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Sample size calculation in three-level cluster randomized trials using generalized estimating equation models.

ABSTRACT: Three-level cluster randomized trials (CRTs) are increasingly used in implementation science, where 2fold-nested-correlated data arise. For example, interventions are randomly assigned to practices, and providers within the same practice who provide care to participants are trained with the assigned intervention. Teerenstra et al proposed a nested exchangeable correlation structure that accounts for two levels of clustering within the generalized estimating equations (GEE) approach. In this article, we utilize GEE models to test the treatment effect in a two-group comparison for continuous, binary, or count data in three-level CRTs. Given the nested exchangeable correlation structure, we derive the asymptotic variances of the estimator of the treatment effect for different types of outcomes. When the number of clusters is small, researchers have proposed bias-corrected sandwich estimators to improve performance in two-level CRTs. We extend the variances of two bias-corrected sandwich estimators to three-level CRTs. The equal provider and practice sizes were assumed to calculate number of practices for simplicity. However, they are not guaranteed in practice. Relative efficiency (RE) is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal provider and practice sizes. The expressions of REs are obtained from both asymptotic variance estimation and bias-corrected sandwich estimators. Their performances are evaluated for different scenarios of provider and practice size distributions through simulation studies. Finally, a percentage increase in the number of practices is proposed due to efficiency loss from unequal provider and/or practice sizes.

SUBMITTER: Liu J

PROVIDER: S-EPMC8351402 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundMulti-centre randomized controlled clinical trials play an important role in modern evidence-based medicine. Advantages of collecting data from more than one site are numerous, including accelerated recruitment and increased generalisability of results. Mixed models can be applied to account for potential clustering in the data, in particular when many small centres contribute patients to the study. Previously proposed methods on sample size calculation for mixed models only considered balanced treatment allocations which is an unlikely outcome in practice if block randomisation with reasonable choices of block length is used.MethodsWe propose a sample size determination procedure for multi-centre trials comparing two treatment groups for a continuous outcome, modelling centre differences using random effects and allowing for arbitrary sample sizes. It is assumed that block randomisation with fixed block length is used at each study site for subject allocation. Simulations are used to assess operation characteristics such as power of the sample size approach. The proposed method is illustrated by an example in disease management systems.ResultsA sample size formula as well as a lower and upper boundary for the required overall sample size are given. We demonstrate the superiority of the new sample size formula over the conventional approach of ignoring the multi-centre structure and show the influence of parameters such as block length or centre heterogeneity. The application of the procedure on the example data shows that large blocks require larger sample sizes, if centre heterogeneity is present.ConclusionUnbalanced treatment allocation can result in substantial power loss when centre heterogeneity is present but not considered at the planning stage. When only few patients by centre will be recruited, one has to weigh the risk of imbalance between treatment groups due to large blocks and the risk of unblinding due to small blocks. The proposed approach should be considered when planning multi-centre trials.

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Sample size calculation in three-level cluster randomized trials using generalized estimating equation models.

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