Abstract
In a cluster-randomized trial (CRT), the number of participants enrolled often varies across clusters. This variation should be considered during both trial design and data analysis to ensure statistical performance goals are achieved. Most methodological literature on the CRT design has assumed equal cluster sizes. This scoping review focuses on methodology for unequal cluster size CRTs. EMBASE, Medline, Google Scholar, MathSciNet and Web of Science databases were searched to identify English-language articles reporting on methodology for unequal cluster size CRTs published until March 2021. We extracted data on the focus of the paper (power calculation, Type I error etc.), the type of CRT, the type and the range of parameter values investigated (number of clusters, mean cluster size, cluster size coefficient of variation, intra-cluster correlation coefficient, etc.), and the main conclusions. Seventy-nine of 5032 identified papers met the inclusion criteria. Papers primarily focused on the parallel-arm CRT (p-CRT, n = 60, 76%) and the stepped-wedge CRT (n = 14, 18%). Roughly 75% of the papers addressed trial design issues (sample size/power calculation) while 25% focused on analysis considerations (Type I error, bias, etc.). The ranges of parameter values explored varied substantially across different studies. Methods for accounting for unequal cluster sizes in the p-CRT have been investigated extensively for Gaussian and binary outcomes. Synthesizing the findings of these works is difficult as the magnitude of impact of the unequal cluster sizes varies substantially across the combinations and ranges of input parameters. Limited investigations have been done for other combinations of a CRT design by outcome type, particularly methodology involving binary outcomes-the most commonly used type of primary outcome in trials. The paucity of methodological papers outside of the p-CRT with Gaussian or binary outcomes highlights the need for further methodological development to fill the gaps.
Highlights
A cluster-randomized trial (CRT), known as a group-randomized trial, is an experimental design for comparing treatment effects by randomly assigning clusters of participants to different treatments, wherein all members of a given cluster receive the same treatment
For design methodology (Branch A), we searched for papers with a keyword list that included both (1) a well-known type of CRT, and (2) a term related to unequal cluster sizes or relevant to trial design
For analysis methodology (Branch B), we searched for papers with a keyword list that included (1) an analysis method commonly used for CRTs and (2) a term referencing cluster or sample size, and (3) a term related to statistical performance
Summary
A cluster-randomized trial (CRT), known as a group-randomized trial, is an experimental design for comparing treatment effects by randomly assigning clusters (groups) of participants to different treatments, wherein all members of a given cluster receive the same treatment. Type I error inflation occurs when statistical methods appropriate for balanced data are applied to data with unequal cluster sizes [15, 16] This problem may be exacerbated when the number of participants in some clusters or the number of clusters is small. Previous literature reviews have identified various key papers (e.g., 11 papers in Turner et al [5], 8 papers in Turner et al [6]), but no systematic scoping review appears to have been published This scoping review is intended to identify: (1) the impact of unequal cluster sizes on the statistical properties in both the design (i.e. power, sample size, etc.) and the analysis (i.e. Type I error rate, bias, coverage, etc.) phases, (2) the existing methods for dealing with unequal cluster sizes, and (3) the gaps in current knowledge and informing directions for development of new methods in this area. Our intent is to assist readers in identifying literature relevant to the design and analysis of their CRTs when cluster sizes are unequal
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