A tutorial on sample size calculation for multiple-period cluster randomized parallel, cross-over and stepped-wedge trials using the Shiny CRT Calculator

Abstract

It has long been recognized that sample size calculations for cluster randomized trials require consideration of the correlation between multiple observations within the same cluster. When measurements are taken at anything other than a single point in time, these correlations depend not only on the cluster but also on the time separation between measurements and additionally, on whether different participants (cross-sectional designs) or the same participants (cohort designs) are repeatedly measured. This is particularly relevant in trials with multiple periods of measurement, such as the cluster cross-over and stepped-wedge designs, but also to some degree in parallel designs. Several papers describing sample size methodology for these designs have been published, but this methodology might not be accessible to all researchers. In this article we provide a tutorial on sample size calculation for cluster randomized designs with particular emphasis on designs with multiple periods of measurement and provide a web-based tool, the Shiny CRT Calculator, to allow researchers to easily conduct these sample size calculations. We consider both cross-sectional and cohort designs and allow for a variety of assumed within-cluster correlation structures. We consider cluster heterogeneity in treatment effects (for designs where treatment is crossed with cluster), as well as individually randomized group-treatment trials with differential clustering between arms, for example designs where clustering arises from interventions being delivered in groups. The calculator will compute power or precision, as a function of cluster size or number of clusters, for a wide variety of designs and correlation structures. We illustrate the methodology and the flexibility of the Shiny CRT Calculator using a range of examples.

The impact of the Trauma Triage App on pre-hospital trauma triage: design and protocol of the stepped-wedge, cluster-randomized TESLA trial

“…A second limitation is the use of an exchangeability correlation structure in the analyses. Since the design of this study, methodological literature has been moving towards more complex correlation structures (e.g., discrete time decay correlation) which might be more appropriate for stepped-wedge study designs [18]. Another potential limitation of the trial is the innovativeness of the TTApp and subsequently its dissimilarity to routinely used static decision schemes.…”

“…With eight clusters, a power of 80%, a significance level of 0.05, and two clusters switching to the intervention after every step, at least 48 severely injured patients will have to be included per cluster per step [16,17]. The expected power given the intra-cluster correlation interval ranges from 0.79 to 0.82 [18]. Approximately 1300-1400 severely injured patients will be transported by the participating EMSs on a yearly basis; therefore, we expect a duration of (less than) 4 months per step.…”

Use of multiple period, cluster randomised, crossover trial designs for comparative effectiveness research

“…Unfortunately, under these more complicated correlation models, sample size inflation cannot be characterised by simple design effects. However, analytical solutions are available; thus, the required number of clusters could be determined given a specified total cluster size and vice versa 61. These calculations require specification of correlation parameters, which are ideally estimated from relevant routinely collected data, from the same set of clusters, and over a similar time period.…”

Evaluation of updated midwifery pre-service training in Kenya

“…To improve the power of the study baseline measurements will also be used, thereby enabling the changes within participants to be measured. For sample size calculations the Shiny app (https://clusterrcts.shinyapps.io/rshinyapp/) developed by Karla Hemming for cluster randomised trials has been used (35). Relevant data on which to base selection of the values for use in sample size / power calculations are not available.…”