Relative efficiency of equal versus unequal cluster sizes in cluster randomized trials with a small number of clusters. 2021

Jingxia Liu, and Chengjie Xiong, and Lei Liu, and Guoqiao Wang, and Luo Jingqin, and Feng Gao, and Ling Chen, and Yan Li
Division of Public Health Sciences, Dept. of Surgery, Washington University School of Medicine (WUSM), St Louis, Missouri, 63110, USA.

To calculate sample sizes in cluster randomized trials (CRTs), the cluster sizes are usually assumed to be identical across all clusters for simplicity. However, equal cluster sizes are not guaranteed in practice, especially when the number of clusters is limited. Therefore, it is important to understand the relative efficiency (RE) of equal versus unequal cluster sizes when designing CRTs with a limited number of clusters. In this paper, we are interested in the RE of two bias-corrected sandwich estimators of the treatment effect in the Generalized Estimating Equation (GEE) models for CRTs with a small number of clusters. Specifically, we derive the RE of two bias-corrected sandwich estimators for binary, continuous, or count data in CRTs under the assumption of an exchangeable working correlation structure. We consider different scenarios of cluster size distributions and investigate RE performance through simulation studies. We conclude that the number of clusters could be increased by as much as 42% to compensate for efficiency loss due to unequal cluster sizes. Finally, we propose an algorithm of increasing the number of clusters when the coefficient of variation of cluster sizes is known and unknown.

UI MeSH Term Description Entries
D003198 Computer Simulation Computer-based representation of physical systems and phenomena such as chemical processes. Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D015982 Bias Any deviation of results or inferences from the truth, or processes leading to such deviation. Bias can result from several sources: one-sided or systematic variations in measurement from the true value (systematic error); flaws in study design; deviation of inferences, interpretations, or analyses based on flawed data or data collection; etc. There is no sense of prejudice or subjectivity implied in the assessment of bias under these conditions. Aggregation Bias,Bias, Aggregation,Bias, Ecological,Bias, Statistical,Bias, Systematic,Ecological Bias,Outcome Measurement Errors,Statistical Bias,Systematic Bias,Bias, Epidemiologic,Biases,Biases, Ecological,Biases, Statistical,Ecological Biases,Ecological Fallacies,Ecological Fallacy,Epidemiologic Biases,Experimental Bias,Fallacies, Ecological,Fallacy, Ecological,Scientific Bias,Statistical Biases,Truncation Bias,Truncation Biases,Bias, Experimental,Bias, Scientific,Bias, Truncation,Biase, Epidemiologic,Biases, Epidemiologic,Biases, Truncation,Epidemiologic Biase,Error, Outcome Measurement,Errors, Outcome Measurement,Outcome Measurement Error
D016000 Cluster Analysis A set of statistical methods used to group variables or observations into strongly inter-related subgroups. In epidemiology, it may be used to analyze a closely grouped series of events or cases of disease or other health-related phenomenon with well-defined distribution patterns in relation to time or place or both. Clustering,Analyses, Cluster,Analysis, Cluster,Cluster Analyses,Clusterings
D016032 Randomized Controlled Trials as Topic Works about clinical trials that involve at least one test treatment and one control treatment, concurrent enrollment and follow-up of the test- and control-treated groups, and in which the treatments to be administered are selected by a random process, such as the use of a random-numbers table. Clinical Trials, Randomized,Controlled Clinical Trials, Randomized,Trials, Randomized Clinical
D018401 Sample Size The number of units (persons, animals, patients, specified circumstances, etc.) in a population to be studied. The sample size should be big enough to have a high likelihood of detecting a true difference between two groups. (From Wassertheil-Smoller, Biostatistics and Epidemiology, 1990, p95) Sample Sizes,Size, Sample,Sizes, Sample

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