On the relative efficiency of model-assisted designs: a conditional approach

In phase I dose-finding trials, model-assisted designs are a novel class of designs that combine the simplicity of algorithm-based methods with the superior performance of model-based methods. Examples of model-assisted designs include the modified toxicity probability (mTPI), Bayesian optimal interval (BOIN) and keyboard designs. To achieve simplicity, these model-assisted methods model only "local" data observed at the current dose, typically using a binomial model, to guide dose assignments. This potentially causes efficiency loss, however, by ignoring the data observed in other doses. To investigate this issue, we propose a conditional approach that utilizes the data from both current and adjacent (i.e., next higher or lower) doses to make the dose-assignment decisions. Specifically, we propose the conditional optimal interval (COIN) design, as the conditional approach extension of the BOIN design. We investigate the theoretical properties of the COIN design and conduct extensive numerical studies to examine its performance in comparison with existing model-assisted designs. We also present the conditional approach to the keyboard design. We observe that the conditional approach improves patient allocation, but yields similar maximum-tolerated dose (MTD) identification accuracy as the model-assisted designs, suggesting only minor efficiency loss using local data under the model-assisted designs.