Small sample performance of bias-corrected sandwich estimators for cluster-randomized trials with binary outcomes

Background and Purpose Power and sample size calculations for cluster randomized trials require prediction of the degree of correlation that will be realized among outcomes of participants in the same cluster. This correlation is typically quantified as the intraclass correlation coefficient (ICC), defined as the Pearson correlation between two members of the same cluster or proportion of the total variance attributable to variance between clusters. It is widely known but perhaps not fully appreciated that for binary outcomes, the ICC is a function of outcome prevalence. Hence, the ICC and the outcome prevalence are intrinsically related, making the ICC poorly generalizable across study conditions and between studies with different outcome prevalences. Methods We use a simple parametrization of the ICC that aims to isolate that part of the ICC that measures dependence among responses within a cluster from the outcome prevalence. We incorporate this parametrization into sample size calculations for cluster randomized trials and compare our method to the traditional approach using the ICC. Results Our dependence parameter, R, may be less influenced by outcome prevalence and has an intuitive meaning that facilitates interpretation. Estimates of R from previous studies can be obtained using simple statistics. Comparison of methods showed that the traditional ICC approach to sample size determination tends to overpower studies under many scenarios, calling for more clusters than truly required. Limitations The methods are developed for equal-sized clusters, whereas cluster size may vary in practice. Conclusions The dependence parameter R is an alternative measure of dependence among binary outcomes in cluster randomized trials that has a number of advantages over the ICC.

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Bayesian network meta-analysis for cluster randomized trials with binary outcomes

Research Synthesis Methods ◽

10.1002/jrsm.1210 ◽

2016 ◽

Vol 8 (2) ◽

pp. 236-250 ◽

Cited By ~ 9

Author(s):

Lorenz Uhlmann ◽

Katrin Jensen ◽

Meinhard Kieser

Keyword(s):

Bayesian Network ◽

Randomized Trials ◽

Meta Analysis ◽

Binary Outcomes ◽

Cluster Randomized Trials ◽

Cluster Randomized

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Is the R coefficient of interest in cluster randomized trials with a binary outcome?

Statistical Methods in Medical Research ◽

10.1177/0962280219900200 ◽

2020 ◽

Vol 29 (9) ◽

pp. 2470-2480

Author(s):

Ariane M Mbekwe Yepnang ◽

Agnès Caille ◽

Sandra M Eldridge ◽

Bruno Giraudeau

Keyword(s):

Sample Size ◽

Simulation Study ◽

Randomized Trials ◽

Intraclass Correlation ◽

Sample Size Calculation ◽

Sample Size Determination ◽

Binary Outcomes ◽

Cluster Randomized Trials ◽

Empirical Power ◽

Cluster Randomized

In cluster randomized trials, the intraclass correlation coefficient (ICC) is classically used to measure clustering. When the outcome is binary, the ICC is known to be associated with the prevalence of the outcome. This association challenges its interpretation and can be problematic for sample size calculation. To overcome these situations, Crespi et al. extended a coefficient named R, initially proposed by Rosner for ophthalmologic data, to cluster randomized trials. Crespi et al. asserted that R may be less influenced by the outcome prevalence than is the ICC, although the authors provided only empirical data to support their assertion. They also asserted that “the traditional ICC approach to sample size determination tends to overpower studies under many scenarios, calling for more clusters than truly required”, although they did not consider empirical power. The aim of this study was to investigate whether R could indeed be considered independent of the outcome prevalence. We also considered whether sample size calculation should be better based on the R coefficient or the ICC. Considering the particular case of 2 individuals per cluster, we theoretically demonstrated that R is not symmetrical around the 0.5 prevalence value. This in itself demonstrates the dependence of R on prevalence. We also conducted a simulation study to explore the case of both fixed and variable cluster sizes greater than 2. This simulation study demonstrated that R decreases when prevalence increases from 0 to 1. Both the analytical and simulation results demonstrate that R depends on the outcome prevalence. In terms of sample size calculation, we showed that an approach based on the ICC is preferable to an approach based on the R coefficient because with the former, the empirical power is closer to the nominal one. Hence, the R coefficient does not outperform the ICC for binary outcomes because it does not offer any advantage over the ICC.

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