Relative efficiency and sample size for cluster randomized trials with variable cluster sizes

You, Zhiying; Williams, O. Dale; Aban, Inmaculada; Kabagambe, Edmond K.; Tiwari, Hemant; Cutter, Gary

doi:10.1177/1740774510391492

Cited by 15 publications

(20 citation statements)

References 10 publications

(28 reference statements)

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“…With respect to sample size calculation, an alternate strategy for better design of CRT with unequal clusters makes use of CV of cluster sizes in the sample size formula(5) and adjusting the sample size using the relative efficiency of unequal to equal cluster size. (7,10) Application of such methods requires knowledge of the CV of cluster size and ICC, neither of which may available at the design stage of the study. We believe that these methods are better suited for sample size re-estimation procedures, where the knowledge gained in the initial phase of a trial is used to revisit the sample size calculation.…”

Section: Discussionmentioning

confidence: 99%

“…(7-9) While these authors provide suggestions for how to choose an ICC if one cannot be derived from prior studies, their result still relies on researchers' ability to determine a reasonable range for the ICC. (8) More recently, You et al (10) also proposed a relative efficiency measure based on the non-centrality parameter. Once again, this method require prior knowledge of the CV of cluster size, which may not be known at the planning stage.…”

Section: Sample Size Calculations In Crtsmentioning

confidence: 99%

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Statistical approaches to computing sample size in cluster randomized trials: a simulation study

Ranjan

Song

Coffey

et al. 2020

Preprint

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Background: Cluster randomized trials, which randomize groups of individuals to an intervention, are common in health services research when one wants to evaluate improvement in a subject's outcome by intervening at an organizational level. For many such trials, sample size calculation is performed under the assumption of equal cluster size. For a variety of reasons, many trials that set out to recruit clusters of the same size end up with unequal clusters. This leads to a misalignment between the method used for sample size calculation and the data analysis, which may affect trial power. Various weighted analysis methods for analyzing cluster means have been suggested to overcome the problem introduced by unbalanced clusters; however, the performance of such methods has not been evaluated extensively. Methods: We examine the use of the general linear model for analysis of clustered randomized trials that assume equal cluster sizes during the planning stage, but for which the realized cluster sizes are unequal. We demonstrate the performance of three approaches using different weights for analyzing the cluster means: (1) the standard analysis of cluster means, (2) weighting by cluster size, and (3) minimum variance weights. Several distributions are used to generate cluster sizes to assess a range of patterns of imbalance. The variability in cluster size is measured by the coefficient of variation (CV). We assess the impact of using each of the three methods of analysis with respect to type I error and power of the study and how each are impacted by the variability in cluster size via simulations. Results: Analyses that assumes equal clusters provide a reasonable approximation when cluster sizes vary minimally (CV < 0.30). For analyses weighted by cluster size type I errors were inflated, and that worsened as the variation in cluster size increases, despite reasonable power. However, minimum variance weighted analyses best maintain target power and level of significance under scenarios considered. Conclusion: Unweighted analyses work well as an approximate method when variation in cluster size is minimal. However, using minimum variance weights performs much better across the full range of variation in cluster size and is recommended.

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Section: Discussionmentioning

confidence: 99%

Section: Sample Size Calculations In Crtsmentioning

confidence: 99%

Statistical approaches to computing sample size in cluster randomized trials: a simulation study

Ranjan

Song

Coffey

et al. 2020

Preprint

View full text Add to dashboard Cite

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“…However, many approaches based on the design effect require that each cluster has an equal number of subjects, which may well not be the case. Several investigations into the impact of this have been performed, though their results are not general [11][12][13][14]. Approximate methods of incorporating the impact of variable cluster size have been proposed, however [15][16][17].…”

Section: Discussionmentioning

confidence: 99%

Calculating Power by Bootstrap, with an Application to Cluster-randomized Trials

Kleinman¹,

Huang

2017

eGEMs

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Background:A key requirement for a useful power calculation is that the calculation mimic the data analysis that will be performed on the actual data, once that data is observed. Close approximations may be difficult to achieve using analytic solutions, however, and thus Monte Carlo approaches, including both simulation and bootstrap resampling, are often attractive. One setting in which this is particularly true is cluster-randomized trial designs. However, Monte Carlo approaches are useful in many additional settings as well. Calculating power for cluster-randomized trials using analytic or simulation-based methods is frequently unsatisfactory due to the complexity of the data analysis methods to be employed and to the sparseness of data to inform the choice of important parameters in these methods.Methods:We propose that among Monte Carlo methods, bootstrap approaches are most likely to generate data similar to the observed data. In bootstrap approaches, real data are resampled to build complete data sets based on real data that resemble the data for the intended analyses. In contrast, simulation methods would use the real data to estimate parameters for the data, and would then simulate data using these parameters. We describe means of implementing bootstrap power calculation.Results:We demonstrate bootstrap power calculation for a cluster-randomized trial with a censored survival outcome and a baseline observation period.Conclusions:Bootstrap power calculation is a natural application of resampling methods. It provides a relatively simple solution to power calculation that is likely to be more accurate than analytic solutions or simulation-based calculations, in the sense that the bootstrap approach does not rely on the assumptions inherent in analytic calculations. This method of calculation has several important strengths. Notably, it is simple to achieve great fidelity to the proposed data analysis method and there is no requirement for parameter estimates, or estimates of their variability, from outside settings. So, for example, for cluster-randomized trials, power calculations need not depend on intracluster correlation coefficient estimates from outside studies. In contrast, bootstrap power calculation requires initial data that resemble data that are to be used in the planned study. We are not aware of bootstrap power calculation being previously proposed or explored for cluster-randomized trials, but it can also be applied for other study designs. We show with a simulation study that bootstrap power calculation can replicate analytic power in cases where analytic power can be accurately calculated. We also demonstrate power calculations for correlated censored survival outcomes in a cluster-randomized trial setting, for which we are unaware of an analytic alternative. The method can easily be used when preliminary data are available, as is likely to be the case when research is performed in health delivery systems or other settings where electronic medical records can be obtained.

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“…In our high variance cluster size set, the cv was fixed at 1.5, which is about twice the size of the largest cv in other CRT papers [ 8 – 10 ]. This ensured that our high variance cluster size power estimates represented a near-upper bound on the number of variable-sized clusters required in practice.…”

Section: Methodsmentioning

confidence: 99%

The Effect of Cluster Size Variability on Statistical Power in Cluster-Randomized Trials

2015

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The frequency of cluster-randomized trials (CRTs) in peer-reviewed literature has increased exponentially over the past two decades. CRTs are a valuable tool for studying interventions that cannot be effectively implemented or randomized at the individual level. However, some aspects of the design and analysis of data from CRTs are more complex than those for individually randomized controlled trials. One of the key components to designing a successful CRT is calculating the proper sample size (i.e. number of clusters) needed to attain an acceptable level of statistical power. In order to do this, a researcher must make assumptions about the value of several variables, including a fixed mean cluster size. In practice, cluster size can often vary dramatically. Few studies account for the effect of cluster size variation when assessing the statistical power for a given trial. We conducted a simulation study to investigate how the statistical power of CRTs changes with variable cluster sizes. In general, we observed that increases in cluster size variability lead to a decrease in power.

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Relative efficiency and sample size for cluster randomized trials with variable cluster sizes

Abstract: The relative efficiency of unequal versus equal cluster sizes defined using the noncentrality parameter suggests a sample size approach that is a flexible alternative and a useful complement to existing methods.

Cited by 15 publications

References 10 publications

Statistical approaches to computing sample size in cluster randomized trials: a simulation study

Statistical approaches to computing sample size in cluster randomized trials: a simulation study

Calculating Power by Bootstrap, with an Application to Cluster-randomized Trials

The Effect of Cluster Size Variability on Statistical Power in Cluster-Randomized Trials

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