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Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models
Author(s) -
Liu Jingxia,
Colditz Graham A.
Publication year - 2018
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201600262
Subject(s) - generalized estimating equation , mathematics , statistics , estimator , sample size determination , estimating equations , crts , cluster (spacecraft) , efficiency , covariate , statistical hypothesis testing , computer science , computer graphics (images) , programming language
There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.