Estimation of Survival Function and Median Survival Time in Interval-Censored Data

구간중도절단자료에서 생존함수와 중간생존시간에 대한 추정

  • Yun, Eun-Young (Department of Nursing, College of Medical and Life Science, Silla University) ;
  • Kim, Choong-Rak (Department of Statistics, Pusan National University)
  • 윤은영 (신라대학교 의생명과학대학 간호학과) ;
  • 김충락 (부산대학교 통계학과)
  • Received : 20100400
  • Accepted : 20100500
  • Published : 2010.06.30


Interval-censored observations are common in medical and epidemiologic studies; however, limited studies exist due to the complexity and special structure of interval-censoring. This paper introduces the imputation method and the self consistency method in the interval-censored data. We propose a new method of generating random numbers under an interval-censoring set-up. Through simulation studies we compare two methods under various simulation schemes in the sense of the mean squared error for estimating the median survival time and the mean integrated squared error for estimating the survival function. Under a moderate censoring percentage, the mean imputation method showed a better performance than the self-consistency method in estimating the median survival time and the survival function.

구간중도절단은 중도절단의 가장 일반적인 개념으로 구간중도절단자료는 의학 및 역학분야의 연구에서 흔히 관찰된다. 본 연구에서는 구간중도절단의 상황에서 생존함수와 중간생존시간을 추정하는 방법으로 평균대치법과 자기일치법을 비교 연구하고, 실제 자료로 혈우병환자에서 선천성면역결핍바이러스 감염시점을 추정하였다. 또한 구간중도절단자료를 생성하는 새로운 방법을 제시하였으며, 생성된 구간중도절단자료를 이용한 모의실험을 통하여 두 추정치에 대한 다양한 비교연구를 시행하였다. 구간중도절단자료에서 생존함수와 중간생존시간을 추정할 경우 중도절단율이 크지 않다면 평균대치법이 자기일치법보다 더 우수한 추정치로 판명되었다.



Supported by : 부산대학교


  1. Finkelstein, D. M. (1986). A proportional hazards model for interval-censored failure time data, Biometrics, 42, 845-854.
  2. Gentleman, R. and Geyer, C. J. (1994). Maximum likelihood for interval censored data: Consistency and computation, Biometrika, 81, 618-623.
  3. Goedert, J. J., Kessler, C. M., Aledort, L. M., Biggar, R. J., Andes, W. A., White, G. C., Drummond, J. E., Vaidya, K., Mann, D. L., Eyster, M. E., Lederman, M. M., Hilgartner, M. W., Ragni, M. V., Cohen, A. R., Gordon, L. B., Rosenberg, P. S., Friedman, R. M., Blattner, W. A., Kroner, B. and Gail, M. H. (1989). A prospective-study of human immunodeficiency virus type-1 infection and the development of AIDS in subjects with hemophilia, New England Journal of Medicine, 321, 1141-1148.
  4. Groeneboom, P. and Wellner, J. A. (1992). Information bounds and nonparametric maximum likelihood estimation, DMV Seminar, Band 19, Birkhauser, New York.
  5. Huang, J. and Wellner, J. A. (1997). Interval censored survival data: A review of recent progress, Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis, eds. Lin, D. and Fleming, T. Springer Verlag, New York, 123-169.
  6. Jongbloed, G. (1998). The iterative convex minorant algorithm for nonparametric estimation, Journal of Computational and Graphical Statistics, 7, 310-321.
  7. Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations, Journal of the American Statistical Association, 53, 457-481.
  8. Odell, P. M., Anderson, K. M. and D'Agostino, R. B. (1992). Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model, Biometrics, 48, 951-959.
  9. Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys, John Wiley, New York.
  10. Sun, J. (1998). Interval Censoring. Encyclopedia of Biostatistics, John Wiley, First Edition, New York, 2090-2095.
  11. Sun, J. (2005). Interval Censoring. Encyclopedia of Biostatistics, John Wiley, Second Edition, New York, 2603-2609.
  12. Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data, Springer Verlag, New York.
  13. Taylor, J. M. G. and Kim, D. K. (1994). Marker values at the time of an AIDS diagnosis, Statistics in Medicine, 13, 2059-2066.
  14. Turnbull, B. W. (1976). The empirical distribution with arbitrarily grouped censored and truncated data, Journal of the Royal Statistical Society, Series B, 38, 290-295.
  15. Wellner, J. and Zhan, Y. (1997). A hybird algorithm for computation of the nonparametric maximum likelihood estimator from censored data, Journal of the American Statistical Association, 92, 945-959.

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