Methods for dealing with unequal cluster sizes in cluster randomized trials: A scoping review

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.

Crown adjustment and chairside efficiency of single‐unit restorations fabricated from immediate and staged impressions using a digital workflow for posterior implants

“…Unbalanced sample sizes have been reported in various clinical fields. 16,17 For the adjustments of crowns, the Shapiro-Wilk Test was utilized to assess the normal distribution of maximum occlusion adjustment, area of occlusion adjustment, maximum mesial adjustment, and maximum distal adjustment. None of these variables followed a normal distribution, thus the nonparametric Kruskal-Wallis test was subsequently performed.…”

Ghosts of the past?

“…To determine whether multilevel analyses were required to handle the nested structure of the data, i.e., multiple children within families, we calculated the intraclass correlation coefficient and design effects based on both the average and maximum cluster size (Zhan et al, 2021). The intraclass correlations (ranging from.43 for parental self-efficacy play to.71 for parenting stress) and design effects (ranging from 1.09 to 1.26 based on average cluster size and from 1.66 to 3.12 based on maximum cluster size) indicated that multilevel models should be used to account for the nested structure of the data (Hox & Maas, 2002;Vajargah & Nikbakht, 2015).…”

“…We also computed design effects based on the maximum cluster size, because the use of average cluster size might result in an underestimation of the design effect (Zhan et al, 2021). The intraclass correlations (.39 for child social competence at 30 months)…”