title: Sample size determinations for stepped-wedge clinical trials from a three-level data hierarchy perspective.
abstract: Stepped-wedge (SW) designs have been steadily implemented in a variety of trials. A SW design typically assumes a three-level hierarchical data structure where participants are nested within times or periods which are in turn nested within clusters. Therefore, statistical models for analysis of SW trial data need to consider two correlations, the first and second level correlations. Existing power functions and sample size determination formulas had been derived based on statistical models for two-level data structures. Consequently, the second-level correlation has not been incorporated in conventional power analyses. In this paper, we derived a closed-form explicit power function based on a statistical model for three-level continuous outcome data. The power function is based on a pooled overall estimate of stratified cluster-specific estimates of an intervention effect. The sampling distribution of the pooled estimate is derived by applying a fixed-effect meta-analytic approach. Simulation studies verified that the derived power function is unbiased and can be applicable to varying number of participants per period per cluster. In addition, when data structures are assumed to have two levels, we compare three types of power functions by conducting additional simulation studies under a two-level statistical model. In this case, the power function based on a sampling distribution of a marginal, as opposed to pooled, estimate of the intervention effect performed the best. Extensions of power functions to binary outcomes are also suggested.
authors.affiliation: 1 Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY, USA.
authors.forename: Moonseong
authors.initials: M
authors.lastname: Heo
authors.affiliation: 2 Department of Radiology, Albert Einstein College of Medicine, Bronx, NY, USA.
authors.forename: Namhee
authors.initials: N
authors.lastname: Kim
authors.affiliation: 3 Department of Pediatrics, Children's Hospital at Montefiore, Albert Einstein College of Medicine, Bronx, NY, USA.
authors.forename: Michael L
authors.initials: ML
authors.lastname: Rinke
authors.affiliation: 1 Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY, USA.|4 Department of Medicine, Albert Einstein College of Medicine, Bronx, NY, USA.
authors.forename: Judith
authors.initials: J
authors.lastname: Wylie-Rosett
mesh_terms: D056808:Biostatistics; D000078985:Clinical Trial Protocols as Topic; D016000:Cluster Analysis; D003198:Computer Simulation; D018592:Cross-Over Studies; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D018401:Sample Size
keywords: Stepped-wedge design; design effect; effect size; sample size; statistical power; three level data