Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
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모수적과 비모수적 위험률 변화점 통계량 비교

Comparison of parametric and nonparametric hazard change-point estimators

  • 김재희 (덕성여자대학교 정보통계학과) ;
  • 이시은 (아주대학교 의과대학 의과학연구소)
  • Kim, Jaehee (Department of Information and Statistics, Duksung Women's University) ;
  • Lee, Sieun (Office of Biostatistics, School of Medicine, Ajou University)
  • 투고 : 2016.08.10
  • 심사 : 2016.09.24
  • 발행 : 2016.09.30
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초록

위험률에 변화점이 존재할 경우 위험률 변화점에 대한 추정 정확한 모수 추정을 위해 매우 필요하다. 본 연구에서는 한 개 위험률 변화점이 존재하는 경우 위험률의 변화점 추정량에 대한 비교 연구를 수행하였다. 우도함수에 기반한 모수적 방법인 Matthews와 Farewell (1982) 위험률 변화점 추정량과 Nelson-Aalen 누적 위험률에 기반한 비모수적 방법의 Zhang 등 (2014) 위험률 변화점 통계량을 고찰하여 특성을 파악하였다. 모의실험에서 지수분포를 따르는 생존데이터에 대해 위험률 변화점이 한 개 있는 경우 중도절단이 없는 경우와 중도절단이 있는 경위험률 추정량의 능력을 평균제곱오차를 계산하여 비교하였다. 실제 데이터에 대한 적용으로 백혈병 생존데이터와 원발성 담백증 경화 생존데이터에 대해 위험률 변화점을 추정하고 비교해 보았다.

When there exists a change-point in hazard function, it should be estimated for exact parameter or hazard estimation. In this research, we compare the hazard change-point estimators. Matthews and Farewell (1982) parametric change-point estimator is based on the likelihood and Zhang et al. (2014) nonparametric estimator is based on the Nelson-Aalen cumulative hazard estimator. Simulation study is done for the data from exponential distribution with one hazard change-point. The simulated data generated without censoring and the data with right censoring are considered. As real data applications, the change-point estimates are computed for leukemia data and primary biliary cirrhosis data.

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참고문헌

  1. Chang, I. S., Chen, C. H. and Hsiung, C. A. (1994). Estimation in change-point hazard rate models with random censorship. IMS Lecture Notes - Monograph Series, 23, 78-92.
  2. Dupuy, J. F. (2006). Estimation in a change-point hazard regression model. Statistics & Probability Letters, 76, 182-190. https://doi.org/10.1016/j.spl.2005.07.013
  3. Gijbels, I. and Gurler, U. (2003). Estimation of a change point in a hazard function based on censored data. Lifetime Data Analysis, 9, 395-411. https://doi.org/10.1023/B:LIDA.0000012424.71723.9d
  4. Goodman, M. S., Li, Y. and Tiwari, R. C. (2010). Detecting multiple change points in piecewise constant hazard functions. Journal of Applied Statistics, 38, 11, 2523-2532. https://doi.org/10.1080/02664763.2011.559209
  5. Henderson, R. (1990). A problem with the likelihood ratio test for a change-point hazard rate model. Biometrika, 77, 835-843. https://doi.org/10.1093/biomet/77.4.835
  6. Jeong, K. M. (1998). Nonparametric estimation of hazard rates change-point. The Korean Journal of Applied Statistics, 11, 163-175.
  7. Jeong, K. M. and Han, M. H. (1998). Estimation for change-point model of hazard rate. Communications for Statistical Applications and Methods, 5, 477-489.
  8. Kim, J. (2009). A change-point estimator with the hazard ratio. Journal of the Korean Statistical Society, 38, 377-382. https://doi.org/10.1016/j.jkss.2009.02.004
  9. Lee, S. and Shim, B. Y. and Kim, J. (2015) Estimation of hazard function and hazard change-point for the rectal cancer data. Journal of the Korean Data & Information Science Society, 26, 1225-1238. https://doi.org/10.7465/jkdi.2015.26.6.1225
  10. Loader, C. R. (1991). Inference for a hazard rate change point. Biometrika, 78, 749-757. https://doi.org/10.1093/biomet/78.4.749
  11. Luo, X., Turnbull, B. W. and Clark, L. C. (1997). Likelihood ratio tests for a changepoint with survival data. Biometrika, 84, 555-565. https://doi.org/10.1093/biomet/84.3.555
  12. Maller, R. A. and Zhou, X. (1996). Survival Analysis with Long-term Survivors, Wiley, New York.
  13. Matthews, D. E. and Farewell, V. T. (1982). On testing for constant hazard against a change-point alternative. Biometrics, 38, 463-468. https://doi.org/10.2307/2530460
  14. Matthews, D. E., Farewell, V. T. and Pyke, R. (1985). Asymptotic score-statistic processes and tests for constant hazard against a change-point alternative. The Annals of Statistics, 13, 583-591. https://doi.org/10.1214/aos/1176349540
  15. Nguyen, H. T., Rogers, G. S. and Walker, E. A. (1984). Estimation in change-point hazard rate models. Biometrika, 71, 299-304. https://doi.org/10.1093/biomet/71.2.299
  16. Pham, T. D. and Nguyen, H. T. (1990). Strong consistency of the maximum likelihood estimators in the change-point hazard bate model. Statistics: A Journal of Theoretical and Applied Statistics, 21, 203-216.
  17. Shin, S. B. and Kim, Y. J. (2014). Statistical analysis of recurrent gap time events with incomplete observation gaps. Journal of the Korean Data & Information Science Society, 25, 327-336. https://doi.org/10.7465/jkdi.2014.25.2.327
  18. Williams, M. R. and Kim, D. (2011). Likelihood ratio tests for continuous monotone hazards with an unknown change point. Statistics & Probability Letters, 81, 1599-1603. https://doi.org/10.1016/j.spl.2011.06.013
  19. Worsley, K. J. (1988). Exact percentage points of the likelihood-ratio test for a change-point hazard-rate model. Biometrics, 44, 259-263. https://doi.org/10.2307/2531914
  20. Yao, Y. C. (1986). Maximum likelihood estimation in hazard rate models with a change-point. Communications in Statistics - Theory and Methods, 15, 2455-2466. https://doi.org/10.1080/03610928608829261
  21. Zhang, W., Qian, L. and Li, Y. (2014). Semiparametric sequential testing for multiple change points in piecewise constant hazard functions with long-term survivors. Communications in Statistics - Simulation and Computation, 43, 1685-1699. https://doi.org/10.1080/03610918.2012.742106
  22. Zhao, X. B., Wu, X. Y. and Zhou, X. (2009). A change-point model for survival data with long-term survivors. Statistica Sinica, 19, 377-390.

피인용 문헌

  1. A Bayesian time series model with multiple structural change-points for electricity data vol.28, pp.4, 2016, https://doi.org/10.7465/jkdi.2017.28.4.889