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Spline nonparametric quasi-likelihood regression within the frame of the accelerated failure time model

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  • Yu, Lili
  • Peace, Karl E.

Abstract

The accelerated failure time model provides direct physical interpretation for right censored data. However, the homogeneity of variance assumption of the log transformed data does not always hold. In this paper, we propose using a generalized linear model for right censored data in which we relax the homogeneity assumption. A new semiparametric analysis method is proposed for this model. The method uses nonparametric quasi-likelihood in which the variance function is estimated by polynomial spline regression. This is based on squared residuals from an initial model fit. The rate of convergence of the nonparametric variance function estimator is derived. It is shown that the regression coefficient estimators are asymptotically normally distributed. Simulations show that for finite samples the proposed nonparametric quasi-likelihood method performs well. The new method is illustrated with one dataset.

Suggested Citation

  • Yu, Lili & Peace, Karl E., 2012. "Spline nonparametric quasi-likelihood regression within the frame of the accelerated failure time model," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2675-2687.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:9:p:2675-2687
    DOI: 10.1016/j.csda.2012.02.009
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    References listed on IDEAS

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    1. Huang, Jianhua Z., 1998. "Functional ANOVA Models for Generalized Regression," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 49-71, October.
    2. Lai, Tze Leung & Ying, Zhiliang, 1992. "Linear rank statistics in regression analysis with censored or truncated data," Journal of Multivariate Analysis, Elsevier, vol. 40(1), pages 13-45, January.
    3. Huang, Jianhua Z., 2003. "Asymptotics for polynomial spline regression under weak conditions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 207-216, November.
    4. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    5. Jianhua Z. Huang & Linxu Liu, 2006. "Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk Form," Biometrics, The International Biometric Society, vol. 62(3), pages 793-802, September.
    6. Mai Zhou, 2005. "Empirical likelihood analysis of the rank estimator for the censored accelerated failure time model," Biometrika, Biometrika Trust, vol. 92(2), pages 492-498, June.
    7. Zhezhen Jin & D. Y. Lin & Zhiliang Ying, 2006. "On least-squares regression with censored data," Biometrika, Biometrika Trust, vol. 93(1), pages 147-161, March.
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    Cited by:

    1. Lili Yu & Liang Liu & Ding-Geng(Din) Chen, 2013. "Weighted Least-Squares Method for Right-Censored Data in Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 69(2), pages 358-365, June.

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