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Confidence bands for the difference of two survival functions under the additive risk model

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  • Jimin Lee
  • Seunggeun Hyun

Abstract

In many clinical studies, a commonly encountered problem is to compare the survival probabilities of two treatments for a given patient with a certain set of covariates, and there is often a need to make adjustments for other covariates that may affect outcomes. One approach is to plot the difference between the two subject-specific predicted survival estimates with a simultaneous confidence band. Such a band will provide useful information about when these two treatments differ and which treatment has a better survival probability. In this paper, we show how to construct such a band based on the additive risk model and we use the martingale central limit theorem to derive its asymptotic distribution. The proposed method is evaluated from a simulation study and is illustrated with two real examples.

Suggested Citation

  • Jimin Lee & Seunggeun Hyun, 2011. "Confidence bands for the difference of two survival functions under the additive risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 785-797, February.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:4:p:785-797
    DOI: 10.1080/02664761003692308
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    References listed on IDEAS

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    1. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
    2. Yu Shen & S. C. Cheng, 1999. "Confidence Bands for Cumulative Incidence Curves Under the Additive Risk Model," Biometrics, The International Biometric Society, vol. 55(4), pages 1093-1100, December.
    3. Gang Li & Ingrid Van Keilegom, 2002. "Likelihood Ratio Confidence Bands in Non–parametric Regression with Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 547-562, September.
    4. McKeague, Ian W. & Zhao, Yichuan, 2006. "Width-scaled confidence bands for survival functions," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 327-339, February.
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    Cited by:

    1. Luis Alexander Crouch & Cheng Zheng & Ying Qing Chen, 2017. "Estimating a Treatment Effect in Residual Time Quantiles Under the Additive Hazards Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 298-315, June.
    2. Nubyra Ahmed & Sundarraman Subramanian, 2016. "Semiparametric simultaneous confidence bands for the difference of survival functions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 504-530, October.
    3. Shoubhik Mondal & Sundarraman Subramanian, 2016. "Simultaneous confidence bands for Cox regression from semiparametric random censorship," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 122-144, January.
    4. Lee Seung-Hwan & Lee Eun-Joo, 2014. "A martingale approach to estimating confidence band with censored data," Monte Carlo Methods and Applications, De Gruyter, vol. 20(4), pages 237-243, December.

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