While statistical methods for analyzing cluster randomized trials with continuous and binary outcomes have been extensively studied and compared, little comparative evidence has been provided for analyzing cluster randomized trials with survival outcomes in the presence of competing risks. Motivated by the Strategies to Reduce Injuries and Develop Confidence in Elders trial, we carried out a simulation study to compare the operating characteristics of several existing population-averaged survival models, including the marginal Cox, marginal Fine and Gray, and marginal multi-state models. For each model, we found that adjusting for the intraclass correlations through the sandwich variance estimator effectively maintained the type I error rate when the number of clusters is large. With no more than 30 clusters, however, the sandwich variance estimator can exhibit notable negative bias, and a permutation test provides better control of type I error inflation. Under the alternative, the power for each model is differentially affected by two types of intraclass correlations—the within-individual and between-individual correlations. Furthermore, the marginal Fine and Gray model occasionally leads to higher power than the marginal Cox model or the marginal multi-state model, especially when the competing event rate is high. Finally, we provide an illustrative analysis of Strategies to Reduce Injuries and Develop Confidence in Elders trial using each analytical strategy considered.
Simulation studies play an important role in evaluating the performance of statistical models developed for analyzing complex survival data such as those with competing risks and clustering. This article aims to provide researchers with a basic understanding of competing risks data generation, techniques for inducing cluster-level correlation, and ways to combine them together in simulation studies, in the context of randomized clinical trials with a binary exposure or treatment. We review data generation with competing and semi-competing risks and three approaches of inducing cluster-level correlation for time-to-event data: the frailty model framework, the probability transform, and Moran’s algorithm. Using exponentially distributed event times as an example, we discuss how to introduce cluster-level correlation into generating complex survival outcomes, and illustrate multiple ways of combining these methods to simulate clustered, competing and semi-competing risks data with pre-specified correlation values or degree of clustering.
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