The optimal design of stepped wedge trials with equal allocation to sequences and a comparison to other trial designs

Optimal designs using generalized estimating equations in cluster randomized crossover and stepped wedge trials

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.

Efficient designs for three-sequence stepped wedge trials with continuous recruitment

BACKGROUND/AIMS

The standard approach to designing stepped wedge trials that recruit participants in a continuous stream is to divide time into periods of equal length. But the choice of design in such cases is infinitely more flexible: each cluster could cross from the control to the intervention at any point on the continuous time-scale. We consider the case of a stepped wedge design with clusters randomised to just three sequences (designs with small numbers of sequences may be preferred for their simplicity and practicality) and investigate the choice of design that minimises the variance of the treatment effect estimator under different assumptions about the intra-cluster correlation.

METHODS

We make some simplifying assumptions in order to calculate the variance: in particular that we recruit the same number of participants, m , from each cluster over the course of the trial, and that participants present at regularly spaced intervals. We consider an intra-cluster correlation that decays exponentially with separation in time between the presentation of two individuals from the same cluster, from a value of ρ for two individuals who present at the same time, to a value of ρ τ for individuals presenting at the start and end of the trial recruitment interval. We restrict attention to three-sequence designs with centrosymmetry - the property that if we reverse time and swap the intervention and control conditions then the design looks the same. We obtain an expression for the variance of the treatment effect estimator adjusted for effects of time, using methods for generalised least squares estimation, and we evaluate this expression numerically for different designs, and for different parameter values.

RESULTS

There is a two-dimensional space of possible three-sequence, centrosymmetric stepped wedge designs with continuous recruitment. The variance of the treatment effect estimator for given ρ and τ can be plotted as a contour map over this space. The shape of this variance surface depends on τ and on the parameter m ρ / ( 1 - ρ ) , but typically indicates a broad, flat region of close-to-optimal designs. The 'standard' design with equally spaced periods and 1:1:1 allocation rarely performs well, however.

CONCLUSIONS

In many different settings, a relatively simple design can be found (e.g. one based on simple fractions) that offers close-to-optimal efficiency in that setting. There may also be designs that are robustly efficient over a wide range of settings. Contour maps of the kind we illustrate can help guide this choice. If efficiency is offered as one of the justifications for using a stepped wedge design, then it is worth designing with optimal efficiency in mind.

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

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.

Information content of stepped wedge designs under the working independence assumption

The stepped wedge design is increasingly popular in pragmatic trials and implementation science research studies for evaluating system-level interventions that are perceived to be beneficial to patient populations. An important step in planning a stepped wedge design is to understand the efficiency of the treatment effect estimator and hence the power of the study. We develop several novel analytical results for designing stepped wedge cluster randomized trials analyzed through generalized estimating equations under a misspecified working independence correlation structure. We first contribute a general variance expression of the treatment effect estimator when data collection is scheduled for each cluster-period. Because resource and patient-centered considerations may intentionally call for an incomplete design with outcome data being omitted for certain cluster-periods, we further derive the information content based on the robust sandwich variance to identify data elements that may be preferentially omitted with minimum loss of precision in estimating the treatment effect. We prove that centrosymmetric pairs of cluster-periods, treatment sequences and periods have identical information content and thus contribute equally to the treatment effect estimation, as long as the true covariance structure for the cluster-period means remains centrosymmetric. Finally, we provide an example of how to obtain an incomplete stepped wedge design that admits a more efficient independence GEE estimator but requires less data collection effort. Our results elegantly extend existing ones from linear mixed models coupled with model-based variances to accommodate a misspecified independence working correlation structure through the robust sandwich variances.

Optimal allocation to treatment sequences in individually randomized stepped-wedge designs with attrition

BACKGROUND/AIMS

The stepped-wedge design has been extensively studied in the setting of the cluster randomized trial, but less so for the individually randomized trial. This article derives the optimal allocation of individuals to treatment sequences. The focus is on designs where all individuals start in the control condition and at the beginning of each time period some of them cross over to the intervention, so that at the end of the trial all of them receive the intervention.

METHODS

The statistical model that takes into account the nesting of repeated measurements within subjects is presented. It is also shown how possible attrition is taken into account. The effect of the intervention is assumed to be sustained so that it does not change after the treatment switch. An exponential decay correlation structure is assumed, implying that the correlation between any two time point decreases with the time lag. Matrix algebra is used to derive the relation between the allocation of units to treatment sequences and the variance of the treatment effect estimator. The optimal allocation is the one that results in smallest variance.

RESULTS

Results are presented for three to six treatment sequences. It is shown that the optimal allocation highly depends on the correlation parameter ρ and attrition rate r between any two adjacent time points. The uniform allocation, where each treatment sequence has the same number of individuals, is often not the most efficient. For 0 . 1 ≤ ρ ≤ 0 . 9 and r = 0 , 0 . 05 , 0 . 2 , its efficiency relative to the optimal allocation is at least 0.8. It is furthermore shown how a constrained optimal allocation can be derived in case the optimal allocation is not feasible from a practical point of view.

CONCLUSION

This article provides the methodology for designing individually randomized stepped-wedge designs, taking into account the possibility of attrition. As such it helps researchers to plan their trial in an efficient way. To use the methodology, prior estimates of the degree of attrition and intraclass correlation coefficient are needed. It is advocated that researchers clearly report the estimates of these quantities to help facilitate planning future trials.

Best (but oft forgotten) practices: Efficient sample sizes for commonly used trial designs

Designing studies such that they have a high level of power to detect an effect or association of interest is an important tool to improve the quality and reproducibility of findings from such studies. Since resources (research subjects, time, and money) are scarce, it is important to obtain sufficient power with minimum use of such resources. For commonly used randomized trials of the treatment effect on a continuous outcome, designs are presented that minimize the number of subjects or the amount of research budget when aiming for a desired power level. This concerns the optimal allocation of subjects to treatments and, in case of nested designs such as cluster-randomized trials and multicenter trials, also the optimal number of centers versus the number of persons per center. Since such optimal designs require knowledge of parameters of the analysis model that are not known in the design stage, in particular outcome variances, maximin designs are presented. These designs guarantee a prespecified power level for plausible ranges of the unknown parameters and minimize research costs for the worst-case values of these parameters. The focus is on a 2-group parallel design, the AB/BA crossover design, and cluster-randomized and multicenter trials with a continuous outcome. How to calculate sample sizes for maximin designs is illustrated for examples from nutrition. Several computer programs that are helpful in calculating sample sizes for optimal and maximin designs are discussed as well as some results on optimal designs for other types of outcomes.

Surmounting Withdrawal to Initiate Fast Treatment with Naltrexone (SWIFT): A stepped wedge hybrid type 1 effectiveness-implementation study

BACKGROUND

Extended-release injectable naltrexone (XR-NTX) is an effective treatment for opioid use disorder (OUD), but initiation remains a barrier to implementation. Standard practice requires a 10- to 15-day inpatient admission prior to XR-NTX initiation and involves a methadone or buprenorphine taper followed by a 7- to 10-day washout, as recommended in the Prescribing Information for XR-NTX. A 5- to 7-day rapid induction approach was developed that utilizes low-dose oral naltrexone and non-opioid medications.

METHODS

The CTN-0097 Surmounting Withdrawal to Initiate Fast Treatment with Naltrexone (SWIFT) study was a hybrid type I effectiveness-implementation trial that compared the effectiveness of the standard procedure (SP) to the rapid procedure (RP) for XR-NTX initiation across six community inpatient addiction treatment units, and evaluated the implementation process. Sites were randomized to RP every 14 weeks in an optimized stepped wedge design. Participants (target recruitment = 450) received the procedure (SP or RP) that the site was implementing at time of admission. The hypothesis was RP will be non-inferior to SP on proportion of inpatients who receive XR-NTX, with a shorter admission time for RP. Superiority testing of RP was planned if the null hypothesis of inferiority of RP to SP was rejected.

DISCUSSION

If RP for XR-NTX initiation is shown to be effective, the shorter inpatient stay could make XR-NTX more feasible and have an important public health impact expanding access to OUD pharmacotherapy. Further, a better understanding of facilitators and barriers to RP implementation can help with future translatability and uptake to other community programs.

TRIAL REGISTRATION

NCT04762537 Registered February 21, 2021.

Reducing HIV-related stigma among young people attending school in Northern Uganda: study protocol for a participatory arts-based population health intervention and stepped-wedge cluster-randomized trial

BACKGROUND

HIV-related stigma negatively impacts HIV prevention, treatment, and care, particularly among children and adolescents in sub-Saharan Africa. Interventions that are culturally grounded and relevant for addressing root causes may reduce the stigma experienced by HIV-positive and HIV-affected young people. This study, to be conducted in a post-conflict, rural setting in Omoro District, Uganda, will develop and evaluate a transformative  arts-based HIV-related stigma intervention rooted in local cultural knowledge to reduce stigma and improve HIV prevention and care for young people living with HIV. The intervention will be delivered to young people attending school by community Elders, with the support of teachers, through the transfer of local cultural knowledge and practices with the aim of re-establishing the important cultural and social role of Elders within a community that has suffered the loss of intergenerational transfer of cultural knowledge throughout a 25-year civil war.

METHODS

A formative research phase consisting of interviews with students, teachers, and Elders will inform the intervention and provide data for study objectives. Workshops will be delivered to Elders and teachers in participating schools to build capacity for arts-based, educational workshops to be conducted with students in the classroom. The intervention will be evaluated using a stepped-wedge cluster-randomized trial. Government-funded schools in Omoro District will be randomized into three blocks, each comprised of two primary and two secondary schools (n=1800 students). Schools will be randomly assigned to a crossover sequence from control to intervention condition in 8-week intervals. A process evaluation will be implemented throughout the study to evaluate pathways between intervention development, implementation, and effects.

DISCUSSION

This study will generate comprehensive, in-depth participatory research and evaluation data to inform an effective and sustainable protocol for implementing arts-based HIV stigma interventions for young people in school settings. Findings will have widespread implications in post-conflict settings for HIV prevention, treatment, and care.

TRIAL REGISTRATION

ClinicalTrials.gov NCT04946071 . Registered on 30 June 2021.

Implementation of a psychological online intervention for low to moderate depression in primary care: study protocol

BACKGROUND

Depression affects millions of people all over the world and implies a great socioeconomic burden. Despite there are different effective evidence-based interventions for treating depression, only a small proportion of these patients receives an appropriate treatment. In this regard, information and communication technologies (ICTs) can be used with therapeutic aims and this can contribute to make interventions more accessible. One example is "Smiling is fun", an internet-based treatment which has proved to be effective and cost-effective for treating depression in Spanish Primary Care (PC). However, the "know-do gap" between research and clinical settings implies that the actual implementation of such interventions could last up to 20 years. To overcome this obstacle, the implementation research establishes the methodology to implement the advances developed in the laboratories to the health care services maintaining the validity of the intervention and offering specific strategies for the implementation process.

OBJECTIVE

This is the protocol of an implementation study for the Internet-based program "Smiling is fun", which will be conducted on patients with mild-to-moderate depression of Spanish PC settings. In the implementation study, the feasibility, efficacy, cost-efficacy, acceptability, adoption, appropriateness, fidelity, penetration, normalization, and sustainability will be assessed.

METHODS

The current investigation is a Hybrid Effectiveness-Implementation Type II design. A Stepped Wedge randomized controlled trial design will be used, with a cohort of 420 adults diagnosed with depression (mild-to-moderate) who will undergo a first control phase (no treatment) followed by the intervention, which will last 16 weeks, and finishing with an optional use of the intervention. All patients will be assessed at baseline, during the treatment, and at post-treatment. The study will be conducted in three Spanish regions: Andalusia, Aragon, and the Balearic Islands. Two primary care centers of each region will participate, one located in the urban setting and the other in the rural setting. The primary outcome will be implementation success of the intervention assessing the reach, clinical effect, acceptability, appropriateness, adoption, feasibility, fidelity, penetration, implementation costs and sustainability services.

DISCUSSION

"Smiling is Fun", which has already been established as effective and cost-effective, will be adapted according to users' experiences and opinions, and the efficacy and cost-efficacy of the program will again be assessed. The study will point out barriers and facilitators to consider in the implementation process of internet-based psychological interventions in health services. The ultimate goal is to break the research-to-practice split, which would undoubtedly contribute to reduce the high burden of depression in our society.

TRIAL REGISTRATION

ClinicalTrials.gov, Identifier: NCT05294614.

Ratio estimators of intervention effects on event rates in cluster randomized trials

We consider five asymptotically unbiased estimators of intervention effects on event rates in non‐matched and matched‐pair cluster randomized trials, including ratio of mean counts r1, ratio of mean cluster‐level event rates r2, ratio of event rates r3, double ratio of counts r4, and double ratio of event rates r5. In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, r1, r2, and r3 estimate the total effect, which comprises the direct and indirect effects, whereas r4 and r5 estimate the direct effect only. We derive the conditions under which each estimator is more precise or powerful than its alternatives. To control bias in studies with a small number of clusters, we propose a set of approximately unbiased estimators. We evaluate their properties by simulation and apply the methods to a trial of seasonal malaria chemoprevention. The approximately unbiased estimators are practically unbiased and their confidence intervals usually have coverage probability close to the nominal level; the asymptotically unbiased estimators perform well when the number of clusters is approximately 32 or more per trial arm. Despite its simplicity, r1 performs comparably with r2 and r3 in trials with a large but realistic number of clusters. When the variability of baseline event rate is large and there is no indirect effect, r4 and r5 tend to offer higher power than r1, r2, and r3. We discuss the implications of these findings to the planning and analysis of cluster randomized trials.

Comparison of small-sample standard-error corrections for generalised estimating equations in stepped wedge cluster randomised trials with a binary outcome: A simulation study

Generalised estimating equations with the sandwich standard-error estimator provide a promising method of analysis for stepped wedge cluster randomised trials. However, they have inflated type-one error when used with a small number of clusters, which is common for stepped wedge cluster randomised trials. We present a large simulation study of binary outcomes comparing bias-corrected standard errors from Fay and Graubard; Mancl and DeRouen; Kauermann and Carroll; Morel, Bokossa, and Neerchal; and Mackinnon and White with an independent and exchangeable working correlation matrix. We constructed 95% confidence intervals using a t-distribution with degrees of freedom including clusters minus parameters (DFC-P), cluster periods minus parameters, and estimators from Fay and Graubard (DFFG), and Pan and Wall. Fay and Graubard and an approximation to Kauermann and Carroll (with simpler matrix inversion) were unbiased in a wide range of scenarios with an independent working correlation matrix and more than 12 clusters. They gave confidence intervals with close to 95% coverage with DFFG with 12 or more clusters, and DFC-P with 18 or more clusters. Both standard errors were conservative with fewer clusters. With an exchangeable working correlation matrix, approximated Kauermann and Carroll and Fay and Graubard had a small degree of under-coverage.

Mixed-effects models for the design and analysis of stepped wedge cluster randomized trials: An overview

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.

Information content of stepped wedge designs with unequal cluster-period sizes in linear mixed models: Informing incomplete designs

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.

Variance formulae for multiphase stepped wedge cluster randomized trial

In a multiphase stepped wedge cluster randomized trial (MSW-CRT), more than one intervention will be initiated on each sequence in a fixed order. Hence, with the MSW-CRT design, the effect of the first intervention can be evaluated when compared to control, as well as the added-on effects of the subsequent interventions. Studies that use MSW-CRT have been proposed, but properties of this design have not been explicitly studied. We derive closed-form variance formulae to test the interventions' effects, which can be readily used for sample size and power calculation. Additionally, we provide relationships between variances to test the interventions' effects and design parameters. Under special conditions, some important properties include: (i) the variances to test different interventions' effects (ie, the first intervention effect and the second intervention effect) may be same; (ii) as the cluster-period mean autocorrelation increases, the variance to test an intervention effect may first increase and then decrease; (iii) as the amount of periods between the initiations of two interventions (ie, lag) increases, the variance to test an intervention effect may remain unchanged. We illustrate the relationships between power and design parameters using the variance formulae. From a few illustrative examples, we observe that the statistical test that uses data only relevant to a specific intervention has inferior power (relative power loss <15%) compared to the test when using all the study data. Also, power is reduced when both the total number of periods and lag are decreased simultaneously (relative power loss <20%).

Intent-to-treat analysis of cluster randomized trials when clusters report unidentifiable outcome proportions

Background

Cluster randomized trials are designed to evaluate interventions at the cluster or group level. When clusters are randomized but some clusters report no or non-analyzable data, intent-to-treat analysis, the gold standard for the analysis of randomized controlled trials, can be compromised. This article presents a very flexible statistical methodology for cluster randomized trials whose outcome is a cluster-level proportion (e.g. proportion from a cluster reporting an event) in the setting where clusters report non-analyzable data (which in general could be due to nonadherence, dropout, missingness, etc.). The approach is motivated by a previously published stratified randomized controlled trial called, “The Randomized Recruitment Intervention Trial (RECRUIT),” designed to examine the effectiveness of a trust-based continuous quality improvement intervention on increasing minority recruitment into clinical trials (ClinicalTrials.gov Identifier: NCT01911208).

Methods

The novel approach exploits the use of generalized estimating equations for cluster-level reports, such that all clusters randomized at baseline are able to be analyzed, and intervention effects are presented as risk ratios. Simulation studies under different outcome missingness scenarios and a variety of intra-cluster correlations are conducted. A comparative analysis of the method with imputation and per protocol approaches for RECRUIT is presented.

Results

Simulation results show the novel approach produces unbiased and efficient estimates of the intervention effect that maintain the nominal type I error rate. Application to RECRUIT shows similar effect sizes when compared to the imputation and per protocol approach.

Conclusion

The article demonstrates that an innovative bivariate generalized estimating equations framework allows one to implement an intent-to-treat analysis to obtain risk ratios or odds ratios, for a variety of cluster randomized designs.

Novel methods for the analysis of stepped wedge cluster randomized trials

Stepped wedge cluster randomized trials (SW-CRTs) have become increasingly popular and are used for a variety of interventions and outcomes, often chosen for their feasibility advantages. SW-CRTs must account for time trends in the outcome because of the staggered rollout of the intervention. Robust inference procedures and nonparametric analysis methods have recently been proposed to handle such trends without requiring strong parametric modeling assumptions, but these are less powerful than model-based approaches. We propose several novel analysis methods that reduce reliance on modeling assumptions while preserving some of the increased power provided by the use of mixed effects models. In one method, we use the synthetic control approach to find the best matching clusters for a given intervention cluster. Another method makes use of within-cluster crossover information to construct an overall estimator. We also consider methods that combine these approaches to further improve power. We test these methods on simulated SW-CRTs, describing scenarios in which these methods have increased power compared with existing nonparametric methods while preserving nominal validity when mixed effects models are misspecified. We also demonstrate theoretical properties of these estimators with less restrictive assumptions than mixed effects models. Finally, we propose avenues for future research on the use of these methods; motivation for such research arises from their flexibility, which allows the identification of specific causal contrasts of interest, their robustness, and the potential for incorporating covariates to further increase power. Investigators conducting SW-CRTs might well consider such methods when common modeling assumptions may not hold.

Information growth for sequential monitoring of clinical trials with a stepped wedge cluster randomized design and unknown intracluster correlation

Background/aims

In a stepped wedge study design, study clusters usually start with the baseline treatment and then cross over to the intervention at randomly determined times. Such designs are useful when the intervention must be delivered at the cluster level and are becoming increasingly common in practice. In these trials, if the outcome is death or serious morbidity, one may have an ethical imperative to monitor the trial and stop before maximum enrollment if the new therapy is proven to be beneficial. In addition, because formal monitoring allows for the stoppage of trials when a significant benefit for new therapy has been ruled out, their use can make a research program more efficient. However, use of the stepped wedge cluster randomized study design complicates the implementation of standard group sequential monitoring methods. Both the correlation of observations introduced by the clustered randomization and the timing of crossover from one treatment to the other impact the rate of information growth, an important component of an interim analysis.

Methods

We simulated cross-sectional stepped wedge study data in order to evaluate the impact of sequential monitoring on the Type I error and power when the true intracluster correlation is unknown. We studied the impact of varying intracluster correlations, treatment effects, methods of estimating the information growth, and boundary shapes.

Results

While misspecified information growth can impact both the Type I error and power of a study in some settings, we observed little inflation of the Type I error and only moderate reductions in power across a range of misspecified information growth patterns in our simulations.

Conclusion

Taking the study design into account and using either an estimate of the intracluster correlation from the ongoing study or other data in the same clusters should allow for easy implementation of group sequential methods in future stepped wedge designs.

Highly efficient stepped wedge designs for clusters of unequal size

The stepped wedge design (SWD) is a form of cluster randomized trial, usually comparing two treatments, which is divided into time periods and sequences, with clusters allocated to sequences. Typically all sequences start with the standard treatment and end with the new treatment, with the change happening at different times in the different sequences. The clusters will usually differ in size but this is overlooked in much of the existing literature. This paper considers the case when clusters have different sizes and determines how efficient designs can be found. The approach uses an approximation to the variance of the treatment effect, which is expressed in terms of the proportions of clusters and of individuals allocated to each sequence of the design. The roles of these sets of proportions in determining an efficient design are discussed and illustrated using two SWDs, one in the treatment of sexually transmitted diseases and one in renal replacement therapy. Cluster-balanced designs, which allocate equal numbers of clusters to each sequence, are shown to have excellent statistical and practical properties; suggestions are made about the practical application of the results for these designs. The paper concentrates on the cross-sectional case, where subjects are measured once, but it is briefly indicated how the methods can be extended to the closed-cohort design.

Variations in stepped-wedge cluster randomized trial design: Insights from the Patient-Centered Care Transitions in Heart Failure trial

The stepped-wedge (SW) cluster randomized controlled trial, in which clusters cross over in a randomized sequence from control to intervention, is ideal for the implementation and testing of complex health service interventions. In certain cases however, implementation of the intervention may pose logistical challenges, and variations in SW design may be required. We examine the logistical and statistical implications of variations in SW design using the optimization of the Patient-Centered Care Transitions in Heart Failure trial for illustration. We review the following complete SW design variations: a typical SW design; an SW design with multiple clusters crossing over per period to achieve balanced cluster sizes at each step; hierarchical randomization to account for higher-level clustering effects; nested substudies to measure outcomes requiring a smaller sample size than the primary outcomes; and hybrid SW design, which combines parallel cluster with SW design to improve efficiency. We also reviewed 3 incomplete SW design variations in which data are collected in some but not all steps to ease measurement burden. These include designs with a learning period that improve fidelity to the intervention, designs with reduced measurements to minimize collection burden, and designs with early and late blocks to accommodate cluster readiness. Variations in SW design offer pragmatic solutions to logistical challenges but have implications to statistical power. Advantages and disadvantages of each variation should be considered before finalizing the design of an SW randomized controlled trial.

How many times should a cluster randomized crossover trial cross over?

Trial planning requires making efficient yet practical design choices. In a cluster randomized crossover trial, clusters of subjects cross back and forth between implementing the control and intervention conditions over the course of the trial, with each crossover marking the start of a new period. If it is possible to set up such a trial with more crossovers, a pertinent question is whether there are efficiency gains from clusters crossing over more frequently, and if these gains are substantial enough to justify the added complexity and cost of implementing more crossovers. We seek to determine the optimal number of crossovers for a fixed trial duration, and then identify other highly efficient designs by allowing the total number of clusters to vary and imposing thresholds on maximum cost and minimum statistical power. Our results pertain to trials with continuous recruitment and a continuous primary outcome, with the treatment effect estimated using a linear mixed model. To account for the similarity between subjects' outcomes within a cluster, we assume a correlation structure in which the correlation decays gradually in a continuous manner as the time between subjects' measurements increases. The optimal design is characterized by crossovers between the control and intervention conditions with each successive subject. However, this design is neither practical nor cost-efficient to implement, nor is it necessary: the gains in efficiency increase sharply in moving from a two-period to a four-period trial design, but approach an asymptote for the scenarios considered as the number of crossovers continues to increase.

Sample size calculation for stepped-wedge cluster-randomized trials with more than two levels of clustering

BACKGROUND/AIMS

Power and sample size calculation formulas for stepped-wedge trials with two levels (subjects within clusters) are available. However, stepped-wedge trials with more than two levels are possible. An example is the CHANGE trial which randomizes nursing homes (level 4) consisting of nursing home wards (level 3) in which nurses (level 2) are observed with respect to their hand hygiene compliance during hand hygiene opportunities (level 1) in the care of patients. We provide power and sample size methods for such trials and illustrate these in the setting of the CHANGE trial.

METHODS

We extend the original sample size methodology derived for stepped-wedge trials based on a random intercepts model, to accommodate more than two levels of clustering. We derive expressions that can be used to determine power and sample size for p levels of clustering in terms of the variances at each level or, alternatively, in terms of intracluster correlation coefficients. We consider different scenarios, depending on whether the same units in a particular level are repeatedly measured as a cohort sample or whether different units are measured cross-sectionally.

RESULTS

A simple variance inflation factor is obtained that can be used to calculate power and sample size for continuous and by approximation for binary and rate outcomes. It is the product of (1) variance inflation due to the multilevel structure and (2) variance inflation due to the stepped-wedge manner of assigning interventions over time. Standard and non-standard designs (i.e. so-called "hybrid designs" and designs with more, less, or no data collection when the clusters are all in the control or are all in the intervention condition) are covered.

CONCLUSIONS

The formulas derived enable power and sample size calculations for multilevel stepped-wedge trials. For the two-, three-, and four-level case of the standard stepped wedge, we provide programs to facilitate these calculations.

Admissible multiarm stepped-wedge cluster randomized trial designs

Numerous publications have now addressed the principles of designing, analyzing, and reporting the results of stepped‐wedge cluster randomized trials. In contrast, there is little research available pertaining to the design and analysis of multiarm stepped‐wedge cluster randomized trials, utilized to evaluate the effectiveness of multiple experimental interventions. In this paper, we address this by explaining how the required sample size in these multiarm trials can be ascertained when data are to be analyzed using a linear mixed model. We then go on to describe how the design of such trials can be optimized to balance between minimizing the cost of the trial and minimizing some function of the covariance matrix of the treatment effect estimates. Using a recently commenced trial that will evaluate the effectiveness of sensor monitoring in an occupational therapy rehabilitation program for older persons after hip fracture as an example, we demonstrate that our designs could reduce the number of observations required for a fixed power level by up to 58%. Consequently, when logistical constraints permit the utilization of any one of a range of possible multiarm stepped‐wedge cluster randomized trial designs, researchers should consider employing our approach to optimize their trials efficiency.

Information content of cluster-period cells in stepped wedge trials

Stepped wedge and other multiple-period cluster randomized trials, which collect data from multiple clusters across multiple time periods, are being conducted with increasing frequency; statistical research into these designs has not kept apace. In particular, some stepped wedge designs with missing cluster-period "cells" have been proposed without any formal justification. Indeed there are no general guidelines regarding which cells of a stepped wedge design contribute the least information toward estimation of the treatment effect, and correspondingly which may be preferentially omitted. In this article, we define a metric of the information content of cluster-period cells, entire treatment sequences, and entire periods of the standard stepped wedge design as the increase in variance of the estimator of the treatment effect when that cell, sequence, or period is omitted. We show that the most information-rich cells are those that occur immediately before or after treatment switches, but also that there are additional cells that contribute almost as much to the estimation of the treatment effect. However, the information content patterns depend on the assumed correlation structure for the repeated measurements within a cluster.