Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Estimation of conditional mean residual life function with random censored data

임의중단자료에서의 조건부 평균잔여수명함수 추정

  • Received : 2010.12.30
  • Accepted : 2011.01.20
  • Published : 2011.01.31
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Abstract

The aims of this study were to propose a method of estimation for mean residual life function (MRLF) from conditional survival function using the Buckley and James's (1979) pseudo random variables, and then to assess the performance of the proposed method through the simulation studies. The mean squared error (MSE) of proposed method were less than those of the Cox's proportional hazard model (PHM) and Beran's nonparametric method for non-PHM case. Futhermore in the case of PHM, the MSE's of proposed method were similar to those of Cox's PHM. Finally, to evaluate the appropriateness of practical use, we applied the proposed method to the gastric cancer data. The data set consist of the 1, 192 patients with gastric cancer underwent surgery at the Department of Surgery, K-University Hospital.

본 연구에서는 Buckley와 James의 방법을 이용하여 중도절단된 자료를 보완한 조건부생존함수 추정량으로부터 조건부평균잔여수명함수를 추정하는 방법을 제안하고, 모의실험을 통하여 제안된 방법의 효율성을 평가하였다. 모의실험 결과 비례위험모형이 아닌 경우 제안된 방법으로 추정한 조건부 평균잔여수명함수의 평균제곱오차가 Cox모형이나 Beran의 비모수적 방법을 이용하여 구한 추정치의 평균제곱오차보다 작게 나타났으며, 비례위험모형인 경우에는 제안된 방법으로 추정한 결과들이 Cox 모형을 이용하여 얻은 결과들과 비슷하게 나타났다. 또한 K대학교병원 외과에서 위암 수술을 받은 1,192명의 환자 자료를 이용하여 제안된 방법의 임상적 적용의 적절성을 평가하였다.

Keywords

References

  1. Aalen, O. O. (1978). Nonparametric inference for a family of counting processes. Annals of Statistics, 6, 701-726. https://doi.org/10.1214/aos/1176344247
  2. Beran, R. J. (1981). Nonparametric regression with randomly censored data, Technical report, University of California, Berkeley.
  3. Buckley, J. J. and James, I. R. (1979). Linear regression with censored data. Biometrika, 66, 429-436. https://doi.org/10.1093/biomet/66.3.429
  4. Cha, Y. J. (2004). Nonparametric estimation of mean residual life by partial moment approximation under proportional hazard model. Journal of Korean Data & Information Science Society, 15, 965-971.
  5. Cox, D. R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Ser. B, 34, 187-220.
  6. Dabrowska, D. M. (1987). Non-paramertic regression with censored survival time data. Scandinavian Journal of Statistics, 14, 181-198.
  7. Ghoriai, J. K. and Rejto L. (1987). Estimation of mean residual life with censored data under proportional hazard model. Communications in Statistics - Theory and Methods, 16, 2097-2114. https://doi.org/10.1080/03610928708829492
  8. Hall, W. J. and Wellner, J. A. (1981). Mean residual life. In Statistics and related topics, Eds. Csorgo, M., Dawson, D. A., Rao, J. N. K. and Saleh, M. E., North-Holland, New York.
  9. Jeong, D. M., Song, M. U. and Song, J. K. (1996). Smoothing mean residual life with censored data. The Korean Communications in Statistics, 3, 129-138.
  10. Jeong, D. M., Song, M. U. and Song, J. K. (1997). A simple estimator of mean residual life function under random censoring. Journal of Korean Data & Information Science Society, 8, 225-230.
  11. Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of American Statistical Association, 53, 457-481. https://doi.org/10.1080/01621459.1958.10501452
  12. Kotz, S. and Shanbhag, D. N. (1980). Some new approaches to probability distributions. Advanced in Applied Probability, 12, 903-921. https://doi.org/10.2307/1426748
  13. Kumazawa, Y. (1987). A note an estimator of life expectancy with random censoring. Biometrika, 74, 655-658. https://doi.org/10.1093/biomet/74.3.655
  14. Lee, W. K. and Song, M. U. (2004). A study on the conditional survival function with random censored data. Journal of Korean Data & Information Science Society, 15, 405-411.
  15. Morrison, D. G. (1978). On linearly increasing mean residual lifetimes. Journal of Applied Probability, 15, 617-620. https://doi.org/10.2307/3213124
  16. Nelson, W. (1972). Theory and applications of hazard plotting for censored failure data. Technometics, 14, 945-965. https://doi.org/10.1080/00401706.1972.10488991
  17. Yang, G. L. (1977). Life expectancy under random censorship. Stochastic Processes and their Applications, 6, 33-39. https://doi.org/10.1016/0304-4149(77)90015-1
  18. Yang, G. L. (1978). Estimation of biometric function. Annals of Statistics, 6, 112-116. https://doi.org/10.1214/aos/1176344070