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

Luis Alexander Crouch, Cheng Zheng, Ying Qing Chen

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)298-315
Number of pages18
JournalStatistics in Biosciences
Issue number1
StatePublished - Jun 1 2017
Externally publishedYes


  • Clinical trial
  • Covariate-specific estimate
  • Hazard function
  • Remaining time
  • Survival analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology (miscellaneous)


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