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Robust Wald-type tests under random censoring.

Abhik Ghosh1, Ayanendranath Basu1, Leandro Pardo2

  • 1Interdisciplinary Statistical Research Unit, Indian Statistical Institute, Kolkata, India.

Statistics in Medicine
|December 29, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces robust statistical tests for censored survival data, crucial for clinical trials. It provides a consistent variance estimator, enabling reliable hypothesis testing even with outliers.

Keywords:
M-estimatorclinical trial analysisinformative censoringminimum density power divergence estimatorrandom censored datarobust hypothesis testing

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Inference

Background:

  • Randomly censored survival data are common in biomedical and clinical research.
  • Existing parametric tests are sensitive to outliers, limiting their reliability.
  • Robust estimators exist, but robust testing procedures for censored data are scarce.

Purpose of the Study:

  • To develop robust statistical tests for hypothesis significance testing with randomly censored data.
  • To address the challenge of estimating asymptotic variance for robust estimators under unknown censoring distributions.
  • To introduce a class of robust Wald-type tests applicable to various hypothesis testing scenarios.

Main Methods:

  • Proposing a consistent estimator for the asymptotic variance of M-estimators with randomly censored data.
  • Developing and studying a class of robust Wald-type tests for simple and composite hypotheses.
  • Discussing robust tests for comparing independent censored samples and for one-sided alternatives.
  • Utilizing minimum density power divergence estimators for test construction.

Main Results:

  • A novel, consistent estimator for the asymptotic variance of M-estimators is proposed for censored data.
  • A class of robust Wald-type tests is introduced and studied for parametric hypotheses.
  • The proposed tests demonstrate robustness against outliers and unknown censoring distributions.
  • The methodology is validated using clinical trial data and other medical datasets.

Conclusions:

  • The developed robust tests offer a reliable alternative to nonrobust likelihood-based methods for censored survival data.
  • This work provides a foundational step towards robust hypothesis testing in the presence of censoring.
  • The proposed methods enhance the validity of statistical inference in clinical trials and biomedical research.