  Cluster randomized trials (CRTs) frequently recruit a small number of
clusters, therefore necessitating the application of small-sample corrections
for valid inference. A recent systematic review indicated that CRTs reporting
right-censored, time-to-event outcomes are not uncommon, and that the marginal
Cox proportional hazards model is one of the common approaches used for primary
analysis. While small-sample corrections have been studied under marginal
models with continuous, binary and count outcomes, no prior research has been
devoted to the development and evaluation of bias-corrected sandwich variance
estimators when clustered time-to-event outcomes are analyzed by the marginal
Cox model. To improve current practice, we propose 9 bias-corrected sandwich
variance estimators for the analysis of CRTs using the marginal Cox model, and
report on a simulation study to evaluate their small-sample properties. Our
results indicate that the optimal choice of bias-corrected sandwich variance
estimator for CRTs with survival outcomes can depend on the variability of
cluster sizes, and can also slightly differ whether it is evaluated according
to relative bias or type I error rate. Finally, we illustrate the new variance
estimators in a real-world CRT where the conclusion about intervention
effectiveness differs depending on the use of small-sample bias corrections.
The proposed sandwich variance estimators are implemented in an R package
CoxBcv.
