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

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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Optimal Sample Allocation Under Unequal Costs in Cluster-Randomized Trials

Journal of Educational and Behavioral Statistics ◽

10.3102/1076998620912418 ◽

2020 ◽

Vol 45 (4) ◽

pp. 446-474

Author(s):

Zuchao Shen ◽

Benjamin Kelcey

Keyword(s):

Optimal Design ◽

Statistical Power ◽

Randomized Trials ◽

Intraclass Correlation ◽

R Package ◽

Design Parameters ◽

Cluster Randomized Trials ◽

Cost Structures ◽

Cluster Randomized ◽

Sample Allocation

Conventional optimal design frameworks consider a narrow range of sampling cost structures that thereby constrict their capacity to identify the most powerful and efficient designs. We relax several constraints of previous optimal design frameworks by allowing for variable sampling costs in cluster-randomized trials. The proposed framework introduces additional design considerations and has the potential to identify designs with more statistical power, even when some parameters are constrained due to immutable practical concerns. The results also suggest that the gains in efficiency introduced through the expanded framework are fairly robust to misspecifications of the expanded cost structure and concomitant design parameters (e.g., intraclass correlation coefficient). The proposed framework is implemented in the R package odr.

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Power analyses for moderator effects with (non)randomly varying slopes in cluster randomized trials

Methodology ◽

10.5964/meth.4003 ◽

2021 ◽

Vol 17 (2) ◽

pp. 92-110

Author(s):

Nianbo Dong ◽

Jessaca Spybrook ◽

Benjamin Kelcey ◽

Metin Bulus

Keyword(s):

Statistical Power ◽

Randomized Trials ◽

Future Research ◽

Size Difference ◽

Detectable Effect ◽

Cluster Randomized Trials ◽

Individual Level ◽

Moderator Effects ◽

Cluster Randomized ◽

Power Analyses

Researchers often apply moderation analyses to examine whether the effects of an intervention differ conditional on individual or cluster moderator variables such as gender, pretest, or school size. This study develops formulas for power analyses to detect moderator effects in two-level cluster randomized trials (CRTs) using hierarchical linear models. We derive the formulas for estimating statistical power, minimum detectable effect size difference and 95% confidence intervals for cluster- and individual-level moderators. Our framework accommodates binary or continuous moderators, designs with or without covariates, and effects of individual-level moderators that vary randomly or nonrandomly across clusters. A small Monte Carlo simulation confirms the accuracy of our formulas. We also compare power between main effect analysis and moderation analysis, discuss the effects of mis-specification of the moderator slope (randomly vs. non-randomly varying), and conclude with directions for future research. We provide software for conducting a power analysis of moderator effects in CRTs.

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Statistical Power in Three-Arm Cluster Randomized Trials

Evaluation & the Health Professions ◽

10.1177/0163278713498392 ◽

2013 ◽

Vol 37 (4) ◽

pp. 470-487

Author(s):

Xiaofeng Steven Liu

Keyword(s):

Statistical Power ◽

Randomized Trials ◽

Cluster Randomized Trials ◽

Cluster Randomized

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The use of islands and cluster-randomized trials to investigate vector control interventions: a case study on the Bijagós archipelago, Guinea-Bissau

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2019.0807 ◽

2020 ◽

Vol 376 (1818) ◽

pp. 20190807 ◽

Cited By ~ 1

Author(s):

Robert T. Jones ◽

Elizabeth Pretorius ◽

Thomas H. Ant ◽

John Bradley ◽

Anna Last ◽

...

Keyword(s):

Vector Control ◽

Statistical Power ◽

Randomized Trials ◽

Control Strategies ◽

Cluster Randomized Trials ◽

Vector Borne Diseases ◽

Guinea Bissau ◽

Vector Borne ◽

Cluster Randomized

Vector-borne diseases threaten the health of populations around the world. While key interventions continue to provide protection from vectors, there remains a need to develop and test new vector control tools. Cluster-randomized trials, in which the intervention or control is randomly allocated to clusters, are commonly selected for such evaluations, but their design must carefully consider cluster size and cluster separation, as well as the movement of people and vectors, to ensure sufficient statistical power and avoid contamination of results. Island settings present an opportunity to conduct these studies. Here, we explore the benefits and challenges of conducting intervention studies on islands and introduce the Bijagós archipelago of Guinea-Bissau as a potential study site for interventions intended to control vector-borne diseases. This article is part of the theme issue ‘Novel control strategies for mosquito-borne diseases'.

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Sample Size Issues for Cluster Randomized Trials With Discrete-Time Survival Endpoints

Methodology ◽

10.1027/1614-2241/a000047 ◽

2012 ◽

Vol 8 (4) ◽

pp. 146-158 ◽

Cited By ~ 4

Author(s):

Mirjam Moerbeek

Keyword(s):

Discrete Time ◽

Cluster Size ◽

Randomized Trials ◽

Cluster Randomized Trial ◽

Smoking Initiation ◽

Fixed Number ◽

Cluster Randomized Trials ◽

Number Of Clusters ◽

Sufficient Power ◽

Cluster Randomized

With cluster randomized trials complete groups of subjects are randomized to treatment conditions. An important question might be whether and when the subjects experience a particular event, such as smoking initiation or recovery from disease. In the social sciences the timing of such events is often measured in discrete time by using time intervals. At the planning phase of a cluster randomized trial one should decide on the number of clusters and cluster size such that parameters are estimated accurately and sufficient power on the test on treatment effect is achieved. On basis of a simulation study it is concluded that regression coefficients are estimated more accurately than the variance of the random cluster effect. In addition, it is shown that power increases with cluster size and number of clusters, and that a sufficient power cannot always be achieved by using larger cluster sizes at a fixed number of clusters.

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