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On the Breslow estimator.

D Y Lin1

  • 1Department of Biostatistics, University of North Carolina, CB#7420, Chapel Hill, NC 27599-7420, USA. lin@bios.unc.edu

Lifetime Data Analysis
|September 5, 2007
PubMed
Summary
This summary is machine-generated.

The Breslow estimator, developed for proportional hazards regression, is a key tool in survival analysis. It significantly impacts both the theory and practical applications of analyzing censored data.

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Inference

Background:

  • Cox's proportional hazards regression is a foundational model in survival analysis.
  • Maximum likelihood estimation is a standard statistical technique.
  • Censored data presents unique challenges in statistical modeling.

Purpose of the Study:

  • To describe the Breslow estimator for the cumulative baseline hazard function.
  • To highlight the impact of the Breslow estimator on survival analysis.
  • To provide context for the estimator's development within Cox regression.

Main Methods:

  • The paper discusses the historical context of the Breslow estimator's development.
  • It reviews the mathematical properties of the maximum likelihood estimator.

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  • The impact is illustrated through its application in Cox regression and semiparametric inference.

    • Main Results:

    • The Breslow estimator provides a practical maximum likelihood estimate for the cumulative baseline hazard function.
    • This estimator is widely adopted in biostatistical practice.
    • It has been instrumental in advancing semiparametric inference for censored data.

    Conclusions:

    • The Breslow estimator is a cornerstone of modern survival analysis.
    • Its development has profoundly influenced both theoretical advancements and practical applications.
    • The estimator remains highly relevant for analyzing time-to-event data.