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Proportional hazards estimate of the conditional survival function

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  • Ronghui Xu
  • John O'Quigley

Abstract

We introduce a new estimator of the conditional survival function given some subset of the covariate values under a proportional hazards regression. The new estimate does not require estimating the base‐line cumulative hazard function. An estimate of the variance is given and is easy to compute, involving only those quantities that are routinely calculated in a Cox model analysis. The asymptotic normality of the new estimate is shown by using a central limit theorem for Kaplan–Meier integrals. We indicate the straightforward extension of the estimation procedure under models with multiplicative relative risks, including non‐proportional hazards, and to stratified and frailty models. The estimator is applied to a gastric cancer study where it is of interest to predict patients' survival based only on measurements obtained before surgery, the time at which the most important prognostic variable, stage, becomes known.

Suggested Citation

  • Ronghui Xu & John O'Quigley, 2000. "Proportional hazards estimate of the conditional survival function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 667-680.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:4:p:667-680
    DOI: 10.1111/1467-9868.00256
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    Cited by:

    1. Wei Zhao & Ying Qing Chen & Li Hsu, 2017. "On estimation of time-dependent attributable fraction from population-based case-control studies," Biometrics, The International Biometric Society, vol. 73(3), pages 866-875, September.
    2. van Geloven, N. & He, Y. & Zwinderman, A.H. & Putter, H., 2021. "Estimation of incident dynamic AUC in practice," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    3. Patrick J. Heagerty & Yingye Zheng, 2005. "Survival Model Predictive Accuracy and ROC Curves," Biometrics, The International Biometric Society, vol. 61(1), pages 92-105, March.
    4. P. Saha & P. J. Heagerty, 2010. "Time-Dependent Predictive Accuracy in the Presence of Competing Risks," Biometrics, The International Biometric Society, vol. 66(4), pages 999-1011, December.
    5. Sean M. Devlin & Mithat Gönen & Glenn Heller, 2020. "Measuring the temporal prognostic utility of a baseline risk score," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 856-871, October.
    6. Patrick Heagerty & Yingye Zheng, 2004. "Survival Model Predictive Accuracy and ROC Curves," UW Biostatistics Working Paper Series 1051, Berkeley Electronic Press.
    7. Xiaochun Li & Ronghui Xu, 2004. "Empirical and Kernel Estimation of Covariate Distribution Conditional on Survival Time," Harvard University Biostatistics Working Paper Series 1011, Berkeley Electronic Press.
    8. Li, Xiaochun & Xu, Ronghui, 2006. "Empirical and kernel estimation of covariate distribution conditional on survival time," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3629-3643, August.
    9. Shiyuan Chen & Sally Wallace, 2008. "Determinants of Education Duration in Jamaica," International Center for Public Policy Working Paper Series, at AYSPS, GSU paper0803, International Center for Public Policy, Andrew Young School of Policy Studies, Georgia State University.

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