1. Department of Biostatistics; Kyoto University School of Public Health; Yoshida Konoe-cho; Sakyo-ku; Kyoto; 606-8501; Japan
2. Department of Mathematical Sciences; Hirosaki University Graduate School of Science and Technology; 3 Bunkyo-cho; Hirosaki; Aomori; 036-8561; Japan
3. Department of Biomedical Statistics; Osaka University Graduate School of Medicine; 2-2 Yamadaoka; Suita; Osaka; 565-0871; Japan