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

TL;DR

This paper develops and evaluates nine bias-corrected sandwich variance estimators for the marginal Cox model in small-sample cluster randomized trials with survival data, improving inference accuracy.

Contribution

It introduces new bias-corrected variance estimators specifically for clustered survival data analyzed by the marginal Cox model, addressing a gap in small-sample correction methods.

Findings

Optimal estimator varies with cluster size variability.

Bias corrections can significantly alter inference outcomes.

New estimators improve small-sample inference accuracy.

Abstract

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.