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A semi-parametric generalization of the Cox proportional hazards regression model: Inference and applications

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  • Devarajan, Karthik
  • Ebrahimi, Nader

Abstract

The assumption of proportional hazards (PH) fundamental to the Cox PH model sometimes may not hold in practice. In this paper, we propose a generalization of the Cox PH model in terms of the cumulative hazard function taking a form similar to the Cox PH model, with the extension that the baseline cumulative hazard function is raised to a power function. Our model allows for interaction between covariates and the baseline hazard and it also includes, for the two sample problem, the case of two Weibull distributions and two extreme value distributions differing in both scale and shape parameters. The partial likelihood approach can not be applied here to estimate the model parameters. We use the full likelihood approach via a cubic B-spline approximation for the baseline hazard to estimate the model parameters. A semi-automatic procedure for knot selection based on Akaike's information criterion is developed. We illustrate the applicability of our approach using real-life data.

Suggested Citation

  • Devarajan, Karthik & Ebrahimi, Nader, 2011. "A semi-parametric generalization of the Cox proportional hazards regression model: Inference and applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 667-676, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:667-676
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    References listed on IDEAS

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    1. Sheila M. Gore & Stuart J. Pocock & Gillian R. Kerr, 1984. "Regression Models and Non‐Proportional Hazards in the Analysis of Breast Cancer Survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 176-195, June.
    2. Fushing Hsieh, 2001. "On heteroscedastic hazards regression models: theory and application," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 63-79.
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    Cited by:

    1. Jiajia Zhang & Timothy Hanson & Haiming Zhou, 2019. "Bayes factors for choosing among six common survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 361-379, April.
    2. Marschner, Ian C. & Gillett, Alexandra C. & O’Connell, Rachel L., 2012. "Stratified additive Poisson models: Computational methods and applications in clinical epidemiology," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1115-1130.
    3. Gradowska, P.L. & Cooke, R.M., 2012. "Least squares type estimation for Cox regression model and specification error," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2288-2302.
    4. M. Avendaño & M. Pardo, 2016. "A semiparametric generalized proportional hazards model for right-censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 353-384, April.
    5. Suraj Peri & Karthik Devarajan & Dong-Hua Yang & Alfred G Knudson & Siddharth Balachandran, 2013. "Meta-Analysis Identifies NF-κB as a Therapeutic Target in Renal Cancer," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-1, October.
    6. Devarajan, Karthik & Ebrahimi, Nader, 2013. "On penalized likelihood estimation for a non-proportional hazards regression model," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1703-1710.
    7. Kulinskaya, Elena & Gitsels, Lisanne A. & Bakbergenuly, Ilyas & Wright, Nigel R., 2020. "Calculation of changes in life expectancy based on proportional hazards model of an intervention," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 27-35.

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