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Empirical power and sample size calculations for cluster-randomized and cluster-randomized crossover studies.

ABSTRACT: In recent years, the number of studies using a cluster-randomized design has grown dramatically. In addition, the cluster-randomized crossover design has been touted as a methodological advance that can increase efficiency of cluster-randomized studies in certain situations. While the cluster-randomized crossover trial has become a popular tool, standards of design, analysis, reporting and implementation have not been established for this emergent design. We address one particular aspect of cluster-randomized and cluster-randomized crossover trial design: estimating statistical power. We present a general framework for estimating power via simulation in cluster-randomized studies with or without one or more crossover periods. We have implemented this framework in the clusterPower software package for R, freely available online from the Comprehensive R Archive Network. Our simulation framework is easy to implement and users may customize the methods used for data analysis. We give four examples of using the software in practice. The clusterPower package could play an important role in the design of future cluster-randomized and cluster-randomized crossover studies. This work is the first to establish a universal method for calculating power for both cluster-randomized and cluster-randomized clinical trials. More research is needed to develop standardized and recommended methodology for cluster-randomized crossover studies.

SUBMITTER: Reich NG

PROVIDER: S-EPMC3338707 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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Empirical power and sample size calculations for cluster-randomized and cluster-randomized crossover studies.

Reich Nicholas G NG Myers Jessica A JA Obeng Daniel D Milstone Aaron M AM Perl Trish M TM

PloS one 20120427 4

In recent years, the number of studies using a cluster-randomized design has grown dramatically. In addition, the cluster-randomized crossover design has been touted as a methodological advance that can increase efficiency of cluster-randomized studies in certain situations. While the cluster-randomized crossover trial has become a popular tool, standards of design, analysis, reporting and implementation have not been established for this emergent design. We address one particular aspect of clus ...[more]

PMID: 22558168

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Project description:Background/aimsGeneralized estimating equations are commonly used to fit logistic regression models to clustered binary data from cluster randomized trials. A commonly used correlation structure assumes that the intracluster correlation coefficient does not vary by treatment arm or other covariates, but the consequences of this assumption are understudied. We aim to evaluate the effect of allowing variation of the intracluster correlation coefficient by treatment or other covariates on the efficiency of analysis and show how to account for such variation in sample size calculations.MethodsWe develop formulae for the asymptotic variance of the estimated difference in outcome between treatment arms obtained when the true exchangeable correlation structure depends on the treatment arm and the working correlation structure used in the generalized estimating equations analysis is: (i) correctly specified, (ii) independent, or (iii) exchangeable with no dependence on treatment arm. These formulae require a known distribution of cluster sizes; we also develop simplifications for the case when cluster sizes do not vary and approximations that can be used when the first two moments of the cluster size distribution are known. We then extend the results to settings with adjustment for a second binary cluster-level covariate. We provide formulae to calculate the required sample size for cluster randomized trials using these variances.ResultsWe show that the asymptotic variance of the estimated difference in outcome between treatment arms using these three working correlation structures is the same if all clusters have the same size, and this asymptotic variance is approximately the same when intracluster correlation coefficient values are small. We illustrate these results using data from a recent cluster randomized trial for infectious disease prevention in which the clusters are groups of households and modest in size (mean 9.6 individuals), with intracluster correlation coefficient values of 0.078 in the control arm and 0.057 in an intervention arm. In this application, we found a negligible difference between the variances calculated using structures (i) and (iii) and only a small increase (typically <5%) for the independent correlation structure (ii), and hence minimal effect on power or sample size requirements. The impact may be larger in other applications if there is greater variation in the ICC between treatment arms or with an additional covariate.ConclusionThe common approach of fitting generalized estimating equations with an exchangeable working correlation structure with a common intracluster correlation coefficient across arms likely does not substantially reduce the power or efficiency of the analysis in the setting of a large number of small or modest-sized clusters, even if the intracluster correlation coefficient varies by treatment arm. Our formulae, however, allow formal evaluation of this and may identify situations in which variation in intracluster correlation coefficient by treatment arm or another binary covariate may have a more substantial impact on power and hence sample size requirements.

Project description:Background/aimsThis article studies the effect of attrition in the cluster randomized crossover trial. The focus is on the two-treatment two-period AB/BA design where attrition occurs during the washout period. Attrition may occur at either the subject level or the cluster level. In the latter case, clusters drop out entirely and provide no measurements in the second period. Subject attrition can only occur in the cohort design, where each subject receives both treatments. Cluster attrition can also occur in the cross-sectional design, where different subjects are measured in the two time periods. Furthermore, this article explores two different strategies to account for potential levels of attrition: increasing sample size and replacing those subjects who drop out by others.MethodsThe statistical model that takes into account the nesting of subjects within clusters, and the nesting of repeated measurements within subjects is presented. The effect of attrition is evaluated on the basis of the efficiency of the treatment effect estimator. Matrix algebra is used to derive the relation between efficiency, the degree of attrition, cluster size and the intraclass correlations: the within-cluster within-period correlation, the within-cluster between-period correlation and (in the case of a cohort design) the within-subject correlation. The methodology is implemented in two Shiny Apps.ResultsAttrition in a cluster randomized crossover trial implies a loss of efficiency. Efficiency decreases with an increase of the attrition rate. The loss of efficiency due to attrition of subjects in a cohort design is largest for small number of subjects per cluster-period, but it may be repaired to a large degree by increasing the number of subjects per cluster-period or by replacing those subjects who drop out by others. Attrition of clusters results in a larger loss of efficiency, but this loss does not depend on the number of subjects per cluster-period. Repairing for this loss requires a large increase in the number of subjects per cluster-period. The methodology of this article is illustrated by an example on the effect of lavender scent on dental patients' anxiety.ConclusionThis article provides the methodology of exploring the effect of attrition in cluster randomized crossover trials, and to repair for attrition. As such, it helps researchers plan their trial in an appropriate way and avoid underpowered trials. To use the methodology, prior estimates of the degree of attrition and intraclass correlation coefficients are needed. It is advocated that researchers clearly report the estimates of these quantities to help facilitate planning future trials.

Project description:BackgroundBefore conducting a microarray experiment, one important issue that needs to be determined is the number of arrays required in order to have adequate power to identify differentially expressed genes. This paper discusses some crucial issues in the problem formulation, parameter specifications, and approaches that are commonly proposed for sample size estimation in microarray experiments. Common methods for sample size estimation are formulated as the minimum sample size necessary to achieve a specified sensitivity (proportion of detected truly differentially expressed genes) on average at a specified false discovery rate (FDR) level and specified expected proportion (pi1) of the true differentially expression genes in the array. Unfortunately, the probability of detecting the specified sensitivity in such a formulation can be low. We formulate the sample size problem as the number of arrays needed to achieve a specified sensitivity with 95% probability at the specified significance level. A permutation method using a small pilot dataset to estimate sample size is proposed. This method accounts for correlation and effect size heterogeneity among genes.ResultsA sample size estimate based on the common formulation, to achieve the desired sensitivity on average, can be calculated using a univariate method without taking the correlation among genes into consideration. This formulation of sample size problem is inadequate because the probability of detecting the specified sensitivity can be lower than 50%. On the other hand, the needed sample size calculated by the proposed permutation method will ensure detecting at least the desired sensitivity with 95% probability. The method is shown to perform well for a real example dataset using a small pilot dataset with 4-6 samples per group.ConclusionsWe recommend that the sample size problem should be formulated to detect a specified proportion of differentially expressed genes with 95% probability. This formulation ensures finding the desired proportion of true positives with high probability. The proposed permutation method takes the correlation structure and effect size heterogeneity into consideration and works well using only a small pilot dataset.

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Empirical power and sample size calculations for cluster-randomized and cluster-randomized crossover studies.

Publications

Empirical power and sample size calculations for cluster-randomized and cluster-randomized crossover studies.

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