Estimation of treatment effect in 2-in-1 adaptive design and some of its extensions

The 2-in-1 adaptive design allows seamless expansion of an ongoing Phase II trial into a Phase III trial to expedite a drug development program. Since its publication, it has generated a lot of interest. So far, most of the related research focused on type I error control. Similar to most adaptive designs, 2-in-1 design could also pose a great challenge on estimation of treatment effect due to the data-driven adaptation. In addition, the use of intermediate endpoint for interim adaptive decision-making is a less well-studied field. In this paper, we investigate the bias and variances in estimation for 2-in-1 design and some of its extensions, and propose some bias-adjusted estimators for 2-in-1 design. The properties of the proposed estimators are further studied theoretically and/or numerically, so as to provide guidance on how to interpret the estimated treatment effect of 2-in-1 design.