Lifetime Data Analysis

, 15:441 | Cite as

Confidence intervals for the first crossing point of two hazard functions

  • Ming-Yen Cheng
  • Peihua Qiu
  • Xianming Tan
  • Dongsheng Tu


The phenomenon of crossing hazard rates is common in clinical trials with time to event endpoints. Many methods have been proposed for testing equality of hazard functions against a crossing hazards alternative. However, there has been relatively few approaches available in the literature for point or interval estimation of the crossing time point. The problem of constructing confidence intervals for the first crossing time point of two hazard functions is considered in this paper. After reviewing a recent procedure based on Cox proportional hazard modeling with Box-Cox transformation of the time to event, a nonparametric procedure using the kernel smoothing estimate of the hazard ratio is proposed. The proposed procedure and the one based on Cox proportional hazard modeling with Box-Cox transformation of the time to event are both evaluated by Monte–Carlo simulations and applied to two clinical trial datasets.


Clinical trials Crossing point Hazard functions Kernel estimates Undersmoothing bandwidth 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Ming-Yen Cheng
    • 1
    • 2
  • Peihua Qiu
    • 3
  • Xianming Tan
    • 4
  • Dongsheng Tu
    • 4
  1. 1.Department of Statistical ScienceUniversity College LondonLondonUK
  2. 2.Department of MathematicsNational Taiwan UniversityTeipeiTaiwan
  3. 3.School of StatisticsUniversity of MinnesotaMinneapolisUSA
  4. 4.NCIC Clinical Trials Group, Cancer Research InstituteQueen’s UniversityKingstonCanada

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