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EM algorithm for the additive risk mixture cure model with interval-censored data

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  • Xiaoguang Wang

    (Dalian University of Technology)

  • Ziwen Wang

    (Dalian University of Technology)

Abstract

Interval-censored failure time data arise in a number of fields and many authors have recently paid more attention to their analysis. However, regression analysis of interval-censored data under the additive risk model can be challenging in maximizing the complex likelihood, especially when there exists a non-ignorable cure fraction in the population. For the problem, we develop a sieve maximum likelihood estimation approach based on Bernstein polynomials. To relieve the computational burden, an expectation–maximization algorithm by exploiting a Poisson data augmentation is proposed. Under some mild conditions, the asymptotic properties of the proposed estimator are established. The finite sample performance of the proposed method is evaluated by extensive simulations, and is further illustrated through a real data set from the smoking cessation study.

Suggested Citation

  • Xiaoguang Wang & Ziwen Wang, 2021. "EM algorithm for the additive risk mixture cure model with interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 91-130, January.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:1:d:10.1007_s10985-020-09507-z
    DOI: 10.1007/s10985-020-09507-z
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    References listed on IDEAS

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    1. Sudipto Banerjee & Bradley P. Carlin, 2004. "Parametric Spatial Cure Rate Models for Interval-Censored Time-to-Relapse Data," Biometrics, The International Biometric Society, vol. 60(1), pages 268-275, March.
    2. 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.
    3. Hu, Tao & Xiang, Liming, 2016. "Partially linear transformation cure models for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 257-269.
    4. Torben Martinussen, 2002. "Efficient estimation in additive hazards regression with current status data," Biometrika, Biometrika Trust, vol. 89(3), pages 649-658, August.
    5. Yeqian Liu & Tao Hu & Jianguo Sun, 2017. "Regression analysis of current status data in the presence of a cured subgroup and dependent censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 626-650, October.
    6. 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.
    7. Yuan Wu & Christina D. Chambers & Ronghui Xu, 2019. "Semiparametric sieve maximum likelihood estimation under cure model with partly interval censored and left truncated data for application to spontaneous abortion," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 507-528, July.
    8. Shuangge Ma, 2011. "Additive risk model for current status data with a cured subgroup," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 117-134, February.
    9. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    10. Mao, Meng & Wang, Jane-Ling, 2010. "Semiparametric Efficient Estimation for a Class of Generalized Proportional Odds Cure Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 302-311.
    11. Ying Zhang & Lei Hua & Jian Huang, 2010. "A Spline‐Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 338-354, June.
    12. Lianming Wang & Christopher S. McMahan & Michael G. Hudgens & Zaina P. Qureshi, 2016. "A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data," Biometrics, The International Biometric Society, vol. 72(1), pages 222-231, March.
    13. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    14. Xue H. & Lam K.F. & Li G., 2004. "Sieve Maximum Likelihood Estimator for Semiparametric Regression Models With Current Status Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 346-356, January.
    15. D. Ghosh, 2001. "Efficiency Considerations in the Additive Hazards Model with Current Status Data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 367-376, November.
    16. Yu Shen & S. C. Cheng, 1999. "Confidence Bands for Cumulative Incidence Curves Under the Additive Risk Model," Biometrics, The International Biometric Society, vol. 55(4), pages 1093-1100, December.
    17. Hu, Tao & Xiang, Liming, 2013. "Efficient estimation for semiparametric cure models with interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 139-151.
    18. Liu, Hao & Shen, Yu, 2009. "A Semiparametric Regression Cure Model for Interval-Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1168-1178.
    19. Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
    20. Osman, Muhtarjan & Ghosh, Sujit K., 2012. "Nonparametric regression models for right-censored data using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 559-573.
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