Planning for a 3-arm cluster randomized trial with a nested intervention and a time-to-event outcome

A researcher recently approached me for advice on a cluster-randomized trial he is developing. He is interested in testing the effectiveness of two interventions and wondered whether a 2×2 factorial design might be the best approach. As we discussed the interventions (I’ll call them \(A\) and \(B\) ), it became clear that \(A\) was the primary focus. Intervention \(B\) might enhance the…