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Power and sample size requirements for GEE analyses of cluster randomized crossover trials.

ABSTRACT: The cluster randomized crossover design has been proposed to improve efficiency over the traditional parallel cluster randomized design, which often involves a limited number of clusters. In recent years, the cluster randomized crossover design has been increasingly used to evaluate the effectiveness of health care policy or programs, and the interest often lies in quantifying the population-averaged intervention effect. In this paper, we consider the two-treatment two-period crossover design, and develop sample size procedures for continuous and binary outcomes corresponding to a population-averaged model estimated by generalized estimating equations, accounting for both within-period and interperiod correlations. In particular, we show that the required sample size depends on the correlation parameters through an eigenvalue of the within-cluster correlation matrix for continuous outcomes and through two distinct eigenvalues of the correlation matrix for binary outcomes. We demonstrate that the empirical power corresponds well with the predicted power by the proposed formulae for as few as eight clusters, when outcomes are analyzed using the matrix-adjusted estimating equations for the correlation parameters concurrently with a suitable bias-corrected sandwich variance estimator.

SUBMITTER: Li F

PROVIDER: S-EPMC6461037 | biostudies-literature | 2019 Feb

REPOSITORIES: biostudies-literature

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Power and sample size requirements for GEE analyses of cluster randomized crossover trials.

Li Fan F Forbes Andrew B AB Turner Elizabeth L EL Preisser John S JS

Statistics in medicine 20181008 4

The cluster randomized crossover design has been proposed to improve efficiency over the traditional parallel cluster randomized design, which often involves a limited number of clusters. In recent years, the cluster randomized crossover design has been increasingly used to evaluate the effectiveness of health care policy or programs, and the interest often lies in quantifying the population-averaged intervention effect. In this paper, we consider the two-treatment two-period crossover design, a ...[more]

PMID: 30298551

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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.

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Power and sample size requirements for GEE analyses of cluster randomized crossover trials.

Publications

Power and sample size requirements for GEE analyses of cluster randomized crossover trials.

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