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Sample size calculation for a stepped wedge trial | Trials. The claim that SWTs are more efficient than a parallel group CRT in terms of sample size [1. SWT design is beneficial only in circumstances when the ICC is high, while it produces no advantage as it approaches 0. This finding was corroborated by [3. Subsequently some of the authors of the original article [1. Moreover, HH appear to suggest that the advantage in power from a SWT seen in their work and that of Woertman comes from the increase in the number of participants (assuming as do HH a design with cross- sectional data collected at every crossover) and not the additional randomised crossover points.
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Kotz et al. [3. 9] argued that power could be amplified to a similar level in standard parallel trials by simply increasing the number of pre- and post- measurements, an assumption supported by Pearson et al. This issue has been recently re- examined by Hemming et al. SWT with more than 4 crossover points may be more efficient than a pre- post RCT. In our work we have also considered the case of cross- sectional data in which each participant provides one measurement to the trial and considered a CRT with the same number of measurements per cluster as a SWT. Under these assumptions, our results are in line with those pointed out above and suggest that, at the cluster size considered, a SWT is more efficient unless the ICC is rather low, for example, much less than 0.
In other words, given cross- sectional data and the same number of participants measured per cluster, the SWT may often be a more efficient trial design and so will require fewer clusters. The SWT is a design in which a lot of information can be gained from each cluster by increasing the number of measurements per cluster, and is suited to settings where clusters are limited or expensive to recruit. In other settings the costs of adding a cluster to a trial may be low, and it may be more efficient for a given total number of measurements in the trial to conduct a CRT with a large number of clusters (few measurements per cluster) than a SWT with a smaller number of clusters. The CRT would then also be of shorter duration. More generally the costs of a trial may relate to the number of clusters, the trial duration, the total number of participants and the total number of measurements all together in a complex way.
- Sample size calculation for a stepped wedge trial. that the advantage in power from a SWT seen. reduce the required sample size in cluster randomized trials.
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Hence, while a SWT is often chosen because there is no alternative trial design, when a SWT or CRT could both be chosen and maximum power is the goal, then the choice between them given the total trial budget requires careful consideration. In our study, the stepped wedge design was found to be relatively insensitive to variations in the ICC, a finding reported previously in [1. We also found that in the case where measurements are taken at each discrete time point in the SWT, for a fixed number of clusters the resulting power increases with the number of randomisation crossover points. This is rather intuitive, since for these designs an increase in the number of crossover points equates to an increase in the number of measurements; hence, more information will be available and the number of subjects required will be lower. In practice, the most extreme situation of having one cluster randomised to the intervention at each time point may be unfeasible for these designs.
On Nov 29, 2008 B Giraudeau (and others) published: Sample size calculation for cluster randomized cross-over trials.
A practical strategy is to simply maximise the number of time intervals given constraints on the number of clusters that can logistically be started at one time point and the desired length of the trial. Moreover, in sensitivity analyses (not shown) it appeared that the gain of increasing the number of crossover points while keeping the number of clusters and the total number of measurements fixed was modest, in comparison with the efficiency gain from adding clusters or measurements to the design.
Increasing the number of subjects per cluster may also result in power gains, but as with CRTs, these may be minimal [4. The failure to consider a time effect when one existed erroneously increased the power. Consequently, we advise researchers to ensure that the effect of time is accounted for in the power calculations, at least as a failsafe measure.
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Inclusion of time as a factor only minimally reduced the power in comparison to the case in which it was included as a continuous variable, using a linear specification. For generalisability of the time effect and simplicity in the interpretation of the model, it is perhaps even more effective to use a set of dummy variables for the time periods, instead of a single factor [4. The inclusion of a random intervention effect produced an increase in the resulting sample size; this was an intuitive result, as our simulations assumed an increase in the underlying variability across the clusters. It is worth bearing this possibility in mind when designing a SWT, as the assumption of a constant intervention effect across the clusters being investigated may often be unrealistic, thus leading to potentially underpowered studies. Again, the flexibility of the simulation- based methods allows the incorporation of this feature in a relatively straightforward way. Not all design possibilities were addressed in our study: for example, the impact of unequal cluster sizes was not considered. In general terms, we would expect a loss of power if the cluster sizes vary substantially, which is consistent with the literature on CRTs [4.
Using a simulation- based approach, relevant information about the expected distribution of cluster sizes in the trial may be easily included in the power computations. The effect of drop- out was also not fully assessed. This may be relevant, since the extended time required for SWTs may reduce retention, resulting in missing data and loss of power.
The impact of drop- out may vary according to how individuals participate in the trial and how measurements are obtained. For cross- sectional data, drop- out can be addressed in a standard manner by inflating the sample size. Drop- out in closed cohort trials, where repeated measurements on individuals are obtained, may be most problematic.
Assumptions about the drop- out mechanism and its variation between clusters can be incorporated into a simulation- based approach and their impact on the resulting sample size assessed at the design stage. Throughout our analysis, time was only considered as a fixed effect.
The reason underlying this assumption is that interest was in controlling for temporal trends and fluctuations in prevalence of the outcomes over the course of the particular trials. Including time as a random effect would also result in a more complex model, as adjacent time periods are unlikely to be independent. However, as noted in [1. In line with other articles in this special issue, our work highlights that while SWTs can produce benefits and provide valuable evidence (particularly in implementation research), they are usually also associated with extra complexity in the planning and analysis stage, in comparison to other well- established trial designs. For this reason, it is important to apply the best available methods to carefully plan the data collection. In our work, we have highlighted some of the features that may hinder this process.
We plan to make an R package available to allow the practitioners to use both analytical and simulation- based methods to perform sample size calculations in an effective way.