Evaluating analytic models for individually randomized group treatment trials with complex clustering in nested and crossed designs.

Many individually randomized group treatment (IRGT) trials randomly assign individuals to study arms but deliver treatments via shared agents, such as therapists, surgeons, or trainers. Post-randomization interactions induce correlations in outcome measures between participants sharing the same agent. Agents can be nested in or crossed with trial arm, and participants may interact with a single agent or with multiple agents. These complications have led to ambiguity in choice of models but there have been no systematic efforts to identify appropriate analytic models for these study designs. To address this gap, we undertook a simulation study to examine the performance of candidate analytic models in the presence of complex clustering arising from multiple membership, single membership, and single agent settings, in both nested and crossed designs and for a continuous outcome. With nested designs, substantial type I error rate inflation was observed when analytic models did not account for multiple membership and when analytic model weights characterizing the association with multiple agents did not match the data generating mechanism. Conversely, analytic models for crossed designs generally maintained nominal type I error rates unless there was notable imbalance in the number of participants that interact with each agent.