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Bootstrap-based methods for estimating standard errors in Cox's regression analyses of clustered event times
Yongling Xiao1, Michal Abrahamowicz
1Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada H3A 1A2.
Statistics in Medicine
|March 10, 2010
Summary
We developed two bootstrap methods to improve standard error calculations in Cox models for clustered event time data. These methods accurately correct for within-cluster correlation, outperforming standard approaches.
Area of Science:
- Biostatistics
- Survival Analysis
- Statistical Modeling
Background:
- Standard Cox models often underestimate standard errors for clustered event time data due to ignored within-cluster correlation.
- Existing methods like robust variance estimators and shared gamma frailty models have limitations.
Purpose of the Study:
- To propose and evaluate two novel bootstrap-based methods for correcting standard errors in Cox models with clustered, right-censored event times.
- To assess the performance of these methods against existing techniques in simulations and real-world data.
Main Methods:
- Cluster-bootstrap: Resampling clusters with replacement.
- Two-step bootstrap: Resampling clusters and then individuals within clusters.
- Simulation studies comparing bootstrap methods with robust variance estimators and shared gamma frailty models.
Main Results:
- Both bootstrap methods provide accurate standard errors and acceptable coverage rates for cluster-level covariates, avoiding underestimation.
- The two-step bootstrap method overestimates variance for individual-level covariates.
- Proposed methods were applied to estimate time-dependent effects in real cluster event time data.
Conclusions:
- Bootstrap methods offer a viable solution for correcting standard errors in Cox models with clustered event time data.
- The cluster-bootstrap method is recommended for its accuracy with both cluster- and individual-level covariates.
- These methods enhance the reliability of statistical inference in clustered survival data analysis.
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