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Analysis of the Frailty Model with Many Ties

동측치가 많은 FRAILTY 모형의 분석

  • Kim Yongdai (Dept. of Statistics, Seoul National University) ;
  • Park Jin-Kyung (Associate Scientfic Analyst, International Vaccine Institute, SNU Research Park)
  • 김용대 (서울대학교 통계학과) ;
  • 박진경 (서울대 연구공원 내, 국제백신연구소(IVI))
  • Published : 2005.03.01

Abstract

Most of the previously proposed methods for the frailty model do not work well when there are many tied observations. This is partly because the empirical likelihood used is not suitable for tied observations. In this paper, we propose a new method for the frailty model with many ties. The proposed method obtains the posterior distribution of the parameters using the binomial form empirical likelihood and Bayesian bootstrap. The proposed method yields stable results and is computationally fast. To compare the proposed method with the maximum marginal likelihood approach, we do simulations.

프레일티모형에 대한 기존의 추론방법은 동측치가 많은 경우에 그 성능이 떨어진다. 그 이유는 사용된 경험적 우도함수가 동측치가 많은 자료에는 적합하지 않기 때문이다. 본 논문에서는 동측치가 많은 프레일티 모형에서의 새로운 추론방법을 제안한다. 이항형태의 경험적우도함수를 바탕으로 베이지안 부스트랩을 사용하여 모수의 사후분포를 구한다. 제안된 방법의 장점은 기존에 제안된 주변최대우도추정량에 비하여 계산이 수월하고 안정적인 결과를 제공하는데 있다. 이를 실증적으로 비교하기 위하여 제안된 방법을 주변최대우도추정량과 가상실험을 통하여 비교한다.

Keywords

References

  1. Breslow N.E. (1974). Covariance analysis of censored survival data, Biometrics, 30, 89-99 https://doi.org/10.2307/2529620
  2. Clayton, G.D. (1991). A monte carlo method for Bayesian inference in frailty models, Biometrics, 47, 467-485 https://doi.org/10.2307/2532139
  3. Cox D.R. (1972). Models and life tables (with discussion), Journal of the Royal Statistical Society B, 34, 187-220
  4. Damien P., Wakefield J., and Walker S.(1999). Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables, Journal of the Royal Statistical Society B, 61, 331-344 https://doi.org/10.1111/1467-9868.00179
  5. Efron B. (1979). Bootstrap methods: another look at the jackknife, Annals of Statistics, 7, 1-26 https://doi.org/10.1214/aos/1176344552
  6. Gruger J., Kay R., and Schumacher M. (1991). The validity of inferences based in incomplete observations in disease state models, Biometrics, 47, 595-605 https://doi.org/10.2307/2532149
  7. Ha I.D., Lee Y., and Song J.K. (2001). Heirachicallikelihood approach for frailty models, Biometrika, 88, 233-243 https://doi.org/10.1093/biomet/88.1.233
  8. Heckman J.J. and Singer(1984). A method for minimizing the impact of distributional assumptions in economic models of duration data, Econometrica, 52, 271-320 https://doi.org/10.2307/1911491
  9. Hedeker, D. and Siddiqui, O. and Hu, F.B. (2000). Random-effects regression analysis of correlated grouped-time survival data, Statistical Methods in Medical Research, 9, 161-179 https://doi.org/10.1191/096228000667253473
  10. Kim Y and Lee J (2003). Bayesian bootstrap for proportional hazard model, Annals of Statistics, 31, 1905-1922 https://doi.org/10.1214/aos/1074290331
  11. Klein J.P. (1992). Semiparametric estimation of random effects using the Cox model based on the EM algorithm, Biometrics, 48, 795-806 https://doi.org/10.2307/2532345
  12. Klein J.P. and Moeschberger M.L. (1997). Survival Analysis: Techniques for Censored and Truncated Data, Springer-Verlag
  13. Laud, P.W. and Damien, P. and Smith, A.F.M.(1998). Bayesian nonparametric and covariate analysis of failure time data, chapter in practical nonparametric and semi parametric Bayesian statistics, Springer-Verlag, 213-225
  14. Lo A.Y. (1993). A Bayesian bootstrap for censored data, Annals of Statistics, 21, 100-123 https://doi.org/10.1214/aos/1176349017
  15. McGlichrist C.A. and Aisbett C.W.(1991). Regresion with frailty in survival analysis, Biometrics, 47, 461 466
  16. Nielsen G.G., Gill D.R., Andersen P.K., and Sorensen I.A.T. (1992). A counting process approach to maximum likelihood estimation in frailty models, Scandinavian Journal of Statistics, 19, 25-44
  17. Prentice R.L. and Gloeckler L.A.(1978). Regression analysis of grouped survival data with application to breast cancer data, Biometrics, 34, 57-67 https://doi.org/10.2307/2529588
  18. Rubin D.B. (1981). The Bayesian bootstrap, Annals of Statistics, 9, 130-134 https://doi.org/10.1214/aos/1176345338
  19. Schumacher, M. and Olschewski, M. and Schmoor, C. (1987). The impact of heterogeneity on the comparison of survival times, Statistics in Medicine, 6 773-784 https://doi.org/10.1002/sim.4780060708
  20. Struther C.A. and Kalbfleisch J.D.(1986). Misspecified proportional hazards models, Biometrika, 73, 363-369
  21. Vaupel, J.W. and Manton, K.G. and Stallard, E.(1979). The impact of heterogeneity in individual frailty on the dynamics of mortality, Demography, 16, 439-454 https://doi.org/10.2307/2061224