Designing multicenter individually randomized group treatment trials

In an individually randomized group treatment (IRGT) trial, participant outcomes can be positively correlated due to, for example, shared therapists in treatment delivery. Oftentimes, because of limited treatment resources or participants at one location, an IRGT trial can be carried out across multiple centers. This design can be subject to potential correlations in the participant outcomes between arms within the same center. While the design of a single-center IRGT trial has been studied, little is known about the planning of a multicenter IRGT trial. To address this gap, this paper provides analytical sample size formulas for designing multicenter IRGT trials with a continuous endpoint under the linear mixed model framework. We found that accounting for the additional center-level correlation at the design stage can lead to sample size reduction, and the magnitude of reduction depends on the amount of between-therapist correlation. However, if the variance components of therapist-level random effects are considered as input parameters in the design stage, accounting for the additional center-level variance component has no impact on the sample size estimation. We presented our findings through numeric illustrations and performed simulation studies to validate our sample size procedures under different scenarios. Optimal design configurations under the multicenter IRGT trials have also been discussed, and two real-world trial examples are drawn to illustrate the use of our method.