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Efficiency of the Breslow estimator in semiparametric transformation models

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  • Theresa P. Devasia

    (National Cancer Institute)

  • Alexander Tsodikov

    (University of Michigan)

Abstract

Semiparametric transformation models for failure time data consist of a parametric regression component and an unspecified cumulative baseline hazard. The nonparametric maximum likelihood estimator (NPMLE) of the cumulative baseline hazard can be summarized in terms of weights introduced into a Breslow-type estimator (Weighted Breslow). At any given time point, the weights invoke an integral over the future of the cumulative baseline hazard, which presents theoretical and computational challenges. A simpler non-MLE Breslow-type estimator (Breslow) was derived earlier from a martingale estimating equation (MEE) setting observed and expected counts of failures equal, conditional on the past history. Despite much successful theoretical and computational development, the simpler Breslow estimator continues to be commonly used as a compromise between simplicity and perceived loss of full efficiency. In this paper we derive the relative efficiency of the Breslow estimator and consider the properties of the two estimators using simulations and real data on prostate cancer survival.

Suggested Citation

  • Theresa P. Devasia & Alexander Tsodikov, 2024. "Efficiency of the Breslow estimator in semiparametric transformation models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(2), pages 291-309, April.
    • Handle: RePEc:spr:lifeda:v:30:y:2024:i:2:d:10.1007_s10985-023-09611-w
    DOI: 10.1007/s10985-023-09611-w
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    References listed on IDEAS

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    1. A. Tsodikov, 2003. "Semiparametric models: a generalized self‐consistency approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 759-774, August.
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    3. Yi-Hau Chen, 2009. "Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models," Biometrika, Biometrika Trust, vol. 96(3), pages 591-600.
    4. Donglin Zeng & D. Y. Lin, 2006. "Efficient estimation of semiparametric transformation models for counting processes," Biometrika, Biometrika Trust, vol. 93(3), pages 627-640, September.
    5. Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
    6. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
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