1. Department of Mathematical Sciences, Hirosaki University Graduate School of Science and Technology, 3 Bunkyocho, Hirosaki, Aomori 036-8561, Japan
2. Department of Biostatistics, Kyoto University School of Public Heath, Kyoto 606-8501, Japan
3. Department of Biomedical Statistics, Osaka University Graduate School of Medicine, Suita 565-0871, Japan
4. Department of Biostatistics, Harvard University School of Public Heath, Boston, MA 02115-6018, USA