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Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models

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  • Yi-Hau Chen

Abstract

A semiparametric transformation model comprises a parametric component for covariate effects and a nonparametric component for the baseline hazard/intensity. The Breslow-type estimator has been proposed for estimating the nonparametric component in some inefficient estimation procedures. We show that introducing weights into this estimator leads to nonparametric maximum likelihood estimation, with the weights depending on the martingale residuals. The weighted Breslow-type estimator suggests an iterative reweighting algorithm for nonparametric maximum likelihood estimation, which can be implemented by a weighted variant of the existing algorithms for inefficient estimation, and can be computationally more efficient than an em -type algorithm. The weighting idea is further extended to semiparametric transformation models with mismeasured covariates. Copyright 2009, Oxford University Press.

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  • Yi-Hau Chen, 2009. "Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models," Biometrika, Biometrika Trust, vol. 96(3), pages 591-600.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:3:p:591-600
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    File URL: http://hdl.handle.net/10.1093/biomet/asp032
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    Cited by:

    1. Qui Tran & Kelley M. Kidwell & Alex Tsodikov, 2018. "A joint model of cancer incidence, metastasis, and mortality," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 385-406, July.
    2. Xi Ning & Yinghao Pan & Yanqing Sun & Peter B. Gilbert, 2023. "A semiparametric Cox–Aalen transformation model with censored data," Biometrics, The International Biometric Society, vol. 79(4), pages 3111-3125, December.
    3. Sangbum Choi & Xuelin Huang, 2014. "Maximum likelihood estimation of semiparametric mixture component models for competing risks data," Biometrics, The International Biometric Society, vol. 70(3), pages 588-598, September.
    4. Ya-Hsuan Hu & Takeshi Emura, 2015. "Maximum likelihood estimation for a special exponential family under random double-truncation," Computational Statistics, Springer, vol. 30(4), pages 1199-1229, December.
    5. Yi‐Hau Chen, 2010. "Semiparametric marginal regression analysis for dependent competing risks under an assumed copula," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 235-251, March.
    6. Chi-Chung Wen & Yi-Hau Chen, 2014. "Semiparametric analysis of incomplete current status outcome data under transformation models," Biometrics, The International Biometric Society, vol. 70(2), pages 335-345, June.
    7. Sangbum Choi & Xuelin Huang, 2012. "A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1126-1135, December.
    8. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    9. Chyong-Mei Chen & Pao-sheng Shen & Yi Liu, 2021. "On semiparametric transformation model with LTRC data: pseudo likelihood approach," Statistical Papers, Springer, vol. 62(1), pages 3-30, February.
    10. John D. Rice & Alex Tsodikov, 2017. "Semiparametric time-to-event modeling in the presence of a latent progression event," Biometrics, The International Biometric Society, vol. 73(2), pages 463-472, June.
    11. Chia-Hui Huang, 2019. "Mixture regression models for the gap time distributions and illness–death processes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 168-188, January.
    12. Guoqing Diao & Donglin Zeng & Song Yang, 2013. "Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data," Biometrics, The International Biometric Society, vol. 69(4), pages 840-849, December.
    13. Chyong-Mei Chen & Pao-Sheng Shen, 2018. "Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 250-272, April.

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