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A kernel nonparametric quantile estimator for right-censored competing risks data.

Caiyun Fan1, Gang Ding2, Feipeng Zhang2

  • 1School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, People's Republic of China.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a smoothed quantile estimator for competing risks data, improving stability and convergence rates for medical and epidemiological research. The new method offers reliable confidence intervals for time-to-event analyses.

Keywords:
Bahadur representationCompeting risksquantileright censoredweak convergence

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Survival Analysis

Background:

  • Medical and epidemiological studies often analyze time-to-event data with competing risks (multiple failure types).
  • Existing nonparametric estimators for competing risks, like cumulative incidence and quantile functions, can be unstable due to their unsmoothness.
  • Accurate estimation of time-to-event distributions is crucial for understanding disease progression and treatment outcomes.

Purpose of the Study:

  • To propose a novel, smoothed kernel nonparametric quantile estimator for right-censored competing risks data.
  • To improve the stability and convergence properties of existing quantile estimators in competing risks settings.
  • To provide reliable statistical tools for analyzing time-to-event data in the presence of multiple failure types.

Main Methods:

  • Developed a kernel-based smoothed estimator as an advancement of Peng and Fine's nonparametric quantile estimator.
  • Established the Bahadur representation for the proposed smoothed estimator.
  • Derived pointwise confidence intervals and simultaneous confidence bands for the estimated quantile functions.

Main Results:

  • The proposed kernel estimator demonstrates substantially faster convergence rates for the remainder term compared to Peng and Fine's estimator.
  • Simulation studies confirmed the good performance and stability of the new estimator.
  • The methodology was successfully applied to real-world datasets, including the Supreme Court Judge and AIDSSI data.

Conclusions:

  • The proposed smoothed kernel nonparametric quantile estimator offers a more stable and efficient approach for analyzing right-censored competing risks data.
  • This method provides improved statistical inference, including confidence intervals and bands, for time-to-event analyses in biostatistics and epidemiology.
  • The enhanced estimator has practical applications in various fields requiring robust analysis of competing risks data.