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Bootstrap‐based methods for estimating standard errors in Cox's regression analyses of clustered event times
Author(s) -
Xiao Yongling,
Abrahamowicz Michal
Publication year - 2010
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3807
Subject(s) - covariate , statistics , estimator , random effects model , event (particle physics) , proportional hazards model , variance (accounting) , computer science , cluster (spacecraft) , econometrics , standard error , regression analysis , mathematics , meta analysis , physics , accounting , quantum mechanics , medicine , business , programming language
We propose two bootstrap‐based methods to correct the standard errors (SEs) from Cox's model for within‐cluster correlation of right‐censored event times. The cluster‐bootstrap method resamples, with replacement, only the clusters, whereas the two‐step bootstrap method resamples (i) the clusters, and (ii) individuals within each selected cluster, with replacement. In simulations, we evaluate both methods and compare them with the existing robust variance estimator and the shared gamma frailty model, which are available in statistical software packages. We simulate clustered event time data, with latent cluster‐level random effects, which are ignored in the conventional Cox's model. For cluster‐level covariates, both proposed bootstrap methods yield accurate SEs, and type I error rates, and acceptable coverage rates, regardless of the true random effects distribution, and avoid serious variance under‐estimation by conventional Cox‐based standard errors. However, the two‐step bootstrap method over‐estimates the variance for individual‐level covariates. We also apply the proposed bootstrap methods to obtain confidence bands around flexible estimates of time‐dependent effects in a real‐life analysis of cluster event times. Copyright © 2010 John Wiley & Sons, Ltd.