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Liu J, Li F. Optimal designs using generalized estimating equations in cluster randomized crossover and stepped wedge trials. Stat Methods Med Res 2024:9622802241247717. [PMID: 38813761 DOI: 10.1177/09622802241247717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
Cluster randomized crossover and stepped wedge cluster randomized trials are two types of longitudinal cluster randomized trials that leverage both the within- and between-cluster comparisons to estimate the treatment effect and are increasingly used in healthcare delivery and implementation science research. While the variance expressions of estimated treatment effect have been previously developed from the method of generalized estimating equations for analyzing cluster randomized crossover trials and stepped wedge cluster randomized trials, little guidance has been provided for optimal designs to ensure maximum efficiency. Here, an optimal design refers to the combination of optimal cluster-period size and optimal number of clusters that provide the smallest variance of the treatment effect estimator or maximum efficiency under a fixed total budget. In this work, we develop optimal designs for multiple-period cluster randomized crossover trials and stepped wedge cluster randomized trials with continuous outcomes, including both closed-cohort and repeated cross-sectional sampling schemes. Local optimal design algorithms are proposed when the correlation parameters in the working correlation structure are known. MaxiMin optimal design algorithms are proposed when the exact values are unavailable, but investigators may specify a range of correlation values. The closed-form formulae of local optimal design and MaxiMin optimal design are derived for multiple-period cluster randomized crossover trials, where the cluster-period size and number of clusters are decimal. The decimal estimates from closed-form formulae can then be used to investigate the performances of integer estimates from local optimal design and MaxiMin optimal design algorithms. One unique contribution from this work, compared to the previous optimal design research, is that we adopt constrained optimization techniques to obtain integer estimates under the MaxiMin optimal design. To assist practical implementation, we also develop four SAS macros to find local optimal designs and MaxiMin optimal designs.
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Affiliation(s)
- Jingxia Liu
- Division of Public Health Sciences, Department of Surgery and Division of Biostatistics, Washington University School of Medicine, St. Louis, MO, USA
| | - Fan Li
- Department of Biostatistics, Yale University, New Haven, CT, USA
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2
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Ouyang Y, Taljaard M, Forbes AB, Li F. Maintaining the validity of inference from linear mixed models in stepped-wedge cluster randomized trials under misspecified random-effects structures. Stat Methods Med Res 2024:9622802241248382. [PMID: 38807552 DOI: 10.1177/09622802241248382] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials. A key consideration for analyzing a stepped-wedge cluster randomized trial is accounting for the potentially complex correlation structure, which can be achieved by specifying random-effects. The simplest random effects structure is random intercept but more complex structures such as random cluster-by-period, discrete-time decay, and more recently, the random intervention structure, have been proposed. Specifying appropriate random effects in practice can be challenging: assuming more complex correlation structures may be reasonable but they are vulnerable to computational challenges. To circumvent these challenges, robust variance estimators may be applied to linear mixed models to provide consistent estimators of standard errors of fixed effect parameters in the presence of random-effects misspecification. However, there has been no empirical investigation of robust variance estimators for stepped-wedge cluster randomized trials. In this article, we review six robust variance estimators (both standard and small-sample bias-corrected robust variance estimators) that are available for linear mixed models in R, and then describe a comprehensive simulation study to examine the performance of these robust variance estimators for stepped-wedge cluster randomized trials with a continuous outcome under different data generators. For each data generator, we investigate whether the use of a robust variance estimator with either the random intercept model or the random cluster-by-period model is sufficient to provide valid statistical inference for fixed effect parameters, when these working models are subject to random-effect misspecification. Our results indicate that the random intercept and random cluster-by-period models with robust variance estimators performed adequately. The CR3 robust variance estimator (approximate jackknife) estimator, coupled with the number of clusters minus two degrees of freedom correction, consistently gave the best coverage results, but could be slightly conservative when the number of clusters was below 16. We summarize the implications of our results for the linear mixed model analysis of stepped-wedge cluster randomized trials and offer some practical recommendations on the choice of the analytic model.
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Affiliation(s)
- Yongdong Ouyang
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
- School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON, Canada
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
- School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON, Canada
| | - Andrew B Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
| | - Fan Li
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
- Center for Methods in Implementation and Prevention Science, Yale School of Public Health, New Haven, CT, USA
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Li F, Chen X, Tian Z, Wang R, Heagerty PJ. Planning stepped wedge cluster randomized trials to detect treatment effect heterogeneity. Stat Med 2024; 43:890-911. [PMID: 38115805 DOI: 10.1002/sim.9990] [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] [Received: 11/06/2022] [Revised: 09/22/2023] [Accepted: 11/30/2023] [Indexed: 12/21/2023]
Abstract
Stepped wedge design is a popular research design that enables a rigorous evaluation of candidate interventions by using a staggered cluster randomization strategy. While analytical methods were developed for designing stepped wedge trials, the prior focus has been solely on testing for the average treatment effect. With a growing interest on formal evaluation of the heterogeneity of treatment effects across patient subpopulations, trial planning efforts need appropriate methods to accurately identify sample sizes or design configurations that can generate evidence for both the average treatment effect and variations in subgroup treatment effects. To fill in that important gap, this article derives novel variance formulas for confirmatory analyses of treatment effect heterogeneity, that are applicable to both cross-sectional and closed-cohort stepped wedge designs. We additionally point out that the same framework can be used for more efficient average treatment effect analyses via covariate adjustment, and allows the use of familiar power formulas for average treatment effect analyses to proceed. Our results further sheds light on optimal design allocations of clusters to maximize the weighted precision for assessing both the average and heterogeneous treatment effects. We apply the new methods to the Lumbar Imaging with Reporting of Epidemiology Trial, and carry out a simulation study to validate our new methods.
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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 School of Public Health, New Haven, Connecticut, USA
| | - Xinyuan Chen
- Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi, USA
| | - Zizhong Tian
- Department of Public Health Sciences, Pennsylvania State University College of Medicine, Hershey, Pennsylvania, USA
| | - Rui Wang
- Department of Population Medicine, Harvard Pilgrim Health Care Institute and Harvard Medical School, Boston, Massachusetts, USA
- Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
| | - Patrick J Heagerty
- Department of Biostatistics, University of Washington, Seattle, Washington, USA
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Surr C, Marsden L, Griffiths A, Cox S, Fossey J, Martin A, Prevost AT, Walshe C, Walwyn R. Researchers' experiences of the design and conduct challenges associated with parallel-group cluster-randomised trials and views on a novel open-cohort design. PLoS One 2024; 19:e0297184. [PMID: 38394190 PMCID: PMC10889884 DOI: 10.1371/journal.pone.0297184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 12/29/2023] [Indexed: 02/25/2024] Open
Abstract
BACKGROUND Two accepted designs exist for parallel-group cluster-randomised trials (CRTs). Closed-cohort designs follow the same individuals over time with a single recruitment period before randomisation, but face challenges in settings with high attrition. (Repeated) cross-sectional designs recruit at one or more timepoints before and/or after randomisation, collecting data from different individuals present in the cluster at these timepoints, but are unsuitable for assessment of individual change over time. An 'open-cohort' design allows individual follow-up with recruitment before and after cluster-randomisation, but little literature exists on acceptability to inform their use in CRTs. AIM To document the views and experiences of expert trialists to identify: a) Design and conduct challenges with established parallel-group CRT designs,b) Perceptions of potential benefits and barriers to implementation of open-cohort CRTs,c) Methods for minimising, and investigating the impact of, bias in open-cohort CRTs. METHODS Qualitative consultation via two expert workshops including triallists (n = 24) who had worked on CRTs over a range of settings. Workshop transcripts were analysed using Descriptive Thematic Analysis utilising inductive and deductive coding. RESULTS Two central organising concepts were developed. Design and conduct challenges with established CRT designs confirmed that current CRT designs are unable to deal with many of the complex research and intervention circumstances found in some trial settings (e.g. care homes). Perceptions of potential benefits and barriers of open cohort designs included themes on: approaches to recruitment; data collection; analysis; minimising/investigating the impact of bias; and how open-cohort designs might address or present CRT design challenges. Open-cohort designs were felt to provide a solution for some of the challenges current CRT designs present in some settings. CONCLUSIONS Open-cohort CRT designs hold promise for addressing the challenges associated with standard CRT designs. Research is needed to provide clarity around definition and guidance on application.
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Affiliation(s)
- Claire Surr
- Centre for Dementia Research, Leeds Beckett University, Leeds, United Kingdom
| | - Laura Marsden
- Clinical Trials Research Unit, University of Leeds, Leeds, United Kingdom
| | - Alys Griffiths
- Institute of Population Health, University of Liverpool, Liverpool, United Kingdom
| | - Sharon Cox
- Department of Behavioural Science and Health, UCL, London, United Kingdom
| | - Jane Fossey
- Faculty of Health and Life Sciences, University of Exeter, Exeter, United Kingdom
| | - Adam Martin
- Academic Unit of Health Economics, University of Leeds, Leeds, United Kingdom
| | - A. Toby Prevost
- Nightingale-Saunders Clinical Trials & Epidemiology Unit, Kings College London, London, United Kingdom
| | - Catherine Walshe
- International Observatory on End of Life Care, Lancaster University, Lancaster, United Kingdom
| | - Rebecca Walwyn
- Clinical Trials Research Unit, University of Leeds, Leeds, United Kingdom
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Hemming K, Copas A, Forbes A, Kasza J. What type of cluster randomized trial for which setting? JOURNAL OF EPIDEMIOLOGY AND POPULATION HEALTH 2024; 72:202195. [PMID: 38477476 DOI: 10.1016/j.jeph.2024.202195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Revised: 01/03/2024] [Accepted: 01/08/2024] [Indexed: 03/14/2024]
Abstract
The cluster randomized trial allows a randomized evaluation when it is either not possible to randomize the individual or randomizing individuals would put the trial at high risk of contamination across treatment arms. There are many variations of the cluster randomized design, including the parallel design with or without baseline measures, the cluster randomized cross-over design, the stepped-wedge cluster randomized design, and more recently-developed variants such as the batched stepped-wedge design and the staircase design. Once it has been clearly established that there is a need for cluster randomization, one ever important question is which form the cluster design should take. If a design in which time is split into multiple trial periods is to be adopted (e.g. as in a stepped-wedge), researchers must decide whether the same participants should be measured in multiple trial periods (cohort sampling); or if different participants should be measured in each period (continual recruitment or cross-sectional sampling). Here we outline the different possible options and weigh up the pros and cons of the different design choices, which revolve around statistical efficiency, study logistics and the assumptions required.
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Affiliation(s)
- Karla Hemming
- Institute of Applied Health Research, University of Birmingham, Birmingham, UK.
| | - Andrew Copas
- MRC Clinical Trials Unit at University College London, London, UK
| | - Andrew Forbes
- School of Public Health and Preventive Medicine, Monash University, Victoria, Australia
| | - Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Victoria, Australia
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Leyrat C, Eldridge S, Taljaard M, Hemming K. Practical considerations for sample size calculation for cluster randomized trials. JOURNAL OF EPIDEMIOLOGY AND POPULATION HEALTH 2024; 72:202198. [PMID: 38477482 DOI: 10.1016/j.jeph.2024.202198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Revised: 01/16/2024] [Accepted: 01/17/2024] [Indexed: 03/14/2024]
Abstract
Cluster randomized trials are an essential design in public health and medical research, when individual randomization is infeasible or undesirable for scientific or logistical reasons. However, the correlation among observations within clusters leads to a decrease in statistical power compared to an individually randomised trial with the same total sample size. This correlation - often quantified using the intra-cluster correlation coefficient - must be accounted for in the sample size calculation to ensure that the trial is adequately powered. In this paper, we first describe the principles of sample size calculation for parallel-arm CRTs, and explain how these calculations can be extended to CRTs with cross-over designs, with a baseline measurement and stepped-wedge designs. We introduce tools to guide researchers with their sample size calculation and discuss methods to inform the choice of the a priori estimate of the intra-cluster correlation coefficient for the calculation. We also include additional considerations with respect to anticipated attrition, a small number of clusters, and use of covariates in the randomisation process and in the analysis.
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Affiliation(s)
- Clémence Leyrat
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK.
| | - Sandra Eldridge
- Wolfson Institute of Population Health, Faculty of Medicine and Dentistry, Queen Mary University of London, London, UK
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada; School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON, Canada
| | - Karla Hemming
- Institute of Applied Health Research, University of Birmingham, Birmingham, UK
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Kasza J, Bowden R, Ouyang Y, Taljaard M, Forbes AB. Does it decay? Obtaining decaying correlation parameter values from previously analysed cluster randomised trials. Stat Methods Med Res 2023; 32:2123-2134. [PMID: 37589088 PMCID: PMC10683336 DOI: 10.1177/09622802231194753] [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: 08/18/2023]
Abstract
A frequently applied assumption in the analysis of data from cluster randomised trials is that the outcomes from all participants within a cluster are equally correlated. That is, the intracluster correlation, which describes the degree of dependence between outcomes from participants in the same cluster, is the same for each pair of participants in a cluster. However, recent work has discussed the importance of allowing for this correlation to decay as the time between the measurement of participants in a cluster increases. Incorrect omission of such a decay can lead to under-powered studies, and confidence intervals for estimated treatment effects can be too narrow or too wide, depending on the characteristics of the design. When planning studies, researchers often rely on previously reported analyses of trials to inform their choice of intracluster correlation. However, most reported analyses of clustered data do not incorporate a correlation decay. Thus, often all that is available are estimates of intracluster correlations obtained under the potentially incorrect assumption of no decay. In this article, we show that it is possible to use intracluster correlation values obtained from models that incorrectly omit a decay to inform plausible choices of decaying correlations. Our focus is on intracluster correlation estimates for continuous outcomes obtained by fitting linear mixed models with exchangeable or block-exchangeable correlation structures. We describe how plausible values for decaying correlations may be obtained given these estimated intracluster correlations. An online app is presented that allows users to obtain plausible values of the decay, which can be used at the trial planning stage to assess the sensitivity of sample size and power calculations to decaying correlation structures.
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Affiliation(s)
- Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
| | - Rhys Bowden
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
| | - Yongdong Ouyang
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, Canada
- School of Epidemiology and Public Health, University of Ottawa, Ottawa, Canada
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, Canada
- School of Epidemiology and Public Health, University of Ottawa, Ottawa, Canada
| | - Andrew B Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
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Hemming K, Taljaard M. Key considerations for designing, conducting and analysing a cluster randomized trial. Int J Epidemiol 2023; 52:1648-1658. [PMID: 37203433 PMCID: PMC10555937 DOI: 10.1093/ije/dyad064] [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: 08/13/2022] [Accepted: 05/02/2023] [Indexed: 05/20/2023] Open
Abstract
Not only do cluster randomized trials require a larger sample size than individually randomized trials, they also face many additional complexities. The potential for contamination is the most commonly used justification for using cluster randomization, but the risk of contamination should be carefully weighed against the more serious problem of questionable scientific validity in settings with post-randomization identification or recruitment of participants unblinded to the treatment allocation. In this paper we provide some simple guidelines to help researchers conduct cluster trials in a way that minimizes potential biases and maximizes statistical efficiency. The overarching theme of this guidance is that methods that apply to individually randomized trials rarely apply to cluster randomized trials. We recommend that cluster randomization be only used when necessary-balancing the benefits of cluster randomization with its increased risks of bias and increased sample size. Researchers should also randomize at the lowest possible level-balancing the risks of contamination with ensuring an adequate number of randomization units-as well as exploring other options for statistically efficient designs. Clustering should always be allowed for in the sample size calculation; and the use of restricted randomization (and adjustment in the analysis for covariates used in the randomization) should be considered. Where possible, participants should be recruited before randomizing clusters and, when recruiting (or identifying) participants post-randomization, recruiters should be masked to the allocation. In the analysis, the target of inference should align with the research question, and adjustment for clustering and small sample corrections should be used when the trial includes less than about 40 clusters.
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Affiliation(s)
- Karla Hemming
- Institute of Applied Health Research, University of Birmingham, Birmingham, UK
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
- School of Epidemiology, Public Health and Preventive Medicine, University of Ottawa, Ottawa, ON, Canada
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Ouyang Y, Hemming K, Li F, Taljaard M. Estimating intra-cluster correlation coefficients for planning longitudinal cluster randomized trials: a tutorial. Int J Epidemiol 2023; 52:1634-1647. [PMID: 37196320 PMCID: PMC10555741 DOI: 10.1093/ije/dyad062] [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] [Received: 09/11/2022] [Accepted: 04/26/2023] [Indexed: 05/19/2023] Open
Abstract
It is well-known that designing a cluster randomized trial (CRT) requires an advance estimate of the intra-cluster correlation coefficient (ICC). In the case of longitudinal CRTs, where outcomes are assessed repeatedly in each cluster over time, estimates for more complex correlation structures are required. Three common types of correlation structures for longitudinal CRTs are exchangeable, nested/block exchangeable and exponential decay correlations-the latter two allow the strength of the correlation to weaken over time. Determining sample sizes under these latter two structures requires advance specification of the within-period ICC and cluster autocorrelation coefficient as well as the intra-individual autocorrelation coefficient in the case of a cohort design. How to estimate these coefficients is a common challenge for investigators. When appropriate estimates from previously published longitudinal CRTs are not available, one possibility is to re-analyse data from an available trial dataset or to access observational data to estimate these parameters in advance of a trial. In this tutorial, we demonstrate how to estimate correlation parameters under these correlation structures for continuous and binary outcomes. We first introduce the correlation structures and their underlying model assumptions under a mixed-effects regression framework. With practical advice for implementation, we then demonstrate how the correlation parameters can be estimated using examples and we provide programming code in R, SAS, and Stata. An Rshiny app is available that allows investigators to upload an existing dataset and obtain the estimated correlation parameters. We conclude by identifying some gaps in the literature.
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Affiliation(s)
- Yongdong Ouyang
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
- School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON, Canada
| | - Karla Hemming
- Institute of Applied Health Research, The University of Birmingham, Birmingham, UK
| | - Fan Li
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
- Center for Methods in Implementation and Prevention Science, Yale School of Public Health, New Haven, CT, USA
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
- School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON, Canada
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10
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Moerbeek M. Optimal allocation of clusters in stepped wedge designs with a decaying correlation structure. PLoS One 2023; 18:e0289275. [PMID: 37585398 PMCID: PMC10431648 DOI: 10.1371/journal.pone.0289275] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Accepted: 07/15/2023] [Indexed: 08/18/2023] Open
Abstract
The cluster randomized stepped wedge design is a multi-period uni-directional switch design in which all clusters start in the control condition and at the beginning of each new period a random sample of clusters crosses over to the intervention condition. Such designs often use uniform allocation, with an equal number of clusters at each treatment switch. However, the uniform allocation is not necessarily the most efficient. This study derives the optimal allocation of clusters to treatment sequences in the cluster randomized stepped wedge design, for both cohort and cross-sectional designs. The correlation structure is exponential decay, meaning the correlation decreases with the time lag between two measurements. The optimal allocation is shown to depend on the intraclass correlation coefficient, the number of subjects per cluster-period and the cluster and (in the case of a cohort design) individual autocorrelation coefficients. For small to medium values of these autocorrelations those sequences that have their treatment switch earlier or later in the study are allocated a larger proportion of clusters than those clusters that have their treatment switch halfway the study. When the autocorrelation coefficients increase, the clusters become more equally distributed across the treatment sequences. For the cohort design, the optimal allocation is almost equal to the uniform allocation when both autocorrelations approach the value 1. For almost all scenarios that were studied, the efficiency of the uniform allocation is 0.8 or higher. R code to derive the optimal allocation is available online.
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Affiliation(s)
- Mirjam Moerbeek
- Department of Methodology and Statistics, Utrecht University, Utrecht, The Netherlands
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Kirsch K, Nagel C, Iribagiza C, Ecklu J, Zawadi GA, Ntabaza PM, Barstow C, Lund AJ, Harper J, Carlton E, Javernick-Will A, Linden K, Thomas E. Study design and baseline to evaluate water service provision among peri-urban communities in Kasai Oriental, Democratic Republic of the Congo. PLoS One 2023; 18:e0283019. [PMID: 37053145 PMCID: PMC10101432 DOI: 10.1371/journal.pone.0283019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Accepted: 02/28/2023] [Indexed: 04/14/2023] Open
Abstract
We present a study design and baseline results to establish the impact of interventions on peri-urban water access, security and quality in Kasai Oriental province of the Democratic Republic of the Congo. In standard development practice, program performance is tracked via monitoring and evaluation frameworks of varying sophistication and rigor. Monitoring and evaluation, while usually occurring nearly concurrently with program delivery, may or may not measure parameters that can identify performance with respect to the project's overall goals. Impact evaluations, often using tightly controlled trial designs and conducted over years, challenge iterative program evolution. This study will pilot an implementation science impact evaluation approach in the areas immediately surrounding 14 water service providers, at each surveying 100 randomly-selected households and conducting water quality assessments at 25 randomly-selected households and five water points every three months. We present preliminary point-of-collection and point-of-use baseline data. This study is utilizing a variety of short- and medium-term monitoring and impact evaluation methods to provide feedback at multiple points during the intervention. Rapid feedback monitoring will assess the continuity of water services, point-of-consumption and point-of-collection microbial water quality, household water security, household measures of health status, ability and willingness to pay for water and sanitation service provision, and service performance monitoring. Long-term evaluation will focus on the use of qualitative comparative analysis whereby we will investigate the combination of factors that lead to improved water access, security and quality.
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Affiliation(s)
- Kathleen Kirsch
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Corey Nagel
- Department of Biostatistics, College of Public Health, University of Arkansas for Medical Sciences, Little Rock, Arkansas, United States of America
| | - Chantal Iribagiza
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - John Ecklu
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Ghislaine Akonkwa Zawadi
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Pacifique Mugaruka Ntabaza
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Christina Barstow
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Andrea J Lund
- Environmental and Occupational Health, Colorado School of Public Health, Denver, Colorado, United States of America
| | - James Harper
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Elizabeth Carlton
- Environmental and Occupational Health, Colorado School of Public Health, Denver, Colorado, United States of America
| | - Amy Javernick-Will
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Karl Linden
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
| | - Evan Thomas
- Mortenson Center in Global Engineering and Resilience, University of Colorado Boulder, Boulder, Colorado, United States of America
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12
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Moyer JC, Heagerty PJ, Murray DM. Analysis of multiple-period group randomized trials: random coefficients model or repeated measures ANOVA? Trials 2022; 23:987. [PMID: 36476294 PMCID: PMC9727985 DOI: 10.1186/s13063-022-06917-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 11/11/2022] [Indexed: 12/12/2022] Open
Abstract
BACKGROUND Multiple-period parallel group randomized trials (GRTs) analyzed with linear mixed models can represent time in mean models as continuous or categorical. If time is continuous, random effects are traditionally group- and member-level deviations from condition-specific slopes and intercepts and are referred to as random coefficients (RC) analytic models. If time is categorical, random effects are traditionally group- and member-level deviations from time-specific condition means and are referred to as repeated measures ANOVA (RM-ANOVA) analytic models. Longstanding guidance recommends the use of RC over RM-ANOVA for parallel GRTs with more than two periods because RC exhibited nominal type I error rates for both time parameterizations while RM-ANOVA exhibited inflated type I error rates when applied to data generated using the RC model. However, this recommendation was developed assuming a variance components covariance matrix for the RM-ANOVA, using only cross-sectional data, and explicitly modeling time × group variation. Left unanswered were how well RM-ANOVA with an unstructured covariance would perform on data generated according to the RC mechanism, if similar patterns would be observed in cohort data, and the impact of not modeling time × group variation if such variation was present in the data-generating model. METHODS Continuous outcomes for cohort and cross-sectional parallel GRT data were simulated according to RM-ANOVA and RC mechanisms at five total time periods. All simulations assumed time × group variation. We varied the number of groups, group size, and intra-cluster correlation. Analytic models using RC, RM-ANOVA, RM-ANOVA with unstructured covariance, and a Saturated random effects structure were applied to the data. All analytic models specified time × group random effects. The analytic models were then reapplied without specifying random effects for time × group. RESULTS Results indicated the RC and saturated analytic models maintained the nominal type I error rate in all data sets, RM-ANOVA with an unstructured covariance did not avoid type I error rate inflation when applied to cohort RC data, and analytic models omitting time-varying group random effects when such variation exists in the data were prone to substantial type I error inflation unless the residual error variance is high relative to the time × group variance. CONCLUSION The time × group RC and saturated analytic models are recommended as the default for multiple period parallel GRTs.
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Affiliation(s)
- Jonathan C. Moyer
- Office of Disease Prevention, National Institutes of Health, Bethesda, MD USA
| | | | - David M. Murray
- Office of Disease Prevention, National Institutes of Health, Bethesda, MD USA
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13
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Hu L, Zhu W, Yu J, Chen Y, Yan J, Liao Q, Zhang T. Family-based improvement for health literacy among the Yi nationality (FAMILY) in Liangshan: protocol of an open cohort stepped wedge cluster randomized controlled trial. BMC Public Health 2022; 22:1543. [PMID: 35964063 PMCID: PMC9375317 DOI: 10.1186/s12889-022-13782-w] [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: 07/03/2022] [Accepted: 07/11/2022] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Improvement of health literacy constitutes a cornerstone to improving public health. However, the overall health literacy of Liangshan Yi Autonomous Prefecture (Liangshan Prefecture) in the southwest Sichuan Province of China has kept extremely low for a long time. How to improve health literacy of the Yi nationality residents is key to be urgently solved. Notably, Family Branch System is a distinctive patrilineal bloodline organization of Yi nationality, which plays an important role in the daily life of Yi nationality. Meanwhile, Contracted Family Doctor Services is conducted in Liangshan Prefecture. Therefore, this study proposes an intervention model of health education based on Family Branch System and Contracted Family Doctor Services, which is a Family-based Improvement for Health Literacy among the Yi nationality (FAMILY) in Liangshan, when improving traditional Innovative Care for Chronic Conditions Framework (ICCC) framework. METHODS An open cohort stepped wedge cluster randomized trial design is used to implement health literacy education interventions including project preparation, core group building, promotion within family branch and competition between family branches while using Contracted Family Doctor Services as control measure. The study will be conducted among Yi nationality residents in Meigu County and Yanyuan County, with health literacy level of residents as the primary outcome. Finally, mixed-effects model and causal inference method will be used to evaluate intervention effect. DISCUSSION This study highlights family, using the unique Family Branch System and Contracted Family Doctor Services in Liangshan Prefecture to design intervention among improved ICCC framework, and combines the mixed-effects model with complier average causal effects (CACE) to estimate the intervention effect under non-compliance for the first time. Besides, other key technologies to be adopted include construction of electronic questionnaire quality control system, with quality control based on artificial intelligence. This trial contributes to exploring an effective way to improve health literacy of Yi nationality residents in Liangshan Prefecture, which will provide reference for other areas, especially poor areas, to improve residents' health literacy. TRIAL REGISTRATION ISRCTN11299863 on June 1, 2022; https://www.isrctn.com/ .
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Affiliation(s)
- Lin Hu
- Department of Epidemiology and Health Statistics, West China School of Public Health and West China Fourth Hospital, Sichuan University, Renmin South Road 3rd Section NO.16, Chengdu, 610041, Sichuan Province, China
| | - Wenhui Zhu
- Department of Epidemiology and Health Statistics, West China School of Public Health and West China Fourth Hospital, Sichuan University, Renmin South Road 3rd Section NO.16, Chengdu, 610041, Sichuan Province, China
| | - Jie Yu
- Department of Epidemiology and Health Statistics, West China School of Public Health and West China Fourth Hospital, Sichuan University, Renmin South Road 3rd Section NO.16, Chengdu, 610041, Sichuan Province, China
| | - Ying Chen
- Department of Epidemiology and Health Statistics, West China School of Public Health and West China Fourth Hospital, Sichuan University, Renmin South Road 3rd Section NO.16, Chengdu, 610041, Sichuan Province, China
| | - Jingmin Yan
- Department of Epidemiology and Health Statistics, West China School of Public Health and West China Fourth Hospital, Sichuan University, Renmin South Road 3rd Section NO.16, Chengdu, 610041, Sichuan Province, China
| | - Qiang Liao
- Liangshan Prefecture Center for Disease Control and Prevention, Xichang, 615000, Sichuan Province, China
| | - Tao Zhang
- Department of Epidemiology and Health Statistics, West China School of Public Health and West China Fourth Hospital, Sichuan University, Renmin South Road 3rd Section NO.16, Chengdu, 610041, Sichuan Province, China.
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14
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Patterson CG, Leland NE, Mormer E, Palmer CV. Alternative Designs for Testing Speech, Language, and Hearing Interventions: Cluster-Randomized Trials and Stepped-Wedge Designs. JOURNAL OF SPEECH, LANGUAGE, AND HEARING RESEARCH : JSLHR 2022; 65:2677-2690. [PMID: 35858257 DOI: 10.1044/2022_jslhr-21-00522] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
PURPOSE Individual-randomized trials are the gold standard for testing the efficacy and effectiveness of drugs, devices, and behavioral interventions. Health care delivery, educational, and programmatic interventions are often complex, involving multiple levels of change and measurement precluding individual randomization for testing. Cluster-randomized trials and cluster-randomized stepped-wedge trials are alternatives where the intervention is allocated at the group level, such as a clinic or a school, and the outcomes are measured at the person level. These designs are introduced along with the statistical implications of similarities among individuals within the same cluster. We also illustrate the parameters that have the most impact on the likelihood of detecting intervention effects, which must be considered when planning these trials. CONCLUSION Cluster-randomized and stepped-wedge designs should be considered by researchers as experimental alternatives to individual-randomized trials when testing speech, language, and hearing care interventions in real-world settings.
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Affiliation(s)
- Charity G Patterson
- Department of Physical Therapy, School of Health and Rehabilitation Sciences, University of Pittsburgh, PA
- School of Health and Rehabilitation Sciences Data Center, University of Pittsburgh, PA
| | - Natalie E Leland
- Department of Occupational Therapy, School of Health and Rehabilitation Sciences, University of Pittsburgh, PA
| | - Elaine Mormer
- Department of Communication Science and Disorders, School of Health and Rehabilitation Sciences, University of Pittsburgh, PA
| | - Catherine V Palmer
- Department of Communication Science and Disorders, School of Health and Rehabilitation Sciences, University of Pittsburgh, PA
- Department of Otolaryngology, School of Medicine, University of Pittsburgh, PA
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15
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Ouyang Y, Li F, Preisser JS, Taljaard M. Sample size calculators for planning stepped-wedge cluster randomized trials: a review and comparison. Int J Epidemiol 2022; 51:2000-2013. [PMID: 35679584 PMCID: PMC9749719 DOI: 10.1093/ije/dyac123] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 05/17/2022] [Indexed: 01/21/2023] Open
Abstract
Recent years have seen a surge of interest in stepped-wedge cluster randomized trials (SW-CRTs). SW-CRTs include several design variations and methodology is rapidly developing. Accordingly, a variety of power and sample size calculation software for SW-CRTs has been developed. However, each calculator may support only a selected set of design features and may not be appropriate for all scenarios. Currently, there is no resource to assist researchers in selecting the most appropriate calculator for planning their trials. In this paper, we review and classify 18 existing calculators that can be implemented in major platforms, such as R, SAS, Stata, Microsoft Excel, PASS and nQuery. After reviewing the main sample size considerations for SW-CRTs, we summarize the features supported by the available calculators, including the types of designs, outcomes, correlation structures and treatment effects; whether incomplete designs, cluster-size variation or secular trends are accommodated; and the analytical approach used. We then discuss in more detail four main calculators and identify their strengths and limitations. We illustrate how to use these four calculators to compute power for two real SW-CRTs with a continuous and binary outcome and compare the results. We show that the choice of calculator can make a substantial difference in the calculated power and explain these differences. Finally, we make recommendations for implementing sample size or power calculations using the available calculators. An R Shiny app is available for users to select the calculator that meets their requirements (https://douyang.shinyapps.io/swcrtcalculator/).
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Affiliation(s)
- Yongdong Ouyang
- Corresponding author. Clinical Epidemiology Program, Ottawa Hospital Research Institute, 1053 Carling Ave, Ottawa, ON K1Y 4E9, Canada. E-mail:
| | - Fan Li
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA,Center for Methods in Implementation and Prevention Science, Yale School of Public Health, New Haven, CT, USA
| | - John S Preisser
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada,School of Epidemiology and Public Health, University of Ottawa, Ottawa, ON, Canada
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16
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Rezaei-Darzi E, Kasza J, Forbes A, Bowden R. Use of information criteria for selecting a correlation structure for longitudinal cluster randomised trials. Clin Trials 2022; 19:316-325. [PMID: 35706343 DOI: 10.1177/17407745221082227] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
BACKGROUND When designing and analysing longitudinal cluster randomised trials, such as the stepped wedge, the similarity of outcomes from the same cluster must be accounted for through the choice of a form for the within-cluster correlation structure. Several choices for this structure are commonly considered for application within the linear mixed model paradigm. The first assumes a constant intra-cluster correlation for all pairs of outcomes from the same cluster (the exchangeable/Hussey and Hughes model); the second assumes that correlations of outcomes measured in the same period are higher than outcomes measured in different periods (the block exchangeable model) and the third is the discrete-time decay model, which allows the correlation between pairs of outcomes to decay over time. Currently, there is limited guidance on how to select the most appropriate within-cluster correlation structure. METHODS We simulated continuous outcomes under each of the three considered within-cluster correlation structures for a range of design and parameter choices, and, using the ASReml-R package, fit each linear mixed model to each simulated dataset. We evaluated the performance of the Akaike and Bayesian information criteria for selecting the correct within-cluster correlation structure for each dataset. RESULTS For smaller total sample sizes, neither criteria performs particularly well in selecting the correct within-cluster correlation structure, with the simpler exchangeable model being favoured. Furthermore, in general, the Bayesian information criterion favours the exchangeable model. When the cluster auto-correlation (which defines the degree of dependence between observations in adjacent time periods) is large and number of periods is small, neither criteria is able to distinguish between the block exchangeable and discrete time decay models. However, for increasing numbers of clusters, periods, and subjects per cluster period, both the Akaike and Bayesian information criteria perform increasingly well in the detection of the correct within-cluster correlation structure. CONCLUSIONS With increasing amounts of data, be they number of clusters, periods or subjects per cluster period, both the Akaike and Bayesian information criteria are increasingly likely to select the correct correlation structure. We recommend that if there are sufficient data available when planning a trial, that the Akaike or Bayesian information criterion is used to guide the choice of within-cluster correlation structure in the absence of other compelling justifications for a specific correlation structure. We also suggest that researchers conduct supplementary analyses under alternate correlation structures to gauge sensitivity to the initial choice.
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Affiliation(s)
- Ehsan Rezaei-Darzi
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia.,Monash University Accident Research Centre, Monash University, Clayton, VIC, Australia
| | - Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
| | - Andrew Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
| | - Rhys Bowden
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
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17
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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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18
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Stepped Wedge Cluster Randomized Trials: A Methodological Overview. World Neurosurg 2022; 161:323-330. [PMID: 35505551 PMCID: PMC9074087 DOI: 10.1016/j.wneu.2021.10.136] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Revised: 10/17/2021] [Accepted: 10/18/2021] [Indexed: 11/21/2022]
Abstract
BACKGROUND Stepped wedge cluster randomized trials enable rigorous evaluations of health intervention programs in pragmatic settings. In the present study, we aimed to update neurosurgeon scientists on the design of stepped wedge randomized trials. METHODS We have presented an overview of recent methodological developments for stepped wedge designs and included an update on the newer associated methodological tools to aid with future study designs. RESULTS We defined the stepped wedge trial design and reviewed the indications for the design in depth. In addition, key considerations, including mainstream methods of analysis and sample size determination, were discussed. CONCLUSIONS Stepped wedge designs can be attractive for study intervention programs aiming to improve the delivery of patient care, especially when examining a small number of heterogeneous clusters.
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19
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Grayling MJ, Wason JMS, Villar SS. Response adaptive intervention allocation in stepped-wedge cluster randomized trials. Stat Med 2022; 41:1081-1099. [PMID: 35064595 PMCID: PMC7612601 DOI: 10.1002/sim.9317] [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: 02/12/2021] [Revised: 11/30/2021] [Accepted: 12/22/2021] [Indexed: 11/09/2022]
Abstract
BACKGROUND Stepped-wedge cluster randomized trial (SW-CRT) designs are often used when there is a desire to provide an intervention to all enrolled clusters, because of a belief that it will be effective. However, given there should be equipoise at trial commencement, there has been discussion around whether a pre-trial decision to provide the intervention to all clusters is appropriate. In pharmaceutical drug development, a solution to a similar desire to provide more patients with an effective treatment is to use a response adaptive (RA) design. METHODS We introduce a way in which RA design could be incorporated in an SW-CRT, permitting modification of the intervention allocation during the trial. The proposed framework explicitly permits a balance to be sought between power and patient benefit considerations. A simulation study evaluates the methodology. RESULTS In one scenario, for one particular RA design, the proportion of cluster-periods spent in the intervention condition was observed to increase from 32.2% to 67.9% as the intervention effect was increased. A cost of this was a 6.2% power drop compared to a design that maximized power by fixing the proportion of time in the intervention condition at 45.0%, regardless of the intervention effect. CONCLUSIONS An RA approach may be most applicable to settings for which the intervention has substantial individual or societal benefit considerations, potentially in combination with notable safety concerns. In such a setting, the proposed methodology may routinely provide the desired adaptability of the roll-out speed, with only a small cost to the study's power.
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Affiliation(s)
- Michael J Grayling
- Population Health Sciences Institute, Newcastle University, Newcastle upon Tyne, UK
| | - James M S Wason
- Population Health Sciences Institute, Newcastle University, Newcastle upon Tyne, UK
| | - Sofía S Villar
- MRC Biostatistics Unit, School of Clinical Medicine, University of Cambridge, Cambridge, UK
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20
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Tian Z, Preisser JS, Esserman D, Turner EL, Rathouz PJ, Li F. Impact of unequal cluster sizes for GEE analyses of stepped wedge cluster randomized trials with binary outcomes. Biom J 2021; 64:419-439. [PMID: 34596912 PMCID: PMC9292617 DOI: 10.1002/bimj.202100112] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Revised: 07/15/2021] [Accepted: 08/07/2021] [Indexed: 12/31/2022]
Abstract
The stepped wedge (SW) design is a type of unidirectional crossover design where cluster units switch from control to intervention condition at different prespecified time points. While a convention in study planning is to assume the cluster‐period sizes are identical, SW cluster randomized trials (SW‐CRTs) involving repeated cross‐sectional designs frequently have unequal cluster‐period sizes, which can impact the efficiency of the treatment effect estimator. In this paper, we provide a comprehensive investigation of the efficiency impact of unequal cluster sizes for generalized estimating equation analyses of SW‐CRTs, with a focus on binary outcomes as in the Washington State Expedited Partner Therapy trial. Several major distinctions between our work and existing work include the following: (i) we consider multilevel correlation structures in marginal models with binary outcomes; (ii) we study the implications of both the between‐cluster and within‐cluster imbalances in sizes; and (iii) we provide a comparison between the independence working correlation versus the true working correlation and detail the consequences of ignoring correlation estimation in SW‐CRTs with unequal cluster sizes. We conclude that the working independence assumption can lead to substantial efficiency loss and a large sample size regardless of cluster‐period size variability in SW‐CRTs, and recommend accounting for correlations in the analysis. To improve study planning, we additionally provide a computationally efficient search algorithm to estimate the sample size in SW‐CRTs accounting for unequal cluster‐period sizes, and conclude by illustrating the proposed approach in the context of the Washington State study.
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Affiliation(s)
- Zibo Tian
- Department of Biostatistics, Yale University School of Public Health, New Haven, CT, USA
| | - John S Preisser
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Denise Esserman
- Department of Biostatistics, Yale University School of Public Health, New Haven, CT, USA.,Yale Center for Analytical Sciences, New Haven, CT, USA
| | - Elizabeth L Turner
- Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, USA.,Duke Global Health Institute, Durham, NC, USA
| | - Paul J Rathouz
- Department of Population Health, The University of Texas at Austin, Austin, TX, USA
| | - Fan Li
- Department of Biostatistics, Yale University School of Public Health, New Haven, CT, USA.,Yale Center for Analytical Sciences, New Haven, CT, USA.,Center for Methods in Implementation and Prevention Science, Yale University, New Haven, CT, USA
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21
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Korevaar E, Kasza J, Taljaard M, Hemming K, Haines T, Turner EL, Thompson JA, Hughes JP, Forbes AB. Intra-cluster correlations from the CLustered OUtcome Dataset bank to inform the design of longitudinal cluster trials. Clin Trials 2021; 18:529-540. [PMID: 34088230 DOI: 10.1177/17407745211020852] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
BACKGROUND Sample size calculations for longitudinal cluster randomised trials, such as crossover and stepped-wedge trials, require estimates of the assumed correlation structure. This includes both within-period intra-cluster correlations, which importantly differ from conventional intra-cluster correlations by their dependence on period, and also cluster autocorrelation coefficients to model correlation decay. There are limited resources to inform these estimates. In this article, we provide a repository of correlation estimates from a bank of real-world clustered datasets. These are provided under several assumed correlation structures, namely exchangeable, block-exchangeable and discrete-time decay correlation structures. METHODS Longitudinal studies with clustered outcomes were collected to form the CLustered OUtcome Dataset bank. Forty-four available continuous outcomes from 29 datasets were obtained and analysed using each correlation structure. Patterns of within-period intra-cluster correlation coefficient and cluster autocorrelation coefficients were explored by study characteristics. RESULTS The median within-period intra-cluster correlation coefficient for the discrete-time decay model was 0.05 (interquartile range: 0.02-0.09) with a median cluster autocorrelation of 0.73 (interquartile range: 0.19-0.91). The within-period intra-cluster correlation coefficients were similar for the exchangeable, block-exchangeable and discrete-time decay correlation structures. Within-period intra-cluster correlation coefficients and cluster autocorrelations were found to vary with the number of participants per cluster-period, the period-length, type of cluster (primary care, secondary care, community or school) and country income status (high-income country or low- and middle-income country). The within-period intra-cluster correlation coefficients tended to decrease with increasing period-length and slightly decrease with increasing cluster-period sizes, while the cluster autocorrelations tended to move closer to 1 with increasing cluster-period size. Using the CLustered OUtcome Dataset bank, an RShiny app has been developed for determining plausible values of correlation coefficients for use in sample size calculations. DISCUSSION This study provides a repository of intra-cluster correlations and cluster autocorrelations for longitudinal cluster trials. This can help inform sample size calculations for future longitudinal cluster randomised trials.
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Affiliation(s)
- Elizabeth Korevaar
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
| | - Jessica Kasza
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada.,School of Epidemiology, Public Health and Preventive Medicine, University of Ottawa, Ottawa, ON, Canada
| | - Karla Hemming
- Institute of Applied Health Research, University of Birmingham, Birmingham, UK
| | - Terry Haines
- School of Primary and Allied Health Care, Monash University, Melbourne, VIC, Australia
| | - Elizabeth L Turner
- Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, USA.,Duke Global Health Institute, Durham, NC, USA
| | - Jennifer A Thompson
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - James P Hughes
- Department of Biostatistics, University of Washington, Seattle, WA, USA
| | - Andrew B Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia
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22
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On the centrosymmetry of treatment effect estimators for stepped wedge and related cluster randomized trial designs. Stat Probab Lett 2021. [DOI: 10.1016/j.spl.2020.109022] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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23
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Li F, Hughes JP, Hemming K, Taljaard M, Melnick ER, Heagerty PJ. Mixed-effects models for the design and analysis of stepped wedge cluster randomized trials: An overview. Stat Methods Med Res 2021; 30:612-639. [PMID: 32631142 PMCID: PMC7785651 DOI: 10.1177/0962280220932962] [Citation(s) in RCA: 86] [Impact Index Per Article: 28.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
The stepped wedge cluster randomized design has received increasing attention in pragmatic clinical trials and implementation science research. The key feature of the design is the unidirectional crossover of clusters from the control to intervention conditions on a staggered schedule, which induces confounding of the intervention effect by time. The stepped wedge design first appeared in the Gambia hepatitis study in the 1980s. However, the statistical model used for the design and analysis was not formally introduced until 2007 in an article by Hussey and Hughes. Since then, a variety of mixed-effects model extensions have been proposed for the design and analysis of these trials. In this article, we explore these extensions under a unified perspective. We provide a general model representation and regard various model extensions as alternative ways to characterize the secular trend, intervention effect, as well as sources of heterogeneity. We review the key model ingredients and clarify their implications for the design and analysis. The article serves as an entry point to the evolving statistical literatures on stepped wedge designs.
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Affiliation(s)
- Fan Li
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
- Center for Methods in Implementation and Preventive Science, Yale University, New Haven, CT, USA
| | - James P Hughes
- Department of Biostatistics, School of Public Health, University of Washington, Seattle, WA, USA
| | - Karla Hemming
- Institute of Applied Health Research, University of Birmingham, Birmingham, UK
| | - Monica Taljaard
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
| | - Edward R. Melnick
- Department of Emergency Medicine, Yale School of Medicine, New Haven, CT, USA
| | - Patrick J Heagerty
- Department of Biostatistics, School of Public Health, University of Washington, Seattle, WA, USA
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24
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Kasza J, Bowden R, Forbes AB. Information content of stepped wedge designs with unequal cluster-period sizes in linear mixed models: Informing incomplete designs. Stat Med 2021; 40:1736-1751. [PMID: 33438255 DOI: 10.1002/sim.8867] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 12/13/2020] [Accepted: 12/16/2020] [Indexed: 12/30/2022]
Abstract
In practice, stepped wedge trials frequently include clusters of differing sizes. However, investigations into the theoretical aspects of stepped wedge designs have, until recently, typically assumed equal numbers of subjects in each cluster and in each period. The information content of the cluster-period cells, clusters, and periods of stepped wedge designs has previously been investigated assuming equal cluster-period sizes, and has shown that incomplete stepped wedge designs may be efficient alternatives to the full stepped wedge. How this changes when cluster-period sizes are not equal is unknown, and we investigate this here. Working within the linear mixed model framework, we show that the information contributed by design components (clusters, sequences, and periods) does depend on the sizes of each cluster-period. Using a particular trial that assessed the impact of an individual education intervention on log-length of stay in rehabilitation units, we demonstrate how strongly the efficiency of incomplete designs depends on which cells are excluded: smaller incomplete designs may be more powerful than alternative incomplete designs that include a greater total number of participants. This also serves to demonstrate how the pattern of information content can be used to inform a set of incomplete designs to be considered as alternatives to the complete stepped wedge design. Our theoretical results for the information content can be extended to a broad class of longitudinal (ie, multiple period) cluster randomized trial designs.
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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
| | - Andrew B Forbes
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Victoria, Australia
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25
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Kasza J, Hooper R, Copas A, Forbes AB. Sample size and power calculations for open cohort longitudinal cluster randomized trials. Stat Med 2020; 39:1871-1883. [PMID: 32133688 PMCID: PMC7217159 DOI: 10.1002/sim.8519] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Revised: 01/15/2020] [Accepted: 02/17/2020] [Indexed: 01/24/2023]
Abstract
When calculating sample size or power for stepped wedge or other types of longitudinal cluster randomized trials, it is critical that the planned sampling structure be accurately specified. One common assumption is that participants will provide measurements in each trial period, that is, a closed cohort, and another is that each participant provides only one measurement during the course of the trial. However some studies have an "open cohort" sampling structure, where participants may provide measurements in variable numbers of periods. To date, sample size calculations for longitudinal cluster randomized trials have not accommodated open cohorts. Feldman and McKinlay (1994) provided some guidance, stating that the participant-level autocorrelation could be varied to account for the degree of overlap in different periods of the study, but did not indicate precisely how to do so. We present sample size and power formulas that allow for open cohorts and discuss the impact of the degree of "openness" on sample size and power. We consider designs where the number of participants in each cluster will be maintained throughout the trial, but individual participants may provide differing numbers of measurements. Our results are a unification of closed cohort and repeated cross-sectional sample results of Hooper et al (2016), and indicate precisely how participant autocorrelation of Feldman and McKinlay should be varied to account for an open cohort sampling structure. We discuss different types of open cohort sampling schemes and how open cohort sampling structure impacts on power in the presence of decaying within-cluster correlations and autoregressive participant-level errors.
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Affiliation(s)
- Jessica Kasza
- School of Public Health and Preventive MedicineMonash UniversityMelbourneVictoriaAustralia
| | - Richard Hooper
- Centre for Primary Care and Public HealthQueen Mary University of LondonLondonUK
| | - Andrew Copas
- MRC Clinical Trials UnitUniversity College LondonLondonUK
| | - Andrew B. Forbes
- School of Public Health and Preventive MedicineMonash UniversityMelbourneVictoriaAustralia
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