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

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 in terms of relative bias and type I error rate. 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 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.

Simulating time-to-event data subject to competing risks and clustering: A review and synthesis

“…assuming the event rates are p 1 , p 2 and the censoring rate is q, the parameters λ 1 , λ 2 , and ζ can be determined from equations (19) to (21). The data generation steps for clustered competing risks data using the probability transform method are shown in Algorithm 4 in Appendix 1.…”

“…And thus we focus on the frailty model rather than a multivariate copula for simulating clustered survival times due to its practicality. We refer readers to Cai and Shen 20 , Zhong and Cook, 63 and Wang et al 21 for additional details in simulating clustered survival times with a multivariate copula.…”

“…Since the marginal hazards are λ 1 exp (βX ij ) and λ 2 , we can again obtain λ 1 , λ 2 , and ζ through equations ( 19) to (21). The data generation steps for clustered competing risks data using Moran's algorithm are shown in Algorithm 7 in Appendix 1.…”

“…2. Calculate λ 1 , λ 2 and ζ from equations (19) to (21), β from hazard ratio, and ρ from ρ = sin τπ 2 .…”

“…In the published literature, Monte Carlo simulation represents powerful tools for statistical research and education, particularly for evaluating newly developed models, 16,14,[17][18][19] comparing existing methods, and helping understand the statistical properties of competing estimators. 20,15,21 Given the importance of this technique, we aim to provide a review and synthesis of existing simulation methods and algorithms and a "one-stop shop" for researchers interested in generating complex survival data with clustering and/or competing or semi-competing risks for their research.…”