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

Binomial Regression ◽

Size Variability ◽

Working Correlation ◽

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.

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

PLoS ONE ◽

10.1371/journal.pone.0119074 ◽

2015 ◽

Vol 10 (4) ◽

pp. e0119074 ◽

Cited By ~ 7

Author(s):

Stephen A. Lauer ◽

Ken P. Kleinman ◽

Nicholas G. Reich

Keyword(s):

Cluster Size ◽

Statistical Power ◽

Randomized Trials ◽

Size Variability ◽

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

10.21203/rs.2.18978/v1 ◽

2019 ◽

Author(s):

Ashutosh Ranjan ◽

Guangzi Song ◽

Christopher S Coffey ◽

Leslie A McClure

Keyword(s):

Sample Size ◽

Simulation Study ◽

Cluster Size ◽

Randomized Trials ◽

Sample Size Calculation ◽

Minimum Variance ◽

Type I ◽

Weighted Analysis ◽

Abstract 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. Many trials that set out to recruit equal clusters end up with unequal clusters for various reasons. 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 assuming equal cluster sizes during the planning stage but ending up with unequal clusters. 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 cover a wide range of patterns of imbalance. The variability in cluster size is measured by the coefficient of variation (CV). By means of a simulation study, we assess the impact of using each of the three analysis methods with respect to type I error and power of the study and how it is affected by the variability in cluster size. Results: Analyses that assumes equal clusters provide a reasonable approximation when cluster sizes vary minimally (CV < 0.30). In an analysis weighted by cluster size type I errors were inflated, and that worsened as the variation in cluster size increases. However, a minimum variance weighted analysis best maintains target power and level of significance under all degrees of imbalance considered. Conclusion: The unweighted analysis works well as an approximate method when the 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.

Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method

International Journal of Epidemiology ◽

10.1093/ije/dyl129 ◽

2006 ◽

Vol 35 (5) ◽

pp. 1292-1300 ◽

Cited By ~ 269

Author(s):

Sandra M Eldridge ◽

Deborah Ashby ◽

Sally Kerry

Keyword(s):

Sample Size ◽

Coefficient Of Variation ◽

Cluster Size ◽

Randomized Trials ◽

Analysis Method ◽

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

10.21203/rs.2.18978/v2 ◽

2020 ◽

Author(s):

Ashutosh Ranjan ◽

Guangzi Song ◽

Christopher S Coffey ◽

Leslie A McClure

Keyword(s):

Sample Size ◽

Cluster Size ◽

Randomized Trials ◽

Sample Size Calculation ◽

Minimum Variance ◽

Type I ◽

Planning Stage ◽

Cluster Randomized ◽

The Impact

Abstract 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.

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

10.1101/2021.04.07.21255090 ◽

2021 ◽

Author(s):

Zibo Tian ◽

John Preisser ◽

Denise Esserman ◽

Elizabeth Turner ◽

Paul Rathouz ◽

...

Keyword(s):

Sample Size ◽

Randomized Trials ◽

Washington State ◽

Binary Outcomes ◽

Stepped Wedge ◽

Study Planning ◽

Working Correlation ◽

Cluster Randomized ◽

Unequal Cluster

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.