Impact of unequal cluster sizes for GEE analyses of stepped wedge cluster randomized trials with binary outcomes

The stepped wedge design is a type of unidirectional crossover design where cluster units switch from control to intervention condition at different pre-specified time points. While a convention in study planning is to assume the cluster-period sizes are identical, stepped wedge cluster randomized trials (SW-CRTs) involving repeated cross-sectional designs frequently have unequal cluster-period sizes, which can impact the efficiency of the treatment effect estimator. In this article, we provide a comprehensive investigation of the efficiency impact of unequal cluster sizes for generalized estimating equation analyses of SW-CRTs, with a focus on binary outcomes as in the Washington State Expedited Partner Therapy trial. Several major distinctions between our work and existing work include: (i) we consider multilevel correlation structures in marginal models with binary outcomes; (ii) we study the implications of both the between-cluster and within-cluster imbalances in sizes; and (iii) we provide a comparison between the independence working correlation versus the true working correlation and detail the consequences of ignoring correlation estimation in SW-CRTs with unequal cluster sizes. We conclude that the working independence assumption can lead to substantial efficiency loss and a large sample size regardless of cluster-period size variability in SW-CRTs, and recommend accounting for correlations in the analysis. To improve study planning, we additionally provide a computationally efficient search algorithm to estimate the sample size in SW-CRTs accounting for unequal cluster-period sizes, and conclude by illustrating the proposed approach in the context of the Washington State study.

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Impact of unequal cluster sizes for GEE analyses of stepped wedge cluster randomized trials with binary outcomes

Biometrical Journal ◽

10.1002/bimj.202100112 ◽

2021 ◽

Author(s):

Zibo Tian ◽

John S. Preisser ◽

Denise Esserman ◽

Elizabeth L. Turner ◽

Paul J. Rathouz ◽

...

Keyword(s):

Randomized Trials ◽

Binary Outcomes ◽

Cluster Randomized Trials ◽

Stepped Wedge ◽

Cluster Randomized ◽

Unequal Cluster

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Sample size estimation for modified Poisson analysis of cluster randomized trials with a binary outcome

Statistical Methods in Medical Research ◽

10.1177/0962280221990415 ◽

2021 ◽

pp. 096228022199041

Author(s):

Fan Li ◽

Guangyu Tong

Keyword(s):

Relative Risk ◽

Sample Size ◽

Poisson Regression ◽

Cluster Size ◽

Randomized Trials ◽

Cluster Randomized Trials ◽

Binomial Regression ◽

Size Variability ◽

Working Correlation ◽

Cluster Randomized

The modified Poisson regression coupled with a robust sandwich variance has become a viable alternative to log-binomial regression for estimating the marginal relative risk in cluster randomized trials. However, a corresponding sample size formula for relative risk regression via the modified Poisson model is currently not available for cluster randomized trials. Through analytical derivations, we show that there is no loss of asymptotic efficiency for estimating the marginal relative risk via the modified Poisson regression relative to the log-binomial regression. This finding holds both under the independence working correlation and under the exchangeable working correlation provided a simple modification is used to obtain the consistent intraclass correlation coefficient estimate. Therefore, the sample size formulas developed for log-binomial regression naturally apply to the modified Poisson regression in cluster randomized trials. We further extend the sample size formulas to accommodate variable cluster sizes. An extensive Monte Carlo simulation study is carried out to validate the proposed formulas. We find that the proposed formulas have satisfactory performance across a range of cluster size variability, as long as suitable finite-sample corrections are applied to the sandwich variance estimator and the number of clusters is at least 10. Our findings also suggest that the sample size estimate under the exchangeable working correlation is more robust to cluster size variability, and recommend the use of an exchangeable working correlation over an independence working correlation for both design and analysis. The proposed sample size formulas are illustrated using the Stop Colorectal Cancer (STOP CRC) trial.

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A new dependence parameter approach to improve the design of cluster randomized trials with binary outcomes

Clinical Trials ◽

10.1177/1740774511423851 ◽

2011 ◽

Vol 8 (6) ◽

pp. 687-698 ◽

Cited By ~ 15

Author(s):

Catherine M Crespi ◽

Weng Kee Wong ◽

Sheng Wu

Keyword(s):

Sample Size ◽

Randomized Trials ◽

Pearson Correlation ◽

Sample Size Determination ◽

Binary Outcomes ◽

Alternative Measure ◽

Cluster Randomized Trials ◽

Sample Size Calculations ◽

Cluster Randomized ◽

Measure Of Dependence

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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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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