 100081, China
5. The Center for Applied Mathematics of Guangxi, Guangxi Normal University, Guilin 541004, China