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Explained randomness in proportional hazards models.

John O'Quigley1, Ronghui Xu, Janez Stare

  • 1Institut Curie, Paris. joq@biomath.jussieu.fr

Statistics in Medicine
|November 9, 2004
PubMed
Summary
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This study unifies two coefficients of explained randomness for proportional hazards regression, showing they are equivalent under independent censoring. It also addresses a SAS coefficient, proposing a fix for censored data analysis.

Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Modeling

Background:

  • Explained randomness is a measure for non-linear models, analogous to explained variation.
  • Kullback-Leibler information gain is central to the concept of explained randomness.
  • Proportional hazards regression is a key statistical method for analyzing time-to-event data.

Purpose of the Study:

  • To demonstrate the equivalence of two coefficients of explained randomness (Kent & O'Quigley and Xu & O'Quigley) for proportional hazards regression under independent censoring.
  • To show that the simpler inferential framework of Xu & O'Quigley can be applied to the Kent & O'Quigley coefficient.
  • To evaluate a commonly used SAS coefficient for explained randomness and propose an adjustment for censored data.

Main Methods:

Related Experiment Videos

  • Theoretical comparison of two coefficients of explained randomness in proportional hazards models.
  • Mathematical derivation under the assumption of independent censoring.
  • Analysis of a sample-based coefficient from the SAS statistical package.

    • Main Results:

    • The population coefficients of Kent & O'Quigley and Xu & O'Quigley are shown to coincide under independent censoring.
    • The simpler inference methods for Xu & O'Quigley are applicable to the Kent & O'Quigley coefficient.
    • The SAS coefficient for explained randomness is suitable for uncensored data but requires modification for independent censoring.

    Conclusions:

    • The equivalence of coefficients simplifies inference in proportional hazards regression.
    • A practical adjustment is proposed for using the SAS coefficient in the presence of censoring.
    • The findings enhance the utility of explained randomness measures in survival analysis.