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Estimating a Treatment Effect in Residual Time Quantiles Under the Additive Hazards Model


  • Luis Alexander Crouch

    (University of Washington)

  • Cheng Zheng

    (University of Wisconsin-Milwaukee)

  • Ying Qing Chen

    () (Fred Hutchinson Cancer Research Center)


Abstract For randomized clinical trials where the endpoint of interest is a time-to-event subject to censoring, estimating the treatment effect has mostly focused on the hazard ratio from the Cox proportional hazards model. Since the model’s proportional hazards assumption is not always satisfied, a useful alternative, the so-called additive hazards model, may instead be used to estimate a treatment effect on the difference of hazard functions. Still, the hazards difference may be difficult to grasp intuitively, particularly in a clinical setting of, e.g., patient counseling, or resource planning. In this paper, we study the quantiles of a covariate’s conditional survival function in the additive hazards model. Specifically, we estimate the residual time quantiles, i.e., the quantiles of survival times remaining at a given time t, conditional on the survival times greater than t, for a specific covariate in the additive hazards model. We use the estimates to translate the hazards difference into the difference in residual time quantiles, which allows a more direct clinical interpretation. We determine the asymptotic properties, assess the performance via Monte-Carlo simulations, and demonstrate the use of residual time quantiles in two real randomized clinical trials.

Suggested Citation

  • Luis Alexander Crouch & Cheng Zheng & Ying Qing Chen, 0. "Estimating a Treatment Effect in Residual Time Quantiles Under the Additive Hazards Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 0, pages 1-18.
  • Handle: RePEc:spr:stabio:v::y::i::d:10.1007_s12561-016-9180-x
    DOI: 10.1007/s12561-016-9180-x

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    References listed on IDEAS

    1. Y. Q. Chen & N. P. Jewell & X. Lei & S. C. Cheng, 2005. "Semiparametric Estimation of Proportional Mean Residual Life Model in Presence of Censoring," Biometrics, The International Biometric Society, vol. 61(1), pages 170-178, March.
    2. 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.
    3. Luis Alexander Crouch & Susanne May & Ying Qing Chen, 2016. "On estimation of covariate-specific residual time quantiles under the proportional hazards model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 299-319, April.
    4. Jong-Hyeon Jeong & Sin-Ho Jung & Joseph P. Costantino, 2008. "Nonparametric Inference on Median Residual Life Function," Biometrics, The International Biometric Society, vol. 64(1), pages 157-163, March.
    5. Peter Hall & Stephen M.-S. Lee & G. Alastair Young, 2000. "Importance of interpolation when constructing double-bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 479-491.
    6. Sin-Ho Jung & Jong-Hyeon Jeong & Hanna Bandos, 2009. "Regression on Quantile Residual Life," Biometrics, The International Biometric Society, vol. 65(4), pages 1203-1212, December.
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