The batched stepped wedge design: A design robust to delays in cluster recruitment

Abstract

Stepped wedge designs are an increasingly popular variant of longitudinal cluster randomized trial designs, and roll out interventions across clusters in a randomized, but step-wise fashion. In the standard stepped wedge design, assumptions regarding the effect of time on outcomes may require that all clusters start and end trial participation at the same time. This would require ethics approvals and data collection procedures to be in place in all clusters before a stepped wedge trial can start in any cluster. Hence, although stepped wedge designs are useful for testing the impacts of many cluster-based interventions on outcomes, there can be lengthy delays before a trial can commence. In this article, we introduce "batched" stepped wedge designs. Batched stepped wedge designs allow clusters to commence the study in batches, instead of all at once, allowing for staggered cluster recruitment. Like the stepped wedge, the batched stepped wedge rolls out the intervention to all clusters in a randomized and step-wise fashion: a series of self-contained stepped wedge designs. Provided that separate period effects are included for each batch, software for standard stepped wedge sample size calculations can be used. With this time parameterization, in many situations including when linear models are assumed, sample size calculations reduce to the setting of a single stepped wedge design with multiple clusters per sequence. In these situations, sample size calculations will not depend on the delays between the commencement of batches. Hence, the power of batched stepped wedge designs is robust to unexpected delays between batches.

Keywords: cluster randomized trial; intracluster correlation; sample size calculation; within-cluster correlation structure.

Conflict of interest statement

The authors declare no potential conflict of interests.

© 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Figures

FIGURE 1

An example of a standard stepped wedge design, with 4 periods and 3 sequences (0 indicates periods in which the control condition is implemented; 1 indicates periods in which the intervention is implemented)

FIGURE 2

Three different ways in which the effect of time can be parameterized in a design where clusters commence study participation in three batches: the βs parameterize the time effects. For example, in the top panel, β1 parameterizes the effect of month 1 on outcomes. The top panel indicates how effects of time are shared across batches when the effects of calendar time are assumed to be constant across batches; the middle panel indicates how the effects of time are shared across batches when time‐on‐trial effects are assumed to be constant across batches; the bottom panel indicates that no time effects are shared across batches when separate time effects are estimated in each batch

FIGURE 3

Four examples of batched stepped wedge designs with identical component designs (0 indicates control periods; 1 indicates intervention periods). Each of these designs has three batches of three‐period stepped wedge designs, with differing degrees of overlap between successive batches. Design 1 (top row): no overlap between successive batches; Design 2 (second from top): overlap of one period between successive batches; Design 3 (second from bottom): overlap of two periods between successive batches; Design 4 (bottom row): variable overlap between successive batches

FIGURE 4

Two examples of batched stepped wedge designs without identical component designs (0 indicates control periods; 1 indicates intervention periods)

FIGURE 5

The design schematic for the PACT‐HF trial: Two batches of a 5‐sequence stepped wedge design

FIGURE 6

Empirical and theoretical type I error rates (left panel) and power (right panel) for the simulated continuous outcomes. ICC, intracluster correlation; CAC, cluster autocorrelation. Within each panel, subpanels correspond to a different value of the CAC. The theoretical and empirical type I error rate or power is displayed for each combination of number of periods of overlap, ICC, and CAC, with the empirical result plus and minus 2 standard errors also displayed

FIGURE 7

Empirical and theoretical type I error rates (left panel) and power (right panel) for the simulated binary outcomes analyzed via GEE. ICC, intracluster correlation. The theoretical and empirical type I error rate or power is displayed for each combination of number of periods of overlap and ICC, with the empirical result plus and minus 2 standard errors also displayed