Sample Size Calculations for Partially Clustered Trials

Partially clustered trials are defined as trials where some observations belong to a cluster and others are independent. 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 being over or underpowered. However, sample size methods have only been developed for limited partially clustered trial designs (e.g., designs with maximum cluster sizes of 2). In this article, we present new design effects that can be used to determine the sample size for two-arm, parallel, partially clustered trials where clusters exist pre-randomization. Design effects are derived algebraically for continuous and binary outcomes, assuming a generalized estimating equations-based approach to estimation with either an independence or exchangeable working correlation structure. Both cluster and individual randomization are considered for the clustered observations. The design effects are shown to depend on the intracluster correlation coefficient, proportion of observations that belong to clusters of each size, method of randomization, type of outcome, and working correlation structure. The design effects are validated through a simulation study. Example sample size calculations are presented to illustrate how the design effects can be used to determine the target sample size for different partially clustered trial designs. The design effects depend on parameters that can be feasibly estimated when planning a trial and can be used to ensure that partially clustered trials are appropriately powered in the future.