An online sample size calculator for designing partially clustered trials

Partially clustered trials are trials that, by design, include a mixture of independent and clustered observations. For example, neonatal trials may include infants from a single, twin or triplet birth. The clustering of observations in partially clustered trials should be accounted for when determining the target sample size to avoid treatment arm comparisons being over or under powered. Limited tools are currently available for calculating the sample size for partially clustered trials, particularly when the maximum cluster size is greater than 2. The aim of this article is to introduce a new online application to calculate the target sample size for partially clustered trials covering a broad range of scenarios.

The target sample size is calculated using design effects recently derived for two-arm partially clustered trials when the clusters exist prior to randomisation and the outcome of interest is continuous or binary. Both cluster and individual randomisation are considered for the clustered observations (resulting in nested and crossed designs, respectively). The sample size depends on quantities needed for typical sample size calculations, such as the effect size of interest, and the desired significance level and power. In addition, the sample size for partially clustered trials also depends on the range of cluster sizes, the proportion of observations that belong to clusters of each size, the intracluster correlation coefficient, the method of randomisation for the clustered observations, and the model that will be used for analysis. We developed an R Shiny web application that implements these methods in an easy-to-use sample size calculator that is freely available online.

The sample size calculator is free to access and provides trialists with the ability to determine the target sample size for different types of partially clustered trials. Step-by-step instructions are provided to illustrate the use of the calculator for designing two hypothetical trials. The target sample size that accounts for partial clustering can be quite different to the sample size that is calculated by methods for an independent design that ignore the clustering.

Partial clustering affects the power and sample size requirements of clinical trials. The calculator presented in this article allows trialists to account for the clustering that occurs in two-arm partially clustered trials for binary and continuous outcomes and ensure their trials are appropriately powered.