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On heteroscedastic hazards regression models: theory and application

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  • Fushing Hsieh

Abstract

A class of non‐proportional hazards regression models is considered to have hazard specifications consisting of a power form of cross‐effects on the base‐line hazard function. The primary goal of these models is to deal with settings in which heterogeneous distribution shapes of survival times may be present in populations characterized by some observable covariates. Although effects of such heterogeneity can be explicitly seen through crossing cumulative hazards phenomena in k‐sample problems, they are barely visible in a one‐sample regression setting. Hence, heterogeneity of this kind may not be noticed and, more importantly, may result in severely misleading inference. This is because the partial likelihood approach cannot eliminate the unknown cumulative base‐line hazard functions in this setting. For coherent statistical inferences, a system of martingale processes is taken as a basis with which, together with the method of sieves, an overidentified estimating equation approach is proposed. A Pearson's χ2 type of goodness‐of‐fit testing statistic is derived as a by‐product. An example with data on gastric cancer patients' survival times is analysed.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:63:y:2001:i:1:p:63-79
    DOI: 10.1111/1467-9868.00276
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    Cited by:

    1. 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.
    2. Lee, Kyu Ha & Chakraborty, Sounak & Sun, Jianguo, 2017. "Variable selection for high-dimensional genomic data with censored outcomes using group lasso prior," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 1-13.
    3. Li, Jianbo & Gu, Minggao & Zhang, Riquan, 2013. "Variable selection for general transformation models with right censored data via nonconcave penalties," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 445-456.
    4. Hsieh Fushing, 2012. "Semiparametric efficient inferences for lifetime regression model with time-dependent covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 1-25, February.
    5. Gu, Minggao & Wu, Yueqin & Huang, Bin, 2014. "Partial marginal likelihood estimation for general transformation models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 1-18.
    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.

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