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Self-Consistent Nonparametric Maximum Likelihood Estimator of the Bivariate Survivor Function.

R L Prentice1

  • 1Fred Hutchinson Cancer Research Center and University of Washington, Seattle, Washington, United States rprentice@fhcrc.org.

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Summary
This summary is machine-generated.

This study introduces a unique nonparametric maximum likelihood estimator for the bivariate survivor function by redefining the estimation problem. This new method improves efficiency for distribution function estimators.

Keywords:
Bivariate survivor functionCensored dataDabrowska estimatorKaplan–Meier estimatorNon-parametric maximum likelihoodSelf-consistency

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Area of Science:

  • Statistics
  • Survival Analysis

Background:

  • The standard nonparametric likelihood for bivariate survivor functions often leads to over-parameterization and non-unique estimators.
  • Existing methods struggle with uniqueness and parameter estimation, particularly for doubly censored data.

Purpose of the Study:

  • To develop a unique and computationally feasible nonparametric maximum likelihood estimator (NPMLE) for the bivariate survivor function.
  • To address the over-parameterization issue in existing formulations.

Main Methods:

  • Redefining the estimation problem to include parameters for marginal and double failure hazard rates at specific informative grid points.
  • Implementing a two-step procedure: initially using the Dabrowska estimator on a subset of data, then incorporating doubly censored observations via self-consistency.
  • Developing a non-iterative NPMLE for the bivariate survivor function.

Main Results:

  • The proposed approach yields a unique NPMLE for the bivariate survivor function.
  • Simulation studies demonstrate moderate sample size efficiency comparable to the Dabrowska estimator for the survivor function.
  • A notable efficiency improvement was observed for the corresponding distribution function estimator, likely due to the avoidance of negative mass assignments.

Conclusions:

  • The redefined estimation strategy successfully resolves uniqueness issues in nonparametric likelihood estimation for bivariate survival data.
  • The proposed non-iterative method offers an efficient alternative for estimating bivariate survivor and distribution functions.
  • This approach provides a robust framework for handling complex survival data with censoring.