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.

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Motivated by a suicide prevention trial with hierarchical treatment allocation (cluster‐level and individual‐level treatments), we address the sample size requirements for testing the treatment effects as well as their interaction. We assume a linear mixed model, within which two types of treatment effect estimands (controlled effect and marginal effect) are defined. For each null hypothesis corresponding to an estimand, we derive sample size formulas based on large‐sample z‐approximation, and provide finite‐sample modifications based on a t‐approximation. We relax the equal cluster size assumption and express the sample size formulas as functions of the mean and coefficient of variation of cluster sizes. We show that the sample size requirement for testing the controlled effect of the cluster‐level treatment is more sensitive to cluster size variability than that for testing the controlled effect of the individual‐level treatment; the same observation holds for testing the marginal effects. In addition, we show that the sample size for testing the interaction effect is proportional to that for testing the controlled or the marginal effect of the individual‐level treatment. We conduct extensive simulations to validate the proposed sample size formulas, and find the empirical power agrees well with the predicted power for each test. Furthermore, the t‐approximations often provide better control of type I error rate with a small number of clusters. Finally, we illustrate our sample size formulas to design the motivating suicide prevention factorial trial. The proposed methods are implemented in the R package H2x2Factorial.

We propose an information borrowing strategy for the design and monitoring of phase II basket trials based on the local multisource exchangeability assumption between baskets (disease types). In our proposed local‐MEM framework, information borrowing is only allowed to occur locally, that is, among baskets with similar response rate and the amount of information borrowing is determined by the level of similarity in response rate, whereas baskets not considered similar are not allowed to share information. We construct a two‐stage design for phase II basket trials using the proposed strategy. The proposed method is compared to competing Bayesian methods and Simon's two‐stage design in a variety of simulation scenarios. We demonstrate the proposed method is able to maintain the family‐wise type I error rate at a reasonable level and has desirable basket‐wise power compared to Simon's two‐stage design. In addition, our method is computationally efficient compared to existing Bayesian methods in that the posterior profiles of interest can be derived explicitly without the need for sampling algorithms. R scripts to implement the proposed method are available at https://github.com/yilinyl/Bayesian-localMEM.