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On the estimators and tests for the semiparametric hazards regression model

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  • Seung-Hwan Lee

    (Illinois Wesleyan University)

Abstract

In the accelerated hazards regression model with censored data, estimation of the covariance matrices of the regression parameters is difficult, since it involves the unknown baseline hazard function and its derivative. This paper provides simple but reliable procedures that yield asymptotically normal estimators whose covariance matrices can be easily estimated. A class of weight functions are introduced to result in the estimators whose asymptotic covariance matrices do not involve the derivative of the unknown hazard function. Based on the estimators obtained from different weight functions, some goodness-of-fit tests are constructed to check the adequacy of the accelerated hazards regression model. Numerical simulations show that the estimators and tests perform well. The procedures are illustrated in the real world example of leukemia cancer. For the leukemia cancer data, the issue of interest is a comparison of two groups of patients that had two different kinds of bone marrow transplants. It is found that the difference of the two groups are well described by a time-scale change in hazard functions, i.e., the accelerated hazards model.

Suggested Citation

  • Seung-Hwan Lee, 2016. "On the estimators and tests for the semiparametric hazards regression model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 531-546, October.
    • Handle: RePEc:spr:lifeda:v:22:y:2016:i:4:d:10.1007_s10985-015-9349-5
    DOI: 10.1007/s10985-015-9349-5
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    References listed on IDEAS

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    1. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    2. Ying Qing Chen, 2001. "Accelerated Hazards Regression Model and Its Adequacy for Censored Survival Data," Biometrics, The International Biometric Society, vol. 57(3), pages 853-860, September.
    3. Lai, Tze Leung & Ying, Zhiliang, 1988. "Stochastic integrals of empirical-type processes with applications to censored regression," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 334-358, November.
    4. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
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