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Westgate PM, Nigam SR, Shoben AB. Reconsidering stepped wedge cluster randomized trial designs with implementation periods: Fewer sequences or the parallel-group design with baseline and implementation periods are potentially more efficient. Clin Trials 2024:17407745241244790. [PMID: 38650332 DOI: 10.1177/17407745241244790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
BACKGROUND/AIMS When designing a cluster randomized trial, advantages and disadvantages of tentative designs must be weighed. The stepped wedge design is popular for multiple reasons, including its potential to increase power via improved efficiency relative to a parallel-group design. In many realistic settings, it will take time for clusters to fully implement the intervention. When designing the HEALing (Helping to End Addiction Long-termSM) Communities Study, implementation time was a major consideration, and we examined the efficiency and practicality of three designs. Specifically, a three-sequence stepped wedge design with implementation periods, a corresponding two-sequence modified design that is created by removing the middle sequence, and a parallel-group design with baseline and implementation periods. In this article, we study the relative efficiencies of these specific designs. More generally, we study the relative efficiencies of modified designs when the stepped wedge design with implementation periods has three or more sequences. We also consider different correlation structures. METHODS We compare efficiencies of stepped wedge designs with implementation periods consisting of three to nine sequences with a variety of corresponding designs. The three-sequence design is compared to the two-sequence modified design and to the parallel-group design with baseline and implementation periods analysed via analysis of covariance. Stepped wedge designs with implementation periods consisting of four or more sequences are compared to modified designs that remove all or a subset of 'middle' sequences. Efficiencies are based on the use of linear mixed effects models. RESULTS In the studied settings, the modified design is more efficient than the three-sequence stepped wedge design with implementation periods. The parallel-group design with baseline and implementation periods with analysis of covariance-based analysis is often more efficient than the three-sequence design. With respect to stepped wedge designs with implementation periods that are comprised of more sequences, there are often corresponding modified designs that improve efficiency. However, use of only the first and last sequences has the potential to be either relatively efficient or inefficient. Relative efficiency is impacted by the strength of the statistical correlation among outcomes from the same cluster; for example, the relative efficiencies of modified designs tend to be greater for smaller cluster auto-correlation values. CONCLUSION If a three-sequence stepped wedge design with implementation periods is being considered for a future cluster randomized trial, then a corresponding modified design using only the first and last sequences should be considered if sole focus is on efficiency. However, a parallel-group design with baseline and implementation periods and analysis of covariance-based analysis can be a practical, efficient alternative. For stepped wedge designs with implementation periods and a larger number of sequences, modified versions that remove 'middle' sequences should be considered. Due to the potential sensitivity of design efficiencies, statistical correlation should be carefully considered.
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Affiliation(s)
- Philip M Westgate
- Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY, USA
| | - Shawn R Nigam
- Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY, USA
| | - Abigail B Shoben
- Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, OH, USA
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Grantham KL, Forbes AB, Hooper R, Kasza J. The staircase cluster randomised trial design: A pragmatic alternative to the stepped wedge. Stat Methods Med Res 2024; 33:24-41. [PMID: 38031417 PMCID: PMC10863363 DOI: 10.1177/09622802231202364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2023]
Abstract
This article introduces the 'staircase' design, derived from the zigzag pattern of steps along the diagonal of a stepped wedge design schematic where clusters switch from control to intervention conditions. Unlike a complete stepped wedge design where all participating clusters must collect and provide data for the entire trial duration, clusters in a staircase design are only required to be involved and collect data for a limited number of pre- and post-switch periods. This could alleviate some of the burden on participating clusters, encouraging involvement in the trial and reducing the likelihood of attrition. Staircase designs are already being implemented, although in the absence of a dedicated methodology, approaches to sample size and power calculations have been inconsistent. We provide expressions for the variance of the treatment effect estimator when a linear mixed model for an outcome is assumed for the analysis of staircase designs in order to enable appropriate sample size and power calculations. These include explicit variance expressions for basic staircase designs with one pre- and one post-switch measurement period. We show how the variance of the treatment effect estimator is related to key design parameters and demonstrate power calculations for examples based on a real trial.
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Affiliation(s)
- Kelsey L Grantham
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
| | - Andrew B Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
| | - Richard Hooper
- Wolfson Institute of Population Health, Queen Mary University of London, London, UK
| | - Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
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Li F, Kasza J, Turner EL, Rathouz PJ, Forbes AB, Preisser JS. Generalizing the information content for stepped wedge designs: A marginal modeling approach. Scand Stat Theory Appl 2023; 50:1048-1067. [PMID: 37601275 PMCID: PMC10434823 DOI: 10.1111/sjos.12615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2022] [Accepted: 09/02/2022] [Indexed: 11/30/2022]
Abstract
Stepped wedge trials are increasingly adopted because practical constraints necessitate staggered roll-out. While a complete design requires clusters to collect data in all periods, resource and patient-centered considerations may call for an incomplete stepped wedge design to minimize data collection burden. To study incomplete designs, we expand the metric of information content to discrete outcomes. We operate under a marginal model with general link and variance functions, and derive information content expressions when data elements (cells, sequences, periods) are omitted. We show that the centrosymmetric patterns of information content can hold for discrete outcomes with the variance-stabilizing link function. We perform numerical studies under the canonical link function, and find that while the patterns of information content for cells are approximately centrosymmetric for all examined underlying secular trends, the patterns of information content for sequences or periods are more sensitive to the secular trend, and may be far from centrosymmetric.
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Affiliation(s)
- Fan Li
- Department of Biostatistics, Yale University School of Public Health, New Haven, Connecticut, USA
- Center for Methods in Implementation and Prevention Science, Yale University, New Haven, Connecticut, USA
| | - Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Victoria, Australia
| | - Elizabeth L. Turner
- Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina, USA
| | - Paul J. Rathouz
- Department of Population Health, The University of Texas at Austin, Austin, Texas, USA
| | - Andrew B. Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Victoria, Australia
| | - John S. Preisser
- Department of Epidemiology, Gillings School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
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Rezaei-Darzi E, Grantham KL, Forbes AB, Kasza J. The impact of iterative removal of low-information cluster-period cells from a stepped wedge design. BMC Med Res Methodol 2023; 23:160. [PMID: 37415140 PMCID: PMC10324156 DOI: 10.1186/s12874-023-01969-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Accepted: 06/08/2023] [Indexed: 07/08/2023] Open
Abstract
BACKGROUND Standard stepped wedge trials, where clusters switch from the control to the intervention condition in a staggered manner, can be costly and burdensome. Recent work has shown that the amount of information contributed by each cluster in each period differs, with some cluster-periods contributing a relatively small amount of information. We investigate the patterns of the information content of cluster-period cells upon iterative removal of low-information cells, assuming a model for continuous outcomes with constant cluster-period size, categorical time period effects, and exchangeable and discrete-time decay intracluster correlation structures. METHODS We sequentially remove pairs of "centrosymmetric" cluster-period cells from an initially complete stepped wedge design which contribute the least amount of information to the estimation of the treatment effect. At each iteration, we update the information content of the remaining cells, determine the pair of cells with the lowest information content, and repeat this process until the treatment effect cannot be estimated. RESULTS We demonstrate that as more cells are removed, more information is concentrated in the cells near the time of the treatment switch, and in "hot-spots" in the corners of the design. For the exchangeable correlation structure, removing the cells from these hot-spots leads to a marked reduction in study precision and power, however the impact of this is lessened for the discrete-time decay structure. CONCLUSIONS Removing cluster-period cells distant from the time of the treatment switch may not lead to large reductions in precision or power, implying that certain incomplete designs may be almost as powerful as complete designs.
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Affiliation(s)
- Ehsan Rezaei-Darzi
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
| | - Kelsey L. Grantham
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
| | - Andrew B. Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
| | - Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
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Mildenberger P, König J. Influence of cluster-period cells in stepped wedge cluster randomized trials. Biom J 2022. [PMID: 36161328 DOI: 10.1002/bimj.202100383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Revised: 08/01/2022] [Accepted: 08/14/2022] [Indexed: 11/09/2022]
Abstract
Stepped wedge cluster randomized trials (SWCRT) are increasingly used for the evaluation of complex interventions in health services research. They randomly allocate treatments to clusters that switch to intervention under investigation at variable time points without returning to control condition. The resulting unbalanced allocation over time periods and the uncertainty about the underlying correlation structures at cluster-level renders designing and analyzing SWCRTs a challenge. Adjusting for time trends is recommended, appropriate parameterizations depend on the particular context. For sample size calculation, the covariance structure and covariance parameters are usually assumed to be known. These assumptions greatly affect the influence single cluster-period cells have on the effect estimate. Thus, it is important to understand how cluster-period cells contribute to the treatment effect estimate. We therefore discuss two measures of cell influence. These are functions of the design characteristics and covariance structure only and can thus be calculated at the planning stage: the coefficient matrix as discussed by Matthews and Forbes and information content (IC) as introduced by Kasza and Forbes. The main result is a new formula for IC that is more general and computationally more efficient. The formula applies to any generalized least squares estimator, especially for any type of time trend adjustment or nonblock diagonal matrices. We further show a functional relationship between IC and the coefficient matrix. We give two examples that tie in with current literature. All discussed tools and methods are implemented in the R package SteppedPower.
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Affiliation(s)
- Philipp Mildenberger
- Institute of Medical Biostatistics, Epidemiology and Informatics (IMBEI), University Medical Center Johannes Gutenberg University Mainz, Mainz, Germany
| | - Jochem König
- Institute of Medical Biostatistics, Epidemiology and Informatics (IMBEI), University Medical Center Johannes Gutenberg University Mainz, Mainz, Germany
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Kasza J, Bowden R, Hooper R, Forbes AB. The batched stepped wedge design: A design robust to delays in cluster recruitment. Stat Med 2022; 41:3627-3641. [PMID: 35596691 PMCID: PMC9541502 DOI: 10.1002/sim.9438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Revised: 04/13/2022] [Accepted: 05/05/2022] [Indexed: 11/08/2022]
Abstract
Stepped wedge designs are an increasingly popular variant of longitudinal cluster randomized trial designs, and roll out interventions across clusters in a randomized, but step-wise fashion. In the standard stepped wedge design, assumptions regarding the effect of time on outcomes may require that all clusters start and end trial participation at the same time. This would require ethics approvals and data collection procedures to be in place in all clusters before a stepped wedge trial can start in any cluster. Hence, although stepped wedge designs are useful for testing the impacts of many cluster-based interventions on outcomes, there can be lengthy delays before a trial can commence. In this article, we introduce "batched" stepped wedge designs. Batched stepped wedge designs allow clusters to commence the study in batches, instead of all at once, allowing for staggered cluster recruitment. Like the stepped wedge, the batched stepped wedge rolls out the intervention to all clusters in a randomized and step-wise fashion: a series of self-contained stepped wedge designs. Provided that separate period effects are included for each batch, software for standard stepped wedge sample size calculations can be used. With this time parameterization, in many situations including when linear models are assumed, sample size calculations reduce to the setting of a single stepped wedge design with multiple clusters per sequence. In these situations, sample size calculations will not depend on the delays between the commencement of batches. Hence, the power of batched stepped wedge designs is robust to unexpected delays between batches.
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Affiliation(s)
- Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Victoria, Australia
| | - Rhys Bowden
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Victoria, Australia
| | - Richard Hooper
- Centre for Primary Care and Public Health, Queen Mary University of London, London, UK
| | - Andrew B Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Victoria, Australia
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Harrison LJ, Wang R. Power calculation for analyses of cross-sectional stepped-wedge cluster randomized trials with binary outcomes via generalized estimating equations. Stat Med 2021; 40:6674-6688. [PMID: 34558112 DOI: 10.1002/sim.9205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Revised: 08/31/2021] [Accepted: 09/06/2021] [Indexed: 11/08/2022]
Abstract
Power calculation for stepped-wedge cluster randomized trials (SW-CRTs) presents unique challenges, beyond those of standard parallel cluster randomized trials, due to the need to consider temporal within cluster correlations and background period effects. To date, power calculation methods specific to SW-CRTs have primarily been developed under a linear model. When the outcome is binary, the use of a linear model corresponds to assessing a prevalence difference; yet trial analysis often employs a nonlinear link function. We propose power calculation methods for cross-sectional SW-CRTs under a logistic model fitted by generalized estimating equations. Firstly, under an exchangeable correlation structure, we show the power based on a logistic model is lower than that from assuming a linear model in the absence of period effects. We then evaluate the impact of background prevalence changes over time on power. To allow the correlation among outcomes in the same cluster to change over time and with treatment status, we generalize the methods to more complex correlation structures. Our simulation studies demonstrate that the proposed power calculation methods perform well with the model-based variance under the true correlation structure and reveal that a working independence structure can result in substantial efficiency loss, while a working exchangeable structure performs well even when the underlying correlation structure deviates from exchangeable. An extension to our methods accounts for variable cluster sizes and reveals that unequal cluster sizes have a modest impact on power. We illustrate the approaches by application to a quality of care improvement trial for acute coronary syndrome.
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Affiliation(s)
- Linda J Harrison
- Department of Biostatistics, Harvard TH Chan School of Public Health, Boston, Massachusetts, USA
| | - Rui Wang
- Department of Biostatistics, Harvard TH Chan School of Public Health, Boston, Massachusetts, USA.,Department of Population Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, Massachusetts, USA
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Zhan D, Xu L, Ouyang Y, Sawatzky R, Wong H. Methods for dealing with unequal cluster sizes in cluster randomized trials: A scoping review. PLoS One 2021; 16:e0255389. [PMID: 34324593 PMCID: PMC8320970 DOI: 10.1371/journal.pone.0255389] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 07/15/2021] [Indexed: 11/18/2022] Open
Abstract
In a cluster-randomized trial (CRT), the number of participants enrolled often varies across clusters. This variation should be considered during both trial design and data analysis to ensure statistical performance goals are achieved. Most methodological literature on the CRT design has assumed equal cluster sizes. This scoping review focuses on methodology for unequal cluster size CRTs. EMBASE, Medline, Google Scholar, MathSciNet and Web of Science databases were searched to identify English-language articles reporting on methodology for unequal cluster size CRTs published until March 2021. We extracted data on the focus of the paper (power calculation, Type I error etc.), the type of CRT, the type and the range of parameter values investigated (number of clusters, mean cluster size, cluster size coefficient of variation, intra-cluster correlation coefficient, etc.), and the main conclusions. Seventy-nine of 5032 identified papers met the inclusion criteria. Papers primarily focused on the parallel-arm CRT (p-CRT, n = 60, 76%) and the stepped-wedge CRT (n = 14, 18%). Roughly 75% of the papers addressed trial design issues (sample size/power calculation) while 25% focused on analysis considerations (Type I error, bias, etc.). The ranges of parameter values explored varied substantially across different studies. Methods for accounting for unequal cluster sizes in the p-CRT have been investigated extensively for Gaussian and binary outcomes. Synthesizing the findings of these works is difficult as the magnitude of impact of the unequal cluster sizes varies substantially across the combinations and ranges of input parameters. Limited investigations have been done for other combinations of a CRT design by outcome type, particularly methodology involving binary outcomes-the most commonly used type of primary outcome in trials. The paucity of methodological papers outside of the p-CRT with Gaussian or binary outcomes highlights the need for further methodological development to fill the gaps.
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Affiliation(s)
- Denghuang Zhan
- School of Population and Public Health, University of British Columbia, Vancouver, British Columbia, Canada
- Centre for Health Evaluation and Outcomes Sciences, University of British Columbia, Vancouver, British Columbia, Canada
| | - Liang Xu
- School of Population and Public Health, University of British Columbia, Vancouver, British Columbia, Canada
- Centre for Health Evaluation and Outcomes Sciences, University of British Columbia, Vancouver, British Columbia, Canada
| | - Yongdong Ouyang
- School of Population and Public Health, University of British Columbia, Vancouver, British Columbia, Canada
- Centre for Health Evaluation and Outcomes Sciences, University of British Columbia, Vancouver, British Columbia, Canada
| | - Richard Sawatzky
- Centre for Health Evaluation and Outcomes Sciences, University of British Columbia, Vancouver, British Columbia, Canada
- School of Nursing, Trinity Western University, Langley City, British Columbia, Canada
| | - Hubert Wong
- School of Population and Public Health, University of British Columbia, Vancouver, British Columbia, Canada
- Centre for Health Evaluation and Outcomes Sciences, University of British Columbia, Vancouver, British Columbia, Canada
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