1. Department of Geriatric Medicine School of Medicine, International University of Health and Welfare Chiba Japan
2. Department of Geriatric Medicine Graduate School of Medicine, The University of Tokyo Tokyo Japan
3. Research Institute and Practice for Involutional Diseases Nagano Japan
4. Department of Medical Statistics Osaka City University Graduate School of Medicine Osaka Japan
5. Japan Osteoporosis Foundation Tokyo Japan
6. Public Health Research Foundation Tokyo Japan
7. Department of Clinical Biostatistics Graduate School of Medicine, Kyoto University Kyoto Japan
8. Department of Orthopedic Surgery Jikei University School of Medicine Tokyo Japan