Effect of weight loss on bone health in overweight/obese postmenopausal breast cancer survivors

2018

Biometrical J

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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.

Section: Introductionmentioning

confidence: 99%

Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

2018

Biometrical J

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“…We obtainn = 46.6 using Equation (13). If the design space is (11,20), then the design of (n = 20, m = 23) is MMD under the budget constraints; on the other hand, if the design space is (41, 50), then the design of (n = 47, m = 18) is MMD under the budget constraints.…”

Section: Figurementioning

confidence: 99%

“…For each K, n MMD and m MMD are calculated from the step-by-step approach, and the corresponding RE is provided. If the design space is (11,20), then the design of (K = 10, n = 20, m = 21) is MMD under the budget constraints; on the other hand, if the design space is (41, 50), then the design of (K = 3, n = 47, m = 18) is MMD under the budget constraints. SAS macros %OD_3Level_FixedK and %OD_3Level_RangeK are developed to find LOD and MMD when the corresponding parameters are provided.…”

Section: Figurementioning

confidence: 99%

“…Generalized estimating equations (GEEs) proposed by Liang and Zeger 19 have been commonly applied to analyze the correlated data in CRTs. [20][21][22][23][24] Liang and Zeger showed that the GEE approach still gives consistent estimates of the regression coefficients provided that the marginal model is correctly specified, even if the working correlation matrix is incorrectly assumed. 19 In this paper, we aim to propose an optimal design (OD) in three-level CRTs, in which "optimal" refers to the minimization of the variance of each measure estimator for a given sampling budget.…”

Section: Introductionmentioning

confidence: 99%

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Optimal designs in three‐level cluster randomized trials with a binary outcome

2019

Statistics in Medicine

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Cluster randomized trials (CRTs) were originally proposed for use when randomization at the subject level is practically infeasible or may lead to a severe estimation bias of the treatment effect. However, recruiting an additional cluster costs more than enrolling an additional subject in an individually randomized trial. Under budget constraints, researchers have proposed the optimal sample sizes in two-level CRTs. CRTs may have a three-level structure, in which two levels of clustering should be considered. In this paper, we propose optimal designs in three-level CRTs with a binary outcome, assuming a nested exchangeable correlation structure in generalized estimating equation models. We provide the variance of estimators of three commonly used measures: risk difference, risk ratio, and odds ratio. For a given sampling budget, we discuss how many clusters and how many subjects per cluster are necessary to minimize the variance of each measure estimator. For known association parameters, the locally optimal design is proposed. When association parameters are unknown but within predetermined ranges, the MaxiMin design is proposed to maximize the minimum of relative efficiency over the possible ranges, that is, to minimize the risk of the worst scenario. KEYWORDS cluster randomized trial (CRT), dissemination and implementation, generalized estimating equation (GEE), intracluster correlation coefficient (ICC), nested correlation structure Statistics in Medicine. 2019;38:3733-3746.wileyonlinelibrary.com/journal/sim

“…The advantage of this approach is that consistent estimates are provided when the marginal model is correctly specified, even if the working correlation matrix is incorrectly assumed. Therefore, GEE has been popularly applied (Dahmen et al., ; Sanda et al., ; Lin et al., ; Park et al., ; Toriola et al., ; Jeffe et al., ).…”

Section: Introductionmentioning

confidence: 99%

Optimal design of longitudinal data analysis using generalized estimating equation models

2016

Biometrical J

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Longitudinal studies are often applied in biomedical research and clinical trials to evaluate the treatment effect. The association pattern within the subject must be considered in both sample size calculation and the analysis. One of the most important approaches to analyze such a study is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which “working correlation structure” is introduced and the association pattern within the subject depends on a vector of association parameters denoted by ρ. The explicit sample size formulas for two-group comparison in linear and logistic regression models are obtained based on the GEE method by Liu and Liang. For cluster randomized trials (CRTs), researchers proposed the optimal sample sizes at both the cluster and individual level as a function of sampling costs and the intracluster correlation coefficient (ICC). In these approaches, the optimal sample sizes depend strongly on the ICC. However, the ICC is usually unknown for cluster randomized and multicenter trials. To overcome this shortcoming, Van Breukelen et al consider a range of possible ICC values identified from literature reviews and present Maximin designs (MMDs) based on relative efficiency (RE) and efficiency under budget and cost constraints. In this paper, the optimal sample size and number of repeated measurements using GEE models with an exchangeable working correlation matrix is proposed under the considerations of fixed budget, where “optimal” refers to maximum power for a given sampling budget. The equations of sample size and number of repeated measurements for a known parameter value ρ are derived and a straightforward algorithm for unknown ρ is developed. Applications in practice are discussed. We also discuss the existence of the optimal design when an AR(1) working correlation matrix is assumed. Our proposed method can be extended under the scenarios when the true and working correlation matrix are different.