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Iterated residuals and time‐varying covariate effects in Cox regression

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  • Angela Winnett
  • Peter Sasieni

Abstract

Summary. The Cox proportional hazards model, which is widely used for the analysis of treatment and prognostic effects with censored survival data, makes the assumption that the hazard ratio is constant over time. Nonparametric estimators have been developed for an extended model in which the hazard ratio is allowed to change over time. Estimators based on residuals are appealing as they are easy to use and relate in a simple way to the more restricted Cox model estimator. After fitting a Cox model and calculating the residuals, one can obtain a crude estimate of the time‐varying coefficients by adding a smooth of the residuals to the initial (constant) estimate. Treating the crude estimate as the fit, one can re‐estimate the residuals. Iteration leads to consistent estimation of the nonparametric time‐varying coefficients. This approach leads to clear guidelines for residual analysis in applications. The results are illustrated by an analysis of the Medical Research Council's myeloma trials, and by simulation.

Suggested Citation

  • Angela Winnett & Peter Sasieni, 2003. "Iterated residuals and time‐varying covariate effects in Cox regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 473-488, May.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:2:p:473-488
    DOI: 10.1111/1467-9868.00397
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    Cited by:

    1. Xiao Song & C. Y. Wang, 2008. "Semiparametric Approaches for Joint Modeling of Longitudinal and Survival Data with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 64(2), pages 557-566, June.
    2. Chin-Tsang Chiang, 2011. "A more flexible joint latent model for longitudinal and survival time data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 151-170, March.
    3. Chin-Tsang Chiang & Mei-Cheng Wang, 2009. "Varying-coefficient model for the occurrence rate function of recurrent events," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 197-213, March.
    4. Guoqing Diao & Donglin Zeng & Song Yang, 2013. "Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data," Biometrics, The International Biometric Society, vol. 69(4), pages 840-849, December.
    5. Wang, Qizhen & Zhu, Yingming & Wang, Yudong, 2017. "The effects of oil shocks on export duration of China," Energy, Elsevier, vol. 125(C), pages 55-61.

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