Numerous publications have now addressed the principles of designing, analyzing, and reporting the results of, stepped-wedge cluster randomized trials. In contrast, there is little research available pertaining to the design and analysis of multi-arm stepped-wedge cluster randomized trials, utilized to evaluate the effectiveness of multiple experimental interventions. In this paper, we address this by explaining how the required sample size in these multi-arm trials can be ascertained when data are to be analyzed using a linear mixed model. We then go on to describe how the design of such trials can be optimized to balance between minimizing the cost of the trial, and minimizing some function of the covariance matrix of the treatment effect estimates. Using a recently commenced trial that will evaluate the effectiveness of sensor monitoring in an occupational therapy rehabilitation program for older persons after hip fracture as an example, we demonstrate that our designs could reduce the number of observations required for a fixed power level by up to 58%. Consequently, when logistical constraints permit the utilization of any one of a range of possible multi-arm stepped-wedge cluster randomized trial designs, researchers should consider employing our approach to optimize their trials efficiency.
Stepped wedge designs (SWDs) are designs for cluster randomized trials that feature staggered, unidirectional cross-over, typically from a control to a treatment condition. Existing literature on statistical power for SWDs primarily focuses on designs with a single treatment. However, SWDs with multiple treatments are being proposed and conducted. We present a linear mixed model for a SWD with two treatments, with and without an interaction between them. We derive closed form solutions for the standard errors of the treatment effect coefficients for such models along with power calculation met…
Multivariate outcomes are common in pragmatic cluster randomized trials. While sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. In this article, we present computationally efficient power and sample size procedures for stepped wedge cluster randomized trials (SW-CRTs) with multivariate outcomes that differentiate the within-period and between-period intracluster correlation coefficients (ICCs). Under a multivariate linear mixed model, we derive the joint distribution of the intervention test stati…
A sensitivity analysis approach to principal stratification with a continuous longitudinal intermediate outcome: Applications to a cohort stepped wedge trial
The Stepped Wedge Design (SWD) is a form of cluster randomized trial, usually comparing two treatments, which is divided into time periods and sequences, with clusters allocated to sequences. Typically all sequences start with the standard treatment and end with the new treatment, with the change happening at different times in the different sequences. The clusters will usually differ in size but this is overlooked in much of the existing literature. This paper considers the case when clusters have different sizes and determines how efficient designs can be found. The approach uses an approxim…
A Framework for Parametric Time-Varying Treatment Effects in Multiple Intervention Stepped Wedge Design Clinical Trials in the Presence of Non-Uniform Cluster-Period Correlation Structures
The Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；UTHealth Houston School of Public Health, The University of Texas Health Science Center at Houston（休斯顿德克萨斯大学健康科学中心休斯顿公共卫生学院）
A generalized multiple-intervention stepped wedge design framework for treatment effect estimation in the presence of non-uniform cluster-period correlation structures
The Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；UTHealth Houston School of Public Health, The University of Texas Health Science Center at Houston（德克萨斯大学健康科学中心休斯顿分校公共卫生学院）
Randomization inference for stepped-wedge designs with noncompliance with application to a palliative care pragmatic trial
University of Chicago（芝加哥大学）；Data Science Institute, University of Chicago（芝加哥大学数据科学研究所）；University of Pennsylvania（宾夕法尼亚大学）；Department of Medicine, University of Pennsylvania（宾夕法尼亚大学医学系）；Department of Mathematics and Statistics, Mississippi State University（密西西比州立大学数学与统计系）；Department of Statistics and Data Science, University of Pennsylvania（宾夕法尼亚大学统计与数据科学系）；Yale School of Public Health（耶鲁公共卫生学院）
Optimal designs for incomplete stepped wedge trials
Wolfson Institute of Population Health, Queen Mary University of London（伦敦大学玛丽女王学院沃尔森人口健康研究所）；Institute of Applied Health Research, University of Birmingham（伯明翰大学应用健康研究院）
Recently, methodology was presented to facilitate the incorporation of interim analyses in stepped-wedge (SW) cluster randomised trials (CRTs). Here, we extend this previous discussion. We detail how the stopping boundaries, allocation sequences, and per-cluster per-period sample size of a group sequential SW-CRT can be optimised. We then describe methods by which point estimates, p-values, and confidence intervals, which account for the sequential nature of the design, can be calculated. We demonstrate that optimal sequential designs can reduce the expected required number of measurements und…
The ability to accurately estimate the sample size required by a stepped-wedge (SW) cluster randomized trial (CRT) routinely depends upon the specification of several nuisance parameters. If these parameters are mis-specified, the trial could be over-powered, leading to increased cost, or under-powered, enhancing the likelihood of a false negative. We address this issue here for cross-sectional SW-CRTs, analyzed with a particular linear mixed model, by proposing methods for blinded and unblinded sample size re-estimation (SSRE). Blinded estimators for the variance parameters of a SW-CRT analyz…
In stepped wedge cluster randomized trials (SW-CRTs), observations collected under the control condition are, on average, from an earlier time than observations collected under the intervention condition. In a cohort design, participants are followed up throughout the study, so correlations between measurements within a participant are dependent of the timing in which the observations are made. Therefore, changes in participants' characteristics over time must be taken into account when estimating intervention effects. For example, participants' age progresses, which may impact the outcome ove…
Background and objective: The stepped wedge cluster randomized trial is a study design increasingly used for public health intervention evaluations. Most previous literature focuses on power calculations for this particular type of cluster randomized trials for continuous outcomes, along with an approximation to this approach for binary outcomes. Although not accurate for binary outcomes, it has been widely used. To improve the approximation for binary outcomes, two new methods for stepped wedge designs (SWDs) of binary outcomes have recently been published. However, these new methods have not…
Can discrete-time analyses be trusted for stepped wedge trials with continuous recruitment?
Yale School of Public Health（耶鲁公共卫生学院）；Yale School of Medicine（耶鲁医学院）；Monash University（莫纳什大学）；The Ottawa Hospital Research Institute（渥太华医院研究所）；University of Ottawa（渥太华大学）
In 2019, the World Health Organization identified dengue as one of the top ten global health threats. For the control of dengue, the Applying Wolbachia to Eliminate Dengue (AWED) study group conducted a cluster-randomized trial in Yogyakarta, Indonesia, and used a novel design, called the cluster-randomized test-negative design (CR-TND). This design can yield valid statistical inference with data collected by a passive surveillance system and thus has the advantage of cost-efficiency compared to traditional cluster-randomized trials. We investigate the statistical assumptions and properties of…
Stepped wedge cluster randomized trials (SW-CRTs) with binary outcomes are increasingly used in prevention and implementation studies. Marginal models represent a flexible tool for analyzing SW-CRTs with population-averaged interpretations, but the joint estimation of the mean and intraclass correlation coefficients (ICCs) can be computationally intensive due to large cluster-period sizes. Motivated by the need for marginal inference in SW-CRTs, we propose a simple and efficient estimating equations approach to analyze cluster-period means. We show that the quasi-score for the marginal mean de…
A tutorial on conducting sample size and power calculations for detecting treatment effect heterogeneity in cluster randomized trials with linear mixed models
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Ottawa Hospital Research Institute（渥太华医院研究所）；University of Ottawa（渥太华大学）；University of Washington（华盛顿大学）；University of Pennsylvania（宾夕法尼亚大学）；Yale School of Medicine（耶鲁医学院）；Yale School of Public Health（耶鲁公共卫生学院）；Harvard Pilgrim Health Care Institute（哈佛皮尔格里姆健康护理研究所）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）
