Just before heading out on vacation last month, I put up a post that purported to compare stepped-wedge study designs with more traditional cluster randomized trials. Either because I rushed or was just lazy, I didnâ€™t exactly do what I set out to do. I did confirm that a multi-site randomized clinical trial can be more efficient than a cluster randomized trial when there is variability across clusters. (I compared randomizing within a cluster with randomization by cluster.) But, this really had nothing to with stepped-wedge designs.
Here, I will try to rectify the shortcomings of that post by actually simulating data from a traditional stepped-wedge design and two variations on that theme with the aim of seeing which approach might be preferable. These variations were inspired by this extremely useful paper by Thompson et al. (If you stop reading here and go to the paper, I will consider mission accomplished.)
The key differences in the various designs are how many sites are exposed to the intervention and what the phase-in schedule looks like. In the examples that follow, I am assuming a study that lasts 24 weeks and with 50 total sites. Each site will include six patients per week. That means if we are collecting data for all sites over the entire study period, we will have \(24 \times 6 \times 50 = 7200\) outcome measurements.
The most important assumption I am making, however, is that the investigators can introduce the intervention at a small number of sites during each time period (for example, because the intervention involves extensive training and there is a limited number of trainers.) In this case, I am assuming that at most 10 sites can start the intervention at any point in time, and we must wait at least 4 weeks until the next wave can be started. (We can proceed slower than 4 weeks, of course, which surprisingly may be the best option.)
I am going to walk through the data generation process for each of the variations and then present the results of a series of power analyses to compare and contrast each design.
Stepped-wedge design
In the stepped-wedge design, all clusters in a trial will receive the intervention at some point, but the start of the intervention will be staggered. The amount of time in each state (control or intervention) will differ for each site (or group of sites if there are waves of more than one site starting up at the same time).
In this design (and in the others as well) time is divided into discrete data collection/phase-in periods. In the schematic figure, the light blue sections are periods during which the sites are in a control state, and the darker blue are periods during which the sites are in the intervention state. Each period in this case is 4 weeks long.
Following the Thompson et al. paper, the periods can be characterized as pre-rollout (where no intervention occurs), rollout (where the intervention is introduced over time), and post-rollout (where the all clusters are under intervention). Here, the rollout period includes periods two through five.
First, we define the data, which will largely be the same across the designs: 6 individual patients per week, an intervention effect of 0.33, and a weekly time effect (which unfortunately is parameterized as â€œperiodâ€�) of 0.02, and standard deviation within each cluster of 3.
library(simstudy)
defS