Stepped-wedge trial

A stepped-wedge trial (or SWT) is a type of randomised controlled trial (or RCT), a scientific experiment which is structured to reduce bias when testing new medical treatments, social interventions, or other testable hypotheses. In a traditional RCT, half of the participants in the experiment are simultaneously and randomly assigned to a group that receives the treatment (the "treatment group") and half to a group that does not (the "control group"). In an SWT, typically a logistical constraint prevents the simultaneous treatment of half of the participants, and instead, participants receive the treatment in "waves" or "clusters."

For instance, suppose a researcher wanted to measure whether teaching college students how to make several meals increased their propensity to cook at home instead of eating out. In a traditional RCT, a sample of students would be selected and half would be trained on how to cook these meals, whereas the other half would not. Both groups would be monitored to see how frequently they ate out. In the end, the number of times the treatment group ate out would be compared to the number of times the control group ate out, most likely with a t-test or some variant. If, however, the researcher could only train a limited number of students each week, then the researcher could employ an SWT, randomly assigning students to which week they would be trained. In an SWT, a classic t-test is inappropriate, and different statistical methods must be used.

The term "stepped wedge" was coined by the Gambia Hepatitis Intervention Study due to the stepped-wedge shape that is apparent from a schematic illustration of the design. The crossover is in one direction, typically from control to intervention, with the intervention not removed once implemented. The stepped-wedge design can be used for individually randomised trials, i.e., trials where each individual is treated sequentially, but is more commonly used as a cluster randomised trial (CRT), as in our example of groups of students being assigned to different weeks to be trained.

Experiment Design and Data Collection

In the context of a cluster randomised trial, the stepped-wedge design involves the collection of observations during a baseline period in which no clusters are exposed to the intervention. Following this, at regular intervals, or steps, a cluster (or group of clusters) is randomised to receive the intervention and all participants are once again measured. This process continues until all clusters have received the intervention. Finally, one more measurement is made after all clusters have received the intervention.

Model

While there are several other potential methods for modeling outcomes in an SWT, the work of Hussey and Hughes "first described methods to determine statistical power available when using a stepped wedge design." What follows is their design.

Suppose there are $N$ samples divided into $C$ clusters. At each time point $t=1,\ldots ,T$, preferably equally spaced in actual time, some number of clusters are treated. Let $Z_{ct}$ be $1$ if cluster $c$ has been treated at time $t$ and $0$ otherwise. In particular, note that if $Z_{ct}=1$ then $Z_{c,t+1}=1$.

For each participant $i$ in cluster $c$, measure the outcome to be studied $y_{ict}$ at time $t$. We model these outcomes as $$y_{ict}=\mu +\alpha _{c}+\beta _{t}+Z_{ct}\theta +\epsilon _{ict}$$where

• $\mu$ is a grand mean,
• $\alpha _{c}\sim N(0,\tau ^{2})$ is a random, cluster-level effect on the outcome,
• $\beta _{t}$ is a time point-specific fixed effect,
• $\theta$ is the measured effect of the treatment, and
• $\epsilon _{ict}\sim N(0,\sigma ^{2})$ is the residual noise.

This model can be viewed as a Hierarchical linear model where at the lowest level $y_{ict}\sim N(\mu _{ct},\sigma ^{2})$ where $\mu _{ct}$ is the mean of a given cluster at a given time, and at the cluster level, each cluster mean $\mu _{ct}\sim N(\mu +\beta _{t},\tau ^{2})$.

Advantages

The primary advantage of the SWT is that it "can reconcile the need for robust evaluations with political or logistical constraints." Specifically, when resources for performing an intervention are scarce, it can be used to measure the effects of treatment even when a treatment and control group cannot be compared simultaneously.

Disadvantages

In an SWT, more clusters are exposed to the intervention at later than earlier time periods. As such, it is possible that an underlying temporal trend may confound the intervention effect, and so the confounding effect of time must be accounted for in both pre-trial power calculations and post-trial analysis.

The design and analysis of stepped-wedge trials is therefore more complex than for other types of randomised trials. Previous systematic reviews highlighted the poor reporting of sample size calculations and a lack of consistency in the analysis of such trials. Hussey and Hughes were the first authors to suggest a structure and formula for estimating power in stepped-wedge studies in which data was collected at each and every step. This has now been expanded for designs in which observations are not made at each step as well as multiple layers of clustering. Additionally, a design effect (used to inflate the sample size of an individually randomised trial to that required in a cluster trial) has been established, which has shown that the stepped wedge CRT could reduce the number of patients required in the trial compared to other designs.

Ongoing Work

The number of studies using the design have been on the increase. In 2015, a thematic series was published in the journal Trials. In 2016, the first international conference dedicated to the topic was held at the University of York.