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Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
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Finite-sample adjustments in variance estimators for clustered competing risks regression.

Xinyuan Chen1, Fan Li2,3,4

  • 1Department of Mathematics and Statistics, Mississippi State University, Starkville, Mississippi, USA.

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|March 15, 2022
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Summary

This study introduces bias-corrected variance estimators for clustered competing risks data, improving upon standard methods when cluster numbers are limited. The Mancl and DeRouen (MD) estimator shows the least bias, enhancing confidence interval accuracy.

Keywords:
Fine-Gray modelcoverage ratecumulative incidence functionproportional subdistribution hazards modelsandwich variance estimatorsmall-sample corrections

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Survival Analysis

Background:

  • Clustered competing risks data are common in multicenter trials and multilevel studies.
  • The Fine-Gray model analyzes covariate associations with cumulative incidence functions.
  • Standard sandwich variance estimators may perform poorly with few clusters.

Purpose of the Study:

  • To propose novel bias-corrected variance estimators for clustered competing risks data.
  • To address the limitations of traditional sandwich variance estimators in small cluster settings.
  • To improve the accuracy of regression parameter estimation in complex survival data.

Main Methods:

  • Extension of bias-correction techniques from generalized estimating equations to competing risks.
  • Development of four new bias-corrected variance estimators.
  • Simulation studies and real-data analyses to evaluate performance.
  • Implementation in a user-friendly R package (crrcbcv).

Main Results:

  • The Mancl and DeRouen (MD) type sandwich variance estimator demonstrated the smallest bias.
  • MD-based Wald confidence intervals provided near-nominal coverage for cluster-level effects with few clusters.
  • Multiplicative bias-corrected or MBN-type variance estimators yielded accurate coverage for individual-level effects.

Conclusions:

  • Proposed bias-corrected variance estimators enhance the reliability of analyses for clustered competing risks data.
  • The MD estimator is recommended for cluster-level effects, while bias-corrected or MBN estimators are suitable for individual-level effects.
  • The crrcbcv R package facilitates the practical application of these improved statistical methods.