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Profile likelihood estimation for the cox proportional hazards (PH) cure model and standard errors

Author

Listed:
  • Khandoker Akib Mohammad

    (WorkSafe New Zealand)

  • Yuichi Hirose

    (Victoria University of Wellington)

  • Budhi Surya

    (Victoria University of Wellington)

  • Yuan Yao

    (Victoria University of Wellington)

Abstract

In survival analysis, Cox PH cure model has attracted attention for decades. The profile likelihood approach is one of the well known estimation methods employed within the Cox PH cure modeling framework. Typically, the parameters in the profile likelihood are estimated using expectation maximization (EM) algorithm. However, there is a challenge in estimating the standard error (SE) of the estimator in the profile likelihood method. In this paper, we propose a new approach to show the asymptotic normality of the maximum profile likelihood estimator and obtain the closed form expression for the SE of the estimator. Real data example and simulation studyshowed that our method is more computationally efficient and performs better in estimating standard errors compared with the bootstrap methods in ‘smcure’ package (Cai et al. 2012).

Suggested Citation

  • Khandoker Akib Mohammad & Yuichi Hirose & Budhi Surya & Yuan Yao, 2024. "Profile likelihood estimation for the cox proportional hazards (PH) cure model and standard errors," Statistical Papers, Springer, vol. 65(1), pages 181-201, February.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:1:d:10.1007_s00362-022-01387-9
    DOI: 10.1007/s00362-022-01387-9
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    References listed on IDEAS

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    1. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    2. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    3. Zhao, Xiaobing & Zhou, Xian, 2006. "Proportional hazards models for survival data with long-term survivors," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1685-1693, September.
    4. Wenbin Lu, 2008. "Maximum likelihood estimation in the proportional hazards cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 545-574, September.
    5. Fushing Hsieh & Yi-Kuan Tseng & Jane-Ling Wang, 2006. "Joint Modeling of Survival and Longitudinal Data: Likelihood Approach Revisited," Biometrics, The International Biometric Society, vol. 62(4), pages 1037-1043, December.
    6. Hong‐Bin Fang & Gang Li & Jianguo Sun, 2005. "Maximum Likelihood Estimation in a Semiparametric Logistic/Proportional‐Hazards Mixture Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 59-75, March.
    7. Yuichi Hirose, 2011. "Efficiency of profile likelihood in semi-parametric models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1247-1275, December.
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