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Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Robust estimation and bias-corrected empirical likelihood in generalized linear models with right censored data.

Liugen Xue1, Junshan Xie1, Xiaohui Yang1

  • 1School of Mathematics and Statistics, Henan University, Kaifeng, People's Republic of China.

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This study introduces robust estimation and empirical likelihood for generalized linear models with censored data. The new methods provide reliable regression parameter estimates and confidence regions, outperforming traditional approaches.

Keywords:
Generalized linear modelempirical likelihoodregression parameterright censored datarobust estimation

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Generalized linear models (GLMs) are widely used but sensitive to outliers and censoring.
  • Robust methods are needed for reliable regression parameter estimation in the presence of data anomalies.
  • Empirical likelihood offers a non-parametric approach to inference, but requires adjustments for censored data.

Purpose of the Study:

  • To develop robust estimation techniques for regression parameters in GLMs with right-censored data.
  • To construct a bias-corrected empirical likelihood ratio statistic for accurate confidence region estimation.
  • To propose a method for selecting tuning parameters in the loss function for robust estimation.

Main Methods:

  • A robust estimating equation is proposed for regression parameter estimation.
  • A bias-corrected empirical log-likelihood ratio statistic is developed and its weak convergence is established.
  • A novel method for tuning parameter selection in the loss function is introduced.

Main Results:

  • The proposed robust estimator is consistent and asymptotically normal.
  • The bias-corrected empirical log-likelihood ratio statistic converges weakly to a standard distribution, enabling direct confidence region construction.
  • Simulation studies demonstrate the robustness of the estimator and the superiority of the bias-corrected empirical likelihood over normal approximation.

Conclusions:

  • The developed robust estimation and bias-corrected empirical likelihood methods are effective for GLMs with right-censored data.
  • The proposed techniques offer improved accuracy and reliability for regression parameter inference.
  • The methods are applicable to real-world problems, as demonstrated by an Alzheimer's disease dataset analysis.