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

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Survival Analysis

Background:

• Cluster randomized trials (CRTs) often have small sample sizes, requiring small-sample corrections for valid statistical inference.
• Time-to-event outcomes are common in CRTs, frequently analyzed using the marginal Cox proportional hazards model.
• Existing small-sample corrections for marginal models do not adequately address clustered time-to-event data.

Purpose of the Study:

• To propose and evaluate novel bias-corrected sandwich variance estimators for CRTs with time-to-event outcomes analyzed via the marginal Cox model.
• To assess the small-sample properties of these new estimators through simulation.

Main Methods:

• Development of nine bias-corrected sandwich variance estimators.
• A simulation study to evaluate the performance of the proposed estimators under various conditions.
• Application of the estimators to a real-world CRT dataset.

Main Results:

• The optimal bias-corrected sandwich variance estimator for CRTs with survival outcomes is influenced by the variability in cluster sizes.
• The choice of estimator can slightly differ based on whether relative bias or type I error rate is prioritized.
• Use of small-sample bias corrections can alter conclusions regarding intervention effectiveness in real-world CRTs.

Conclusions:

• The proposed bias-corrected sandwich variance estimators enhance the analysis of CRTs with time-to-event outcomes.
• Careful selection of the variance estimator is crucial for accurate inference, considering cluster size variability and desired statistical properties.
• The R package CoxBcv is available for implementing these improved analytical methods.