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Hazard‐based nonparametric survivor function estimation

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  • Ross L. Prentice
  • F. Zoe Moodie
  • Jianrong Wu

Abstract

Summary. A representation is developed that expresses the bivariate survivor function as a function of the hazard function for truncated failure time variables. This leads to a class of nonparametric survivor function estimators that avoid negative mass. The transformation from hazard function to survivor function is weakly continuous and compact differentiable, so that such properties as strong consistency, weak convergence to a Gaussian process and bootstrap applicability for a hazard function estimator are inherited by the corresponding survivor function estimator. The set of point mass assignments for a survivor function estimator is readily obtained by using a simple matrix calculation on the set of hazard rate estimators. Special cases arise from a simple empirical hazard rate estimator, and from an empirical hazard rate estimator following the redistribution of singly censored observations within strips. The latter is shown to equal van der Laan's repaired nonparametric maximum likelihood estimator, for which a Greenwood‐like variance estimator is given. Simulation studies are presented to compare the moderate sample performance of various nonparametric survivor function estimators.

Suggested Citation

  • Ross L. Prentice & F. Zoe Moodie & Jianrong Wu, 2004. "Hazard‐based nonparametric survivor function estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 305-319, May.
  • Handle: RePEc:bla:jorssb:v:66:y:2004:i:2:p:305-319
    DOI: 10.1046/j.1369-7412.2003.05182.x
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    Cited by:

    1. Alan D. Hutson, 2016. "Nonparametric rank based estimation of bivariate densities given censored data conditional on marginal probabilities," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-14, December.
    2. Franc{c}ois Dufresne & Enkelejd Hashorva & Gildas Ratovomirija & Youssouf Toukourou, 2016. "On bivariate lifetime modelling in life insurance applications," Papers 1601.04351, arXiv.org.
    3. Ying Guo & Amita K. Manatunga, 2007. "Nonparametric Estimation of the Concordance Correlation Coefficient under Univariate Censoring," Biometrics, The International Biometric Society, vol. 63(1), pages 164-172, March.
    4. Dai, Hongsheng & Bao, Yanchun, 2009. "An inverse probability weighted estimator for the bivariate distribution function under right censoring," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1789-1797, August.
    5. Lopez, Olivier, 2012. "A generalization of the Kaplan–Meier estimator for analyzing bivariate mortality under right-censoring and left-truncation with applications in model-checking for survival copula models," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 505-516.

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