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Cluster randomized trials (CRTs) frequently recruit a small number ofclusters, therefore necessitating the application of small-sample correctionsfor valid inference. A recent systematic review indicated that CRTs reportingright-censored, time-to-event outcomes are not uncommon, and that the marginalCox proportional hazards model is one of the common approaches used for primaryanalysis. While small-sample corrections have been studied under marginalmodels with continuous, binary and count outcomes, no prior research has beendevoted to the development and evaluation of bias-corrected sandwich varianceestimators when clustered time-to-event outcomes are analyzed by the marginalCox model. To improve current practice, we propose 9 bias-corrected sandwichvariance estimators for the analysis of CRTs using the marginal Cox model, andreport on a simulation study to evaluate their small-sample properties. Ourresults indicate that the optimal choice of bias-corrected sandwich varianceestimator for CRTs with survival outcomes can depend on the variability ofcluster sizes, and can also slightly differ whether it is evaluated accordingto relative bias or type I error rate. Finally, we illustrate the new varianceestimators in a real-world CRT where the conclusion about interventioneffectiveness differs depending on the use of small-sample bias corrections.The proposed sandwich variance estimators are implemented in an R packageCoxBcv.

Improving sandwich variance estimation for marginal Cox analysis of cluster randomized trials