Communications for Statistical Applications and Methods

  • 제22권4호
  • /
  • Pages.313-320
  • /
  • 2015
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

A Comparison Study of the Test for Right Censored and Grouped Data

  • Park, Hyo-Il (Department of Statistics, Chong-Ju University)
  • 투고 : 2014.12.07
  • 심사 : 2015.06.15
  • 발행 : 2015.07.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this research, we compare the efficiency of two test procedures proposed by Prentice and Gloeckler (1978) and Park and Hong (2009) for grouped data with possible right censored observations. Both test statistics were derived using the likelihood ratio principle, but under different semi-parametric models. We review the two statistics with asymptotic normality and consider obtaining empirical powers through a simulation study. The simulation study considers two types of models the location translation model and the scale model. We discuss some interesting features related to the grouped data and obtain null distribution functions with a re-sampling method. Finally we indicate topics for future research.

키워드

참고문헌

  1. Aalen, O. O. (1980). A model for nonparametric regression analysis of counting processes. In W. Klonecki, A. Kozek and J. Rosinski (Eds.), Mathematical Statistics and Probability Theory, Springer, New York, 1-25.
  2. Aalen, O. O. (1989). A linear regression model for the analysis of life times, Statistics in Medicine, 8, 907-925. https://doi.org/10.1002/sim.4780080803
  3. Cox, D. R. (1972). Regression models and life-tables, Journal of Royal Statistical Society Series B (Methodological), 34, 187-220.
  4. Embury, S. H., Elias, L., Heller, P. H., Hood, C. E., Greenberg, P. L. and Schrier, S. L. (1977). Remission maintenance therapy in acute myelogenous leukemia, Western Journal of Medicine, 126, 267-272.
  5. Gerds, T. A., Kattan, M. W., Schumacher, M. and Yu, C. (2013). Estimating a time-dependent con- cordance index for survival prediction models with covariate dependent censoring, Statistics in Medicine, 32, 2173-2184. https://doi.org/10.1002/sim.5681
  6. Gill, R. D. (1980). Censoring and stochastic integrals, Statistica Neerlandica, 34, 124. https://doi.org/10.1111/j.1467-9574.1980.tb00692.x
  7. Good, P. (2000). Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses (2nd ed.), Springer, New York.
  8. Heitjan, D. F. (1989). Inference from grouped continuous data: A review, Statistical Science, 4, 164-179. https://doi.org/10.1214/ss/1177012601
  9. Huffer, F. W. and McKeague, I. W. (1991). Weighted test squares estimation for Aalen's additive risk model, Journal of the American, 86, 114-129.
  10. Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data, Wiley, New York.
  11. Lin, D. Y. and Ying, Z. (1994). Semiparametric analysis of the additive risk model, Biometrika, 81, 61-71. https://doi.org/10.1093/biomet/81.1.61
  12. Martinussen, T. and Scheike, T. H. (2006). Additive hazards models, In Dynamic Regression Models for Survival Data, Springer, New York, 103-173
  13. Martinussen, T., Vansteelandt, S., Gerster, M. and von Hjelmborg, J. (2011). Estimation of direct effects for survival data by using the Aalen additive hazards model, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73, 773-788. https://doi.org/10.1111/j.1467-9868.2011.00782.x
  14. McKeague, I. W. (1988). A counting process approach to the regression analysis of grouped survival data, Stochastic Processes and Their Applications, 28, 221-239. https://doi.org/10.1016/0304-4149(88)90097-X
  15. McKeague, I. W. and Sasieni, P. D. (1994). A partly parametric additive risk model, Biometrika, 81, 501-514. https://doi.org/10.1093/biomet/81.3.501
  16. Neuhaus, G. (1993). Conditional rank tests for the two-sample problem under random censorship, Annals of Statistics, 21, 1760-1779. https://doi.org/10.1214/aos/1176349396
  17. Park, H. I. (1993). Nonparametric rank-order tests for the right censored and grouped data in linear model, Communications in Statistics-Theory and Methods, 22, 3143-3158. https://doi.org/10.1080/03610929308831207
  18. Park, H. I. and Hong, S. M. (2009). A test procedure for right censored data under the additive model, Communications of the Korean Statistics Society, 16, 325-334. https://doi.org/10.5351/CKSS.2009.16.2.325
  19. 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
  20. Scheike, T. H. (2002). The additive nonparametric and semiparametric Aalen model as the rate function for a counting process, Lifetime Data Analysis, 8, 247-262. https://doi.org/10.1023/A:1015849821021
  21. Yin, G. and Cai, J. (2004). Additive hazards model with multivariate failure time data, Biometrika, 91, 801-818. https://doi.org/10.1093/biomet/91.4.801
  22. Zeng, D. and Cai, J. (2010). A semiparametric additive rate model for recurrent events with an informative terminal event, Biometrika, 97, 699-712. https://doi.org/10.1093/biomet/asq039