scholarly journals Sample size calculation in three‐level cluster randomized trials using generalized estimating equation models

2020 ◽  
Vol 39 (24) ◽  
pp. 3347-3372
Author(s):  
Jingxia Liu ◽  
Graham A. Colditz
Keyword(s):  
Sample Size ◽  
Randomized Trials ◽  
Sample Size Calculation ◽  
Estimating Equation ◽  
Generalized Estimating Equation ◽  
Cluster Randomized Trials ◽  
Cluster Randomized ◽  
Level Cluster ◽  
Generalized Estimating

A readily available improvement over method of moments for intra-cluster correlation estimation in the context of cluster randomized trials and fitting a GEE–type marginal model for binary outcomes

2018 ◽  
Vol 16 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Philip M Westgate
Keyword(s):  
Correlation Coefficient ◽  
Randomized Trials ◽  
Estimating Equation ◽  
Generalized Estimating Equation ◽  
Cluster Randomized Trials ◽  
Coefficient Estimation ◽  
Pseudo Likelihood ◽  
Cluster Randomized ◽  
Cluster Correlation ◽  
Generalized Estimating

Background/aims Cluster randomized trials are popular in health-related research due to the need or desire to randomize clusters of subjects to different trial arms as opposed to randomizing each subject individually. As outcomes from subjects within the same cluster tend to be more alike than outcomes from subjects within other clusters, an exchangeable correlation arises that is measured via the intra-cluster correlation coefficient. Intra-cluster correlation coefficient estimation is especially important due to the increasing awareness of the need to publish such values from studies in order to help guide the design of future cluster randomized trials. Therefore, numerous methods have been proposed to accurately estimate the intra-cluster correlation coefficient, with much attention given to binary outcomes. As marginal models are often of interest, we focus on intra-cluster correlation coefficient estimation in the context of fitting such a model with binary outcomes using generalized estimating equations. Traditionally, intra-cluster correlation coefficient estimation with generalized estimating equations has been based on the method of moments, although such estimators can be negatively biased. Furthermore, alternative estimators that work well, such as the analysis of variance estimator, are not as readily applicable in the context of practical data analyses with generalized estimating equations. Therefore, in this article we assess, in terms of bias, the readily available residual pseudo-likelihood approach to intra-cluster correlation coefficient estimation with the GLIMMIX procedure of SAS (SAS Institute, Cary, NC). Furthermore, we study a possible corresponding approach to confidence interval construction for the intra-cluster correlation coefficient. Methods We utilize a simulation study and application example to assess bias in intra-cluster correlation coefficient estimates obtained from GLIMMIX using residual pseudo-likelihood. This estimator is contrasted with method of moments and analysis of variance estimators which are standards of comparison. The approach to confidence interval construction is assessed by examining coverage probabilities. Results Overall, the residual pseudo-likelihood estimator performs very well. It has considerably less bias than moment estimators, which are its competitor for general generalized estimating equation–based analyses, and therefore, it is a major improvement in practice. Furthermore, it works almost as well as analysis of variance estimators when they are applicable. Confidence intervals have near-nominal coverage when the intra-cluster correlation coefficient estimate has negligible bias. Conclusion Our results show that the residual pseudo-likelihood estimator is a good option for intra-cluster correlation coefficient estimation when conducting a generalized estimating equation–based analysis of binary outcome data arising from cluster randomized trials. The estimator is practical in that it is simply a result from fitting a marginal model with GLIMMIX, and a confidence interval can be easily obtained. An additional advantage is that, unlike most other options for performing generalized estimating equation–based analyses, GLIMMIX provides analysts the option to utilize small-sample adjustments that ensure valid inference.

scholarly journals Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials

2014 ◽  
Vol 26 (2) ◽  
pp. 583-597 ◽  
Author(s):  
JoAnna M Scott ◽  
Allan deCamp ◽  
Michal Juraska ◽  
Michael P Fay ◽  
Peter B Gilbert
Keyword(s):  
Treatment Effects ◽  
Randomized Trials ◽  
Estimating Equation ◽  
Small Sample ◽  
Generalized Estimating Equation ◽  
Cluster Randomized Trials ◽  
Stepped Wedge ◽  
Population Average ◽  
Cluster Randomized ◽  
Generalized Estimating

Stepped wedge designs are increasingly commonplace and advantageous for cluster randomized trials when it is both unethical to assign placebo, and it is logistically difficult to allocate an intervention simultaneously to many clusters. We study marginal mean models fit with generalized estimating equations for assessing treatment effectiveness in stepped wedge cluster randomized trials. This approach has advantages over the more commonly used mixed models that (1) the population-average parameters have an important interpretation for public health applications and (2) they avoid untestable assumptions on latent variable distributions and avoid parametric assumptions about error distributions, therefore, providing more robust evidence on treatment effects. However, cluster randomized trials typically have a small number of clusters, rendering the standard generalized estimating equation sandwich variance estimator biased and highly variable and hence yielding incorrect inferences. We study the usual asymptotic generalized estimating equation inferences (i.e., using sandwich variance estimators and asymptotic normality) and four small-sample corrections to generalized estimating equation for stepped wedge cluster randomized trials and for parallel cluster randomized trials as a comparison. We show by simulation that the small-sample corrections provide improvement, with one correction appearing to provide at least nominal coverage even with only 10 clusters per group. These results demonstrate the viability of the marginal mean approach for both stepped wedge and parallel cluster randomized trials. We also study the comparative performance of the corrected methods for stepped wedge and parallel designs, and describe how the methods can accommodate interval censoring of individual failure times and incorporate semiparametric efficient estimators.

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

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.

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

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 ◽  
Cluster Randomized Trials ◽  
Weighted Analysis ◽  
Cluster Randomized

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.

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