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

Journal Pre-proof Variations in stepped-wedge cluster randomized trial design: Insights from the ‘patient-centered care transitions in heart failure’ trial

Rudy R. Unni, Shun Fu Lee, Lehana Thabane, Stuart Connolly, Harriette GC Van Spall PII:

S0002-8703(19)30222-4

DOI:

https://doi.org/10.1016/j.ahj.2019.08.017

Reference:

YMHJ 5969

To appear in:

American Heart Journal

Received date:

22 January 2019

Accepted date:

26 August 2019

Please cite this article as: R.R. Unni, S.F. Lee, L. Thabane, et al., Variations in steppedwedge cluster randomized trial design: Insights from the ‘patient-centered care transitions in heart failure’ trial, American Heart Journal(2019), https://doi.org/10.1016/ j.ahj.2019.08.017

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© 2019 Published by Elsevier.

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Title: Variations in stepped-wedge cluster randomized trial design: Insights from the ‘Patient-Centered Care Transitions in Heart Failure’ trial Rudy R. Unni1, Shun Fu Lee2, Lehana Thabane3, Stuart Connolly2, Harriette GC Van Spall2,3,4*.

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1. Department of Medicine, University of Ottawa, Ottawa, Ontario, Canada 2. Population Health Research Institute, McMaster University, Hamilton, Ontario,

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Canada

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3. Department of Health Research Methods, Evidence, and Impact, McMaster

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University, Hamilton, Ontario, Canada

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4. Department of Medicine, McMaster University, Hamilton, Ontario Canada Corresponding Author: Harriette GC Van Spall, M.D, MPH, FRCPC. Population Health Research Institute, 20 Copeland Avenue David Braley Research Institute Suite

C3-117,

Hamilton

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Building,

ON

L8L

0A3.

Electronic

address:

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[email protected]. Phone: (905) 527-4322 Ext. 40309

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Short Title: Variations in stepped-wedge trial design Funding: This study is funded by Canadian Institutes of Health Research and Ontario’s Ministry of Health and Long Term Care Health System Research Fund. Dr. Van Spall receives research salary support from Ontario’s Ministry of Health and Hamilton Health Sciences Career Award. Disclosures: None The senior author is responsible for the design and conduct of the PACT-HF study. The authors are responsible for the present analyses, drafting and editing of the paper, and its final contents.

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Abstract The stepped-wedge (SW) cluster randomized controlled trial (RCT), 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.

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We examine the logistical and statistical implications of variations in SW design, using

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the optimization of the Patient-Centered Care Transitions in Heart Failure (PACT-HF)

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trial for illustration. We review the following complete SW design variations: a typical

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SW design; a SW design with multiple clusters crossing over per period to achieve

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balanced cluster sizes at each step; hierarchical randomization to account for higherlevel clustering effects; nested sub-studies to measure outcomes requiring a smaller

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sample size than the primary outcomes; and hybrid SW design, which combines parallel

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cluster with SW design to improve efficiency. We also reviewed three incomplete SW design variations in which data is collected in some but not all steps to ease

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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 a SW RCT.

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Introduction The stepped-wedge (SW) cluster randomized controlled trial (RCT) is one in which clusters initially assigned to control cross over unidirectionally to the intervention in a randomized sequence (Figure 1) [1]. This differs from a parallel cluster design in which clusters are randomized to either control or intervention without cross over [2], and from a cluster randomized cross-over design in which clusters initially randomized to

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intervention or control cross over one or more times to the opposite arm [3]. The SW

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design has increased in popularity, particularly in studies testing complex health-care

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service interventions [1,4,5]. Relative to a parallel cluster design, advantages of a SW

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design include delivery of the intervention to all clusters, a staged approach to and associated lead time for implementation, and need for fewer clusters to achieve

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statistical power [2]. Relative to a parallel cluster design, limitations of a SWD include

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methodological complexity, longer trial duration, and susceptibility to temporal effects.

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The “Patient-Centered Care Transitions in Heart Failure” (PACT-HF) trial was a multicenter SW trial that evaluated the effectiveness of a transitional care model

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delivered in hospital, at home, and in ambulatory clinics after hospitalization for heart failure (HF) [6]. The primary outcomes were composites of clinical endpoints measured at 3 months and 30 days. Secondary outcomes included patient-reported measures of discharge preparedness, quality of care, and quality of life. Given the complexity of the intervention and the integration required across institutions that typically function independently of each other, we considered variations to the SW design. This paper describes the features and rationale for SW design, variations in SW methodology and implications on statistical power, using the PACT-HF trial for illustration.

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Rationale for a SW trial All clusters receive intervention The SW design is advantageous over parallel cluster designs when it is desirable for all participating clusters to receive the intervention; there may be preliminary evidence that the intervention offers clinical benefit with minimal risk, and there may be a desire to implement the intervention and test its effect on a range of outcomes in real world

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settings [2,7]. Other types of cluster randomized cross-over designs can also facilitate

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delivery of the intervention in all clusters, but not all clusters receive the intervention at

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the end of the trial; because as all clusters in a SW design are receiving the intervention

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by trial’s end, there is no incremental work to implement the intervention following the

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trial [3].

Decision-makers in the hospitals enrolled in PACT-HF preferred a SW over a parallel

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cluster design so that all hospitals received the intervention. Provincial policy initiatives

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at the time provided incentives for hospitals to implement interventions aimed at

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reducing readmissions in HF. The transitional care services comprising the PACT-HF intervention were shown in prior explanatory RCTs to decrease readmissions among individuals hospitalized for HF [8,9]. The goal of the PACT-HF trial was to assess whether combining these services and implementing them in hospitals improved a range of clinical, cost, and patient-reported outcomes. Because study outcomes were not available for several months after the trial’s end, there would have been insufficient justification to implement the intervention among control sites had a parallel cluster design been used. Sequential implementation allows lead-time 4

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall The sequential implementation of a SW design can facilitate the lead-time and focused attention required for preparation of each cluster to initiate the intervention. This is of benefit in complex health service interventions [2,10]. The PACT-HF model involved the delivery of transitional care services across 10 hospital clusters and their regional home care agencies and ambulatory clinics. The intervention required training of personnel and integration of services across institutions that typically function independently of

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each other in a publicly funded health care system. The complexity of the work was

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simplified by initiating the intervention in a single cluster at each step; the lead-time at

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each cluster provided by the SW design was required to reliably redesign the

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ambulatory services, train personnel, and deliver services. While a modified parallel cluster design would have also allowed sequential implementation, this would have only

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pertained to the intervention group and all hospitals would not have received the

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intervention[11].

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Fewer clusters are required

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A SW trial typically requires fewer clusters than a parallel cluster RCT to achieve acceptable statistical power, making it ideal in situations where a limited number of clusters are available for trial participation [12,13]. Each cluster in a SW trial is exposed to both control and intervention. Thus, each cluster acts as its own control and reduces the impact of clustering effects (the correlation between any two individuals of the same cluster). This results in a gain in statistical power that is most notable when the clustering effects are large [13,14]. This gain can be attenuated or absent if clustering effects are small. [15]. This is in contrast to a parallel cluster design, where solely intercluster treatment effects can be examined, and the maximum power attained with few clusters cannot be overcome with increased cluster sizes[12]. The complexity of 5

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall services in the PACT-HF trial made it undesirable to recruit a large number of clusters, and the desired number of clusters would have provided insufficient statistical power for a parallel cluster RCT to answer the primary research question. General Principles of SW Design Design pattern and step length

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The steps in a SW design mark the periods when clusters sequentially cross over

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unidirectionally from control to intervention, resulting in two ‘stepped wedges’ of

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treatment allocation (Figure 1). Outcomes are measured at baseline before intervention

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and at each crossover step, including after the final cluster crosses over to receive the

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intervention.

Step length is an important consideration. For a complex intervention requiring a period

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of time after implementation for fidelity to be achieved, measurements recorded

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immediately after crossover may not accurately reflect the intervention’s effect. Increasing the length of each step to allow for a learning or adjustment period could

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more reliably reflect the intervention’s effectiveness [14,16]. However, the resultant increase in trial duration may increase study costs, increase susceptibility to temporal effects (see “Limitations of SW Design” below), delay intervention delivery to participating clusters, and potentially deter participation. The PACT-HF clinical trial had a total duration of 1 year, with 11 steps that each lasting 1 month in duration. This was based on sample size estimations, the intervention lead time required per site, and feasibility of collecting outcomes (provincial databases report outcomes on a monthly basis).

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall

Cross-sectional vs. cohort SW design The PACT-HF trial was a cross-sectional SW design [14], in which unique trial participants – patients discharged after hospitalization for HF – were recruited at each time step. Treatment allocation to control or intervention depended on when the patients

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were hospitalized relative to their hospital’s crossover date [17]. Measurements were

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recorded from different participants at each step. Patients were recruited during their

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index hospitalization and censored if rehospitalized, so only included in the analysis

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once.

A ‘cohort’ SW trial describes a protocol where individuals are identified at the beginning

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of the trial and are measured repeatedly as they are exposed to both control and

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intervention [2,17,18]. Cohort SW trials can add measurement burden on participants if the measures are collected directly from them (versus from databases that track their

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outcomes), increasing the risk of participants leaving the trial prior to completion. The

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induced correlation between measurements drawn from the same participant in a cohort SW design must be accounted for in analysis [18]. Additionally, a cohort SW trial may not be ideal when achieving an outcome that may change a patient’s response to treatment during the remainder of the trial [17]; in such cases, the patient may need to be censored, and this needs to be accounted for in sample size calculations to avoid ‘healthy survivor bias’. Sample size calculations for cross-sectional SW

designs are often applied

inappropriately to cohort designs, and further efforts are required to characterize this design, determine its applications, and validate statistical analytic approaches [4,17]. 7

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall

Sample Size Calculation and Power Randomizing clusters instead of individuals in cluster RCTs results in a loss of statistical power because responses within a cluster are more similar than responses of different

𝜎𝑏2 2 2) (𝜎𝑏 +𝜎𝑤

(1)

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𝜌=

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clusters; this can be quantified by the intra-cluster correlation (ICC) denoted as 𝜌:

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where 𝜎𝑏2 is the between-cluster variance, and 𝜎𝑤2 is the within-cluster variance [19].

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This measure describes the proportion of total variance attributable to clustering. The

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ICC, number of clusters, and trial duration are used in sample size calculations for cluster RCTs [20].

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Hussey and Hughes [1] were first to describe power formulae for the SW design in

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2007. From this work, Woertman et al. [21] derived a now widely-used approach to

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calculate a single inflation factor or “design effect” denoted as 𝐷𝐸𝑠𝑤 . This is multiplied by the sample size required for an equivalent individually randomized trial to produce the sample size for a SW [17–20], given by: 𝐷𝐸𝑠𝑤 = (𝑡 + 1)

1+𝜌(𝑡𝑚+𝑚−1) 3(1−𝜌) 1+𝜌(

𝑡𝑚 +𝑚−1) 2

∙

1 𝑡

2(𝑡− )

(2)

where 𝑡 is the number of steps, 𝜌 is the ICC, and 𝑚 is the number of subjects within a period in a cluster. The statistical power of a parallel cluster trial drops as the ICC increases, requiring additional clusters to retain power; increasing cluster size is of limited utility [18]. In 8

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall contrast, the statistical power of a SW trial is relatively insensitive to the value of ICC because clusters act as their own control [10,18]. In the absence of temporal trends and when the ICC and cluster sizes are large, trials with the SW design can be more statistically efficient than those with parallel cluster designs [15,21,22]. For the first primary outcome of PACT-HF, the design effect approach was used to estimate that a sample size of 320 patients per hospital across 10 hospitals and 11

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steps would provide ≥ 80% statistical power to detect a 25% difference in the first

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primary outcome. This assumed a typical SW design and an annual event rate of 28%

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in the control group. With the same assumptions, a parallel cluster design would have

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provided a statistical power of only 43% to detect the same difference in primary

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Variations in SW trial design

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outcome.

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Complete versus incomplete SW trial design. In a ‘complete’ SW design, data is

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collected from each cluster at every step, requiring more resources but optimizing statistical power [10]. In an ‘incomplete’ SW design, data from each cluster is collected during some but not all steps, reducing the measurement burden, data collection and also the statistical power – unless adjustments are made to the duration of each step, number of clusters, or cluster size. In the following sections, we evaluate potential variations of complete and incomplete SW designs and assess their efficiency by estimating their statistical power using the PACT-HF trial as an example (Table 1). As outlined in the supporting information (S1 Appendix), estimated power was calculated

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall using a statistical modelling approach based on Hussey and Hughes’ power formulae (alpha < 0.05, 2-tailed for all estimations) [1].

Complete typical SW design In a complete ‘typical’ SW trial (Figure 1), the number of steps is equal to one greater

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than the total number of clusters, and data is collected at each step. The sample size

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and power estimations assume balanced cluster sizes, fixed step durations, and

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intervention fidelity without a required learning period. Given the number and size of

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clusters in PACT-HF, a complete typical SW design was estimated to yield a statistical power of 82% to demonstrate a 25% change in the primary composite outcome (alpha <

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0.05, 2-tailed).

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Complete SW design with grouping multiple clusters per crossover

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Randomization can be stratified by cluster size in order to facilitate balanced cluster sizes across steps between control and intervention. This may ease the burden of implantation with a small number of steps particularly when the number of clusters is large for a small trade off in power. Figure 2 illustrates this design variation, with a modified PACT-HF trial and two clusters crossing over to intervention per step. The number of steps is reduced to six and statistical power for the primary composite outcome is modestly reduced from 82% to 80%.

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Complete SW design with multi-level clustering Multi-level clustering may be considered when clusters are not independent because higher-level factors influence outcomes within them [10]. This design is depicted in Figure 3, in which the intervention is implemented sequentially across 4 geographic regions, each containing multiple hospital sites that share transitional care service

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providers and resources. Randomization in this model would first occur at the level of the region, and then at the level of the hospital. This would allow for the practical

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deployment of regional resources to clusters, while minimizing the contamination that

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may occur due to a prolonged delay in crossover between some clusters and others.

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Analysis is complex however, and limited progress has been made in fully

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characterizing this variation [10].

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Complete SW design with unequal cluster size per period Statistical power calculations for SW trials are often estimated under the assumption of

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equal cluster size which can sometimes be impossible to achieve in practice [23]. While significant imbalance in cluster sizes may lead to loss of statistical power, allowing for unequal cluster sizes in the estimation of statistical power could encourage recruitment of diverse clusters and improve generalizability of results. For example, smaller community hospital sites as well as larger academic ones could both be used to examine an intervention’s effect. The coefficient of variation of cluster size (CV) is a measure for the degree of variation in cluster sizes. It is defined as the ratio of the standard deviation of cluster size to the

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall mean cluster size. It can be incorporated into the design effect (see equation (2) in “Sample Size Calculation and Power” above) to account for unequally sized clusters, by multiplying the cluster size per period per cluster 𝑚, by (1+CV2) [24]. In the PACT-HF trial, it was estimated that 320 patients per cluster during the trial would provide a statistical power of 82% to detect a 25% change in the primary outcome. In the setting of imbalanced cluster size with a CV of 0.42, an average cluster size of 377 patients per

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cluster would be required to retain a power of 82%. Without an increase in average

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cluster size, the statistical power to detect a change in the primary outcome would

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decrease to 77%.

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Complete SW design with nested sub-study

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A nested sub-study may be considered when a study includes secondary aims or substudies that require a smaller sample size than the primary aim. This approach can

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reduce measurement burden. The secondary outcomes of the PACT-HF clinical

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included patient reported measures that required only 8 clusters to yield 90% power to detect a 5% difference in outcomes after accounting for dropout, loss of follow-up, and death rates before data collection. Investigating these secondary outcomes in all 10 hospitals would result in overpowering. A nested sub-study was thus designed for collection of these outcomes within the existing SW trial (Figure 4).

Complete SW combined with parallel cluster design (hybrid SW design)

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall A ‘hybrid’ SW trial combines a parallel cluster and complete SW design, such that a balanced proportion of clusters are randomized to either intervention or control without crossing over; and the remainder of the clusters cross over unidirectionally in a randomized sequence as in typical SW design. The inclusion of clusters that do not cross over helps reduce the potential bias of temporal changes across the trial. Consequently, a hybrid SW trial is more statistically efficient than a complete SW trial

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[25]. One obvious drawback to a hybrid design is that some clusters will not receive

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intervention during the trial. Just as with parallel cluster designs, this may deter cluster

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enrollment if all clusters wish to receive a potentially beneficial intervention.

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Varying combinations of parallel cluster and SW design can be examined. Using the

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PACT-HF trial’s sample size of 10 hospitals, possibilities included: (1) a 20:80 hybrid combination, with a parallel design involving 2 sites and a SW design involving 8 sites,

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as seen in Figure 5; (2) 40:60 hybrid combination; and (3) a 60:40 hybrid combination.

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The lower the proportion of SW design clusters in a hybrid design, the lower the statistical power. The estimated power for each of these hybrid SW design

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combinations is 85%, 85% and 80%, respectively.

Incomplete SW design with a learning period In an incomplete SW trial with a ‘learning period’, data is not collected during the initial step(s) after crossover to intervention at each site [10]. This is to allow for the time and site-specific optimization that may be required before the intervention is delivered with fidelity, and before outcomes reflect the effectiveness of the intervention. An incomplete design can allow participating clusters to focus resources on uptake of the intervention 13

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall without simultaneously collecting data. Figure 6 shows an incomplete SW trial with a ‘1step’ learning period. Outcomes are collected at baseline in each cluster, but not during the first crossover step – where there is learning, adjustment to, and efforts to improve fidelity to the intervention. Measurement of outcomes restarts at the second time period after crossover, as the next cluster begins its crossover step. Similar to a complete SW design, all clusters receive intervention for the final time step. The total number of time

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steps in the trial is greater by 1 than an equivalent complete SW design, potentially

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increasing the duration of the trial. Under the same assumptions for the PACT-HF trial

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outlined above, the estimated statistical power for primary outcomes for the incomplete

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design with learning period would drop from 82% to 74%.

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Incomplete SW design with limited measurements prior to and after crossover Another iteration of incomplete SW trial includes limited measurements per cluster, with

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the intention of reducing the measurement burden and costs at participating clusters

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[10]. Figure 7 shows a modified PACT-HF study design pattern in which data is measured during one time step per cluster prior to crossover and two time steps after. This protocol reduces the total and simultaneous data collection required. However, the estimated loss in power with a fixed number of clusters is significant with such omission of data. If the design outlined in Figure 7 was utilized for the PACT-HF trial, holding sample size and cluster number constant, the estimated power would have dropped from 82% in a complete design to 52%. This reduction in power could be attenuated by increasing the number of before and after measurements, the sample size, and the number of clusters. 14

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall

Incomplete SW design with early and late blocks For a typical SW design, clusters must be ready to deliver the intervention and adhere to measurement and reporting protocols prior to randomization. Cluster specific-factors such as scheduling conflicts and lack of resources may limit the willingness of some

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clusters to cross over from usual care to intervention early in the study. We devised a

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possible option to address this limitation by stratifying the participating sites into two

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equal blocks - representing ‘early’ and ‘late’ implementation blocks - and randomizing the sequence of crossover within each block. Figure 8 is an illustration of this

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incomplete design using the PACT-HF trial. Half of the participating clusters can be

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randomized within the early block and the other half randomized within the late block – akin to two separate SW trials run in sequence. Analysis should include adjustment of

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outcomes for the early or late block to address bias, as allocation to each block is not

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random and the late block may include sites with different characteristics than the early

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block. Using the PACT-HF trial as an example with the above assumptions, this design would reduce the statistical power from 82% (typical complete SW design) to 75%, assuming the sample size is constant per cluster.

Limitations of SW trials Prolonged exposure to intervention A SW trial can prolong the exposure of patients to potential risks of intervention because of its longer duration and limited precision compared to randomization at the 15

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall individual level [26,27]. In the setting of adverse effects, de-implementation in a SW design may be more complex than in a randomized RCT or parallel cluster trial [22]. Additionally, due to the greater number of measurements in control than in treatment arms early in a SW design, interim analyses are unreliable unlike a parallel or individually randomized RCT [22].

For these reasons, a SW design is not

recommended when there is clinical equipoise. Measured outcomes take longer to

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establish due to the longer trial duration and this needs consideration [7,13,28,29].

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Parallel cluster designs may also provide information on an intervention’s efficacy faster

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than an equivalent SW design, which could accelerate systems-wide implementation or

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trial discontinuation.

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Complexity and measurement burden

The complexity of a SW protocol requires preparation and consensus between

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investigators and all stakeholders. Stakeholders from each cluster should ideally be

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involved in the trial design to ensure that clusters are able to meet training,

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implementation, measuring, and reporting protocols. Planning must be undertaken to ensure adherence to crossover schedules, fidelity to the protocol, and prevention of contamination[30]. In the PACT-HF trial, the sequence and date of crossover from control to intervention were concealed from participating clusters until three months prior to their intervention phase. Training sessions and resources for the intervention were provided to clusters only in the month immediately preceding crossover to prevent inadvertent implementation of the intervention prior to the intervention phase. Investigators must consider the local socio-economic, political, cultural, and health-care infrastructure contexts into which a SW trial is to be implemented. The measurement 16

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall burden on clusters, researchers and individuals from the repeated measurements in a SW should also be considered during the planning stages. However, the amount of measurement burden depends on the type of SWD and the outcomes chosen. In PACTHF, there was no measurement burden for the primary clinical outcomes as these were obtained from administrative datasets. Each patient had the same number of measures

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for the primary outcomes.

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Temporal effects must be considered

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Temporal trends must be considered in the planning of a SW design [31]. Because clusters in a SW design begin the trial as control and sequentially crossover to

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intervention, earlier measurements are made up primarily of control cluster data, while

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those made near the end of the trial are mostly sourced from intervention cluster. External factors influencing cluster behavior or measurements (such as new health

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system policies or regulations affecting some or all clusters) can thus add bias if their

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impact arises during a SW trial. Temporal or seasonal trends in the data should be

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accounted for in the analysis as a fixed-effects variable [1,32]. Delayed effects of intervention, and heterogeneity of intervention effect across the steps also contribute to complexity of statistical modelling [33]. PACT-HF included time as a fixed effect in its analysis. Additionally, unlike in parallel cluster designs, extending data collection after completion of the initially planned trial protocol to meet recruitment targets, will only result in further intervention data. This should be considered during the planning stages of a SW trial. Understanding this limitation, we recruited an extra cluster in the event that any of our assumptions to estimate statistical power were not met.

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Rationale of selected design for PACT-HF trial Given the challenges posed by organizing and executing a multicentre study of a complex health service intervention alongside multiple community and hospital stakeholders, we considered each SW design variation and its implications. For the final design we chose the complete typical SW design involving 10 clusters to adequately

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power the study for the primary outcomes and allow all sites to receive the intervention. Randomizing one cluster to cross over per time step allowed for focused direction of

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resources at each site prior to the intervention phase and limited the risk of pooling

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together dissimilar sites. We included a nested sub-study involving a subset of 8

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hospital sites for the secondary outcomes to conserve resources and limit measurement

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burden.

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Conclusions and future directions

The SW trial is a type of cluster RCT that can be used to evaluate cluster-level

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interventions with a sequential implementation approach. It is ideal for the assessment of health services interventions when there is some evidence that benefits of the intervention outweigh risks, when all clusters wish to receive the intervention, and when there is limited cluster availability. Variations in SW design methodology can be considered for logistic or statistical reasons, but further research is warranted to facilitate accurate estimation of statistical power [34,35].

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Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Table 1: Summary of SW design methodological implications and estimated statistical power for the primary outcome.

METHODOLOGICAL IMPLICATIONS

Multi-level clustering

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Unequal cluster sizes (CV = 0.60)

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40:60 Hybrid SW 60:40 Hybrid SW Incomplete SW

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20:80 Hybrid SW

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Learning period (1 time step)

Reduced measurements (1 time step prior crossover, 2 time steps after crossover)

82% 80% (2 clusters cross over/time step)

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Grouped Cluster Crossover

Standard design Reduction in crossover points and time steps, balanced crossover Includes nonindependency between clusters May increase recruitment Some clusters do not receive intervention. Increased efficiency. “ “ “ Allows extended optimization of intervention. Increases fidelity of data

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Complete SW Typical SW

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SW DESIGN VARIATION

ESTIMATED STATISTICAL POWER FOR PRIMARY OUCOME OF PACTHF*

Reduces measurement burden

--77% 85% 85% 80%

74%

52%

Accommodates varying 75% cluster readiness SW, Stepped-wedge (cluster randomized trial); PACT-HF, Patient-Centered Care Transitions in Heart Failure; CV, Coefficient of Variation. Early and Late Blocks

Statistical power for Multi-level clustering was not completed due to complexity of analysis. *

Power estimations are calculated assuming 320 index patients per cluster, 10 clusters, a control event rate of 28% at 1 year, and an ICC of 0.01. All power calculations were estimated to demonstrate a 25% change in the primary composite outcome, and with α < 0.05, 2-tailed. The number of time steps and measurements are modified between variations. 19

Journal Pre-proof Unni, Lee, Thabane, Connolly, Van Spall Figures:

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Figure 1. Complete typical SW design: The PACT-HF design (complete, typical SW) for the clinical outcomes, where “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. There are 10 hospital sites, 11 steps, 55 control cross-sections, and 55 intervention cross-sections. The clear cells represent the control wedge and the shaded cells represent the intervention wedge. There are 11*10 = 110 observations for the clinical outcomes.

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Figure 2. Complete SWD with grouped cluster crossover. An alternative PACT-HF complete SW design, with 2 “grouped” clusters crossing over at each time step. “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. The clear cells represent the control wedge and the shaded cells represent the intervention wedge. There are 10 hospital sites, 6 steps, 30 control cross-sections, and 30 intervention cross-sections. There are 6*10 = 60 observations for the clinical outcomes.

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Figure 3. Complete SW design with multi-level clustering. An alternative PACT-HF complete SW with multi-level clustering at the level of region and hospital site. “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. The clear cells represent the control wedge and the shaded cells represent the intervention wedge. There are 4 regions, 10 hospital sites, 11 steps, 55 control cross-sections, and 55 intervention cross-sections.

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Figure 4. Complete SW design with nested sub-study. The PACT-HF study design pattern of a complete SW with a nested sub-study for the patient-reported outcomes. “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. The clear cells represent the control wedge and the shaded cells represent the intervention wedge. The cells within bolded borders represent the 8 sites (of a total of 10 possible sites) collecting the secondary patient-centered outcomes. There are 11*10 = 110 observations for the clinical outcomes, and 9*8 = 72 observations for the patient-centered outcomes.

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Figure 5. Complete SW combined with parallel cluster design (hybrid SW design). An alternative PACT-HF study design pattern of a Hybrid 20:80 design with 2 parallel clusters and 8 clusters in a modified SW. Clusters 1 and 10 are parallel clusters exposed to only control or intervention throughout the trial. Clusters 2 through 9 are arranged in a modified complete typical SW. “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. The clear cells represent the control wedge and the shaded cells represent the intervention wedge. There are 9*8 = 72 observations in the modified SW, and 9*2 = 18 observations in the parallel design component.

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Figure 6. Incomplete SW design with a learning period. An alternative PACT-HF study design pattern of an ‘Incomplete SW’ with a learning period. “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. “.” represents sites during the implementation period where measurements are not collected. There is an increased number of time steps (12). The total number of observations is the same as in an equivalent complete SW of 10*11 = 110.

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Figure 7. Incomplete SW design with limited measurements prior to and after crossover. There are 10 clusters/hospital sites, 12 steps, 10 control cross-sections, and 20 intervention cross-sections. “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. The clear cells represent the control wedge and the shaded cells represent the intervention wedge. Each cluster is measured over one time period prior to crossover, and over two time periods after crossover. There are 3*10 = 30 total observations.

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Figure 8. Incomplete SW with early and late blocks. “0” represents sites not exposed to the intervention and “1” represents sites exposed to the intervention. The clear cells represent the control wedge and the shaded cells represent the intervention wedge. The first 5 clusters are stratified to the ‘Early’ block and receive intervention in the first half of the design. The second 5 clusters are stratified to the ‘Late’ block and receive intervention in the second half of the design. There are 5*6*2=60 total observations.

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Variations in stepped-wedge cluster randomized trial design: Insights from the ‘PatientCentered Care Transitions in Heart Failure’ trial

Highlights

A stepped wedge (SW) design is a type of cluster randomized trial



All clusters in a SW design sequentially cross over from control to intervention

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SW design is useful to study the effect of implementing an intervention

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Variations in SW can be used to address methodologic or logistical constraints

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Variations include SWs with fewer steps, reduced measurements and nested substudies

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