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Vertical modeling: analysis of competing risks data with a cure fraction

Author

Listed:
  • Mioara Alina Nicolaie

    (Catholic University of Louvain)

  • Jeremy M. G. Taylor

    (University of Michigan)

  • Catherine Legrand

    (Catholic University of Louvain)

Abstract

In this paper, we extend the vertical modeling approach for the analysis of survival data with competing risks to incorporate a cure fraction in the population, that is, a proportion of the population for which none of the competing events can occur. The proposed method has three components: the proportion of cure, the risk of failure, irrespective of the cause, and the relative risk of a certain cause of failure, given a failure occurred. Covariates may affect each of these components. An appealing aspect of the method is that it is a natural extension to competing risks of the semi-parametric mixture cure model in ordinary survival analysis; thus, causes of failure are assigned only if a failure occurs. This contrasts with the existing mixture cure model for competing risks of Larson and Dinse, which conditions at the onset on the future status presumably attained. Regression parameter estimates are obtained using an EM-algorithm. The performance of the estimators is evaluated in a simulation study. The method is illustrated using a melanoma cancer data set.

Suggested Citation

  • Mioara Alina Nicolaie & Jeremy M. G. Taylor & Catherine Legrand, 2019. "Vertical modeling: analysis of competing risks data with a cure fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 1-25, January.
    • Handle: RePEc:spr:lifeda:v:25:y:2019:i:1:d:10.1007_s10985-018-9417-8
    DOI: 10.1007/s10985-018-9417-8
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    References listed on IDEAS

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    1. Peng, Yingwei, 2003. "Estimating baseline distribution in proportional hazards cure models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 187-201, February.
    2. Yingwei Peng & Jeremy M. G. Taylor, 2017. "Residual-based model diagnosis methods for mixture cure models," Biometrics, The International Biometric Society, vol. 73(2), pages 495-505, June.
    3. 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.
    4. Sanjib Basu & Ram C. Tiwari, 2010. "Breast cancer survival, competing risks and mixture cure model: a Bayesian analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 307-329, April.
    5. 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.
    6. Martin G. Larson & Gregg E. Dinse, 1985. "A Mixture Model for the Regression Analysis of Competing Risks Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 201-211, November.
    7. Choi, K. C. & Zhou, X., 2002. "Large Sample Properties of Mixture Models with Covariates for Competing Risks," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 331-366, August.
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