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This study introduces new statistical methods for analyzing right-censored data with missing indicators, offering robust estimations for distribution functions and quantile differences. These techniques improve data analysis accuracy in survival studies.

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Handling right-censored data is crucial in survival analysis.
  • Missing censoring indicators introduce complexity in statistical modeling.
  • Accurate estimation of distribution functions and quantile differences is essential for reliable inference.

Purpose of the Study:

  • To develop and validate novel estimators for distribution functions with right-censored data and missing at random censoring indicators.
  • To propose empirical likelihood-based methods for estimating two-sample quantile differences, incorporating auxiliary information.
  • To establish the theoretical properties and assess the performance of the proposed statistical methods.

Main Methods:

  • Definition of estimators for distribution functions under missing at random censoring.
  • Establishment of strong representations and asymptotic normality for the proposed estimators.
  • Application of the empirical likelihood method to derive maximum empirical likelihood estimators and smoothed log-empirical likelihood ratios for quantile differences.
  • Derivation of asymptotic distributions for the two-sample quantile difference estimators.

Main Results:

  • Strong representations and asymptotic normality were established for the distribution function estimators.
  • Asymptotic distributions were proven for the empirical likelihood-based estimators of two-sample quantile differences.
  • Simulation studies demonstrated the finite sample performance of the developed methods.
  • Real data analysis confirmed the practical applicability of the proposed techniques.

Conclusions:

  • The proposed estimators provide reliable statistical inference for right-censored data with missing censoring indicators.
  • Empirical likelihood methods effectively handle quantile difference estimation, with or without auxiliary information.
  • The study offers valuable tools for researchers dealing with complex survival data.