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Model assisted Cox regression

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  • Mondal, Shoubhik
  • Subramanian, Sundarraman

Abstract

Semiparametric random censorship (SRC) models (Dikta, 1998) [7], derive their rationale from their ability to utilize parametric ideas within the random censorship environment. An extension of this approach is developed for Cox regression, producing new estimators of the regression parameter and baseline cumulative hazard function. Under correct parametric specification, the proposed estimator of the regression parameter and the baseline cumulative hazard function are shown to be asymptotically as or more efficient than their standard Cox regression counterparts. Numerical studies are presented to showcase the efficacy of the proposed approach even under significant misspecification. Two real examples are provided. A further extension to the case of missing censoring indicators is also developed and an illustration with pseudo-real data is provided.

Suggested Citation

  • Mondal, Shoubhik & Subramanian, Sundarraman, 2014. "Model assisted Cox regression," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 281-303.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:281-303
    DOI: 10.1016/j.jmva.2013.09.013
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    References listed on IDEAS

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    1. 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.
    2. Anastasios A. Tsiatis, 2002. "Multiple imputation methods for testing treatment differences in survival distributions with missing cause of failure," Biometrika, Biometrika Trust, vol. 89(1), pages 238-244, March.
    3. Ming Yuan, 2005. "Semiparametric censorship model with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 489-514, December.
    4. Subramanian, Sundarraman, 2012. "Model-based likelihood ratio confidence intervals for survival functions," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 626-635.
    5. 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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    Cited by:

    1. Nubyra Ahmed & Sundarraman Subramanian, 2016. "Semiparametric simultaneous confidence bands for the difference of survival functions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 504-530, October.
    2. Shoubhik Mondal & Sundarraman Subramanian, 2016. "Simultaneous confidence bands for Cox regression from semiparametric random censorship," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 122-144, January.
    3. Dikta, Gerhard & Reißel, Martin & Harlaß, Carsten, 2016. "Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 273-284.
    4. Subramanian, Sundarraman, 2016. "Bootstrap likelihood ratio confidence bands for survival functions under random censorship and its semiparametric extension," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 58-81.

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