1. Department of Biomedical Statistics; Osaka University Graduate School of Medicine; Osaka Japan
2. Office of Biostatistics and Data Management, Research and Development Initiative Center; National Cerebral and Cardiovascular Center; Osaka Japan
3. Department of Mathematical Sciences; Graduate School of Science and Technology, Hirosaki University; Aomori Japan
4. Department of Biostatistics and the Center for Biostatistics in AIDS Research; Harvard School of Public Health; Boston MA U.S.A.
5. Department of Biostatistics; Kyoto University School of Public Health; Kyoto Japan