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. 2021;91(18):3744-3770.
doi: 10.1080/00949655.2021.1946806. Epub 2021 Jul 15.

Using the potential outcome framework to estimate optimal sample size for cluster randomized trials: a simulation-based algorithm

Ruoshui Zhai  1 , Roee Gutman  1
Affiliations

Using the potential outcome framework to estimate optimal sample size for cluster randomized trials: a simulation-based algorithm

Ruoshui Zhai et al. J Stat Comput Simul. 2021.

Abstract

In cluster randomized trials (CRTs) groups rather than individuals are randomized to different interventions. Individuals' responses within clusters are commonly more similar than those across clusters. This dependency introduces complexity when calculating the number of clusters required to reach a specified statistical power for nominal significance levels and effect sizes. Current CRTs' sample size estimation approaches rely on asymptotic-based formulae or Monte Carlo methods. We propose a new Monte Carlo procedure which is based on the potential outcomes framework. By explicitly defining the causal estimand, the data generating, the sampling, and the treatment assignment mechanisms, this procedure allows for sample size calculations in a broad range of study designs including sample size calculations in finite and infinite populations. It can also address financial and administrative considerations by allowing for unequal allocation of clusters. The R package CRTsampleSearch implements the method and we provide examples for using this package.

Keywords: causal estimand; cluster randomized trials; potential outcomes framework; sample size estimation.

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Conflict of interest statement

Disclosure statement No potential conflict of interest was reported by the author(s).

Figures

Figure 1.
Figure 1.
The log-Normal distribution of cluster sizes in Simulation 6.1.
Figure 2.
Figure 2.
The total number of clusters needed when the size of clusters are generated from a log-Normal in Simulation 6.1. (a) Estimand (13), (b) Estimand (14).
Figure 3.
Figure 3.
The total number of clusters needed when the outcomes are generated from a zero-inflated log-Normal model in Simulation 6.2.
Figure 4.
Figure 4.
The total number of clusters needed when the outcomes are from a Beta-Bernoulli model in Simulation 6.3.
Figure 5.
Figure 5.
The total number of clusters needed when the outcomes are generated from a Gamma–Poisson model in Simulation 6.4.1.
Figure 6.
Figure 6.
The total number of clusters needed when the outcomes are generated from a Gamma-ZIP model in Simulation 6.4.2.
Figure 7.
Figure 7.
The size of nursing homes recruited in the influenza study.
Figure 8.
Figure 8.. Estimations from the ZIP(P0, λ0) model for every nursing homes in the flu vaccine data.
Note: (a) The proportion of zeros (P0) in the binary component. (b) The event rate (λ0) in the Poisson component.
Figure 9.
Figure 9.. The percentage of African American residents per nursing home in the flu vaccine data.
Note: Stratum 1: ≤ 1.47% (204 nursing homes, 25.06% of the total); stratum 2: (1.47%, 6.25%] (204 nursing homes, 25.06% of the total); stratum 3: (6.25%, 17.9%] (204 nursing homes, 25.06% of the total); stratum 4: > 17.9% (202 nursing homes, 24.82% of the total).
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References

    1. Moberg J, Kramer M. A brief history of the cluster randomised trial design. J R Soc Med. 2015;108(5):192–198. - PMC - PubMed
    1. Donner A, Klar N. Design and analysis of cluster randomization trials in health research. London: Arnold; 2000.
    1. Donner A, Klar N. Pitfalls of and controversies in cluster randomization trials. Am J Public Health. 2004;94(3):416–422. - PMC - PubMed
    1. Rotondi MA, Donner A. Sample size estimation in cluster randomized educational trials: an empirical Bayes approach. J Educ Behav Stat. 2009;34(2):229–237.
    1. Hayes RJ, Bennett S. Simple sample size calculation for cluster-randomized trials. Int J Epidemiol. 1999;28(2):319–326. - PubMed

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