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Likelihood approaches to the non-parametric two-sample problem for right-censored data.

James F Troendle1, Kai F Yu

  • 1Biometry and Mathematical Statistics Branch, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, National Institutes of Health, DHHS, Bethesda, MD 20892, USA. jt3t@nih.gov

Statistics in Medicine
|October 12, 2005
PubMed
Summary

Non-parametric likelihood methods offer robust statistical tests for comparing two groups with censored data. These novel approaches demonstrate excellent error control and superior power for certain alternatives compared to existing methods.

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • The two-sample problem with random right-censoring is a common challenge in statistical analysis.
  • Existing methods may have limitations in power or applicability for certain data distributions.

Purpose of the Study:

  • To introduce non-parametric likelihood techniques for hypothesis testing in the presence of random right-censoring.
  • To evaluate the performance of these new methods for both identity and non-parametric Behrens-Fisher hypotheses.

Main Methods:

  • Development of non-parametric likelihood-based tests for the identity and non-parametric Behrens-Fisher hypotheses.
  • Utilizing an imputed permutation distribution for the identity hypothesis.
  • Employing simulation from constrained non-parametric maximum likelihood estimates for the non-parametric Behrens-Fisher hypothesis.

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Main Results:

  • The proposed tests exhibit excellent control of Type I error rates, even with small sample sizes.
  • Likelihood-based methods show comparable power to the logrank test for Lehmann-type alternatives.
  • Significant power advantage observed for non-Lehmann-type alternatives compared to the logrank test.

Conclusions:

  • Non-parametric likelihood techniques provide effective and powerful tools for analyzing two-sample problems with censored data.
  • These methods offer a valuable alternative to existing approaches, particularly for non-Lehmann-type alternatives.