A comparison of analytical strategies for cluster randomized trials with survival outcomes in the presence of competing risks

Abstract

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.

Finite‐sample adjustments in variance estimators for clustered competing risks regression

“…An attractive feature of is that its validity does not require the correct specification of the within‐cluster correlations between the failure times, and therefore is robust under the independence working assumption. However, while sandwich variance estimator remains approximately unbiased when the number of clusters is large, it has been shown to carry negative finite‐sample bias in simulations when is no larger than 30 25 . This is because usually underestimates the true covariance .…”

“…However, while sandwich variance estimator VUC remains approximately unbiased when the number of clusters n is large, it has been shown to carry negative finite-sample bias in simulations when n is no larger than 30. 25 This is because Σ( βk ) usually underestimates the true covariance 𝚺(𝜷 k ). The underestimation of 𝚺(𝜷 k ) in finite samples will lead to inflated type I error rates in the associated Wald tests and undercoverage of the confidence intervals, thus threatening the validity of statistical inference under clustered competing risks regression modeling.…”

“…An exception is Fay and Graubard, 10 who have developed a bias‐corrected sandwich variance estimator for general estimating equations and exemplified the application to the Cox proportional hazards model in the absence of clustering. Furthermore, a recent simulation study conducted by Li et al 25 revealed that marginal Fine‐Gray model with the sandwich variance estimator 2 carried substantially inflated type I error rate with no more than 30 clusters. However, to the best of our knowledge, the bias‐corrected sandwich variance estimators have not yet been extended to accommodate clustered competing risks regression.…”

Bayesian semi-parametric inference for clustered recurrent events with zero-inflation and a terminal event/4163305

“…The impact upon the survival function from the previous recurrent event occurrence is primarily controlled by the shared hierarchical frailty terms, γ ij and µ j , from the two hazards. An alternative modeling strategy can be based on the multi-state model (Lee et al, 2016;Li et al, 2022), where one can more explicitly split the event occurrence paths into 1) recurrent events only, 2) recurrent events followed by the terminal event, and 3) terminal event only, and characterize state-specific hazard functions for each of them in conjunction with different random effects. Under multi-state modeling, we may be able to capture the influence from both fixed and random effects on different hazard functions, potentially allowing for richer information extraction.…”

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

“…One typical feature of the standard sandwich variance estimator (we also refer to this estimator as the uncorrected sandwich variance estimator in subsequent text), V s , is that it is unbiased in large samples regardless of the correct specification of the working independent correlation assumption. However, when the number of clusters is small, as is more often the case in CRTs (frequently fewer than 30), this default sandwich variance estimator tends to underestimate the variance, leading to inflated type I error rates and under-coverage, which necessitates small-sample bias corrections to maintain valid statistical inference (Li et al, 2022).…”