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Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model

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  • Cheng, Philip E.
  • Lin, Gwo Dong

Abstract

Let X and Y be two independent competing lifetimes wih survival functions SF(t) and SG(t). In this paper we, study a proportional-hazards competing risks model characterized by Armitage (1959): SG(t) = SG(t)][beta] for certain positive constant [beta]. The maximum likelihood estimator for SF is proposed, examined and compared with the product limit estimator of Kaplan and Meier (1958). The MLE is shown to be asymptotically more efficient that the PLE under the specified model.

Suggested Citation

  • Cheng, Philip E. & Lin, Gwo Dong, 1987. "Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 75-80, January.
    • Handle: RePEc:eee:stapro:v:5:y:1987:i:1:p:75-80
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    Citations

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    Cited by:

    1. Uña-Álvarez, Jacobo de & González-Manteiga, Wenceslao, 1999. "Strong consistency under proportional censorship when covariables are present," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 283-292, April.
    2. Akim Adekpedjou & Edsel Peña, 2012. "Semiparametric estimation with recurrent event data under informative monitoring," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 733-752.
    3. Uttam Bandyopadhyay & Atanu Biswas & Rahul Bhattacharya, 2010. "A covariate‐adjusted adaptive design for two‐stage clinical trials with survival data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 202-226, May.
    4. Adekpedjou, Akim & Stocker, Russell & De Mel, Withanage A., 2013. "A class of inference procedures for validating the generalized Koziol–Green model with recurrent events," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 83-92.
    5. Winfried Stute, 2008. "Almost sure representations of weighted -statistics with applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 191-205.
    6. Kirmani, Syed N. U. A. & Dauxois, Jean-Yves, 2004. "Testing the Koziol-Green model against monotone conditional odds for censoring," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 327-334, February.
    7. Ghorai, J. K. & Schmitter, J., 1999. "The asymptotic distribution of the suprema of the standardized empirical processes under the Koziol-Green model," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 303-313, February.
    8. Zhang, Haimeng & Rao, M. Bhaskara, 2006. "A note on the generalized maximum likelihood estimator in partial Koziol-Green model," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 813-820, April.
    9. Wen, Xuerong Meggie, 2010. "On sufficient dimension reduction for proportional censorship model with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1975-1982, August.
    10. Zheng, Gang & Gastwirth, Joseph L., 2001. "On the Fisher information in randomly censored data," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 421-426, May.
    11. Noel Veraverbeke & Carmen Cadarso-Suárez, 2000. "Estimation of the conditional distribution in a conditional Koziol-green model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 97-122, June.
    12. Sun, Liuquan & Zhu, Lixing, 2000. "A semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 217-227, July.
    13. Jean-Yves Dauxois & Agathe Guilloux & Syed N. U. A. Kirmani, 2004. "Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling with Censoring," Working Papers 2004-02, Center for Research in Economics and Statistics.
    14. M. A. Jácome & R. Cao, 2008. "Strong representation of the presmoothed quantile function estimator for censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 425-440, November.

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