RESUMO
Nowadays, in oncology drug development, when an experimental treatment shows a promising anti-tumor effect in Phase I efficacy expansion, a Phase III pivotal trial may be launched directly. To mitigate the risk of skipping the traditional randomized Phase II proof of concept (POC) study, the 2-in-1 design was proposed by Chen et al. (2018). This design has gained great research and application interest since its publication and been extended in many ways. The original 2-in-1 design controls family-wise type I error rate (FWER) for one hypothesis in Phase II part and one hypothesis in Phase III part. However, in practice, for a stand-alone Phase III study usually there are multiple hypotheses with group sequential interim analyses and the multiplicity is controlled by the graphical approach. It is desirable that these features of the Phase III design are retained when 2-in-1 design is considered. The multiplicity control for a 2-in-1 design with multiple hypotheses in Phase III has been addressed mainly by the Bonferroni approach in the literature. For the more powerful graphical approach, while Jin and Zhang (2021) discussed the FWER control for a special 2-in-1 design, in which Phase II and Phase III have exactly the same hypotheses, the FWER control for a more common 2-in-1 design (i.e., one hypothesis in Phase II and multiple hypotheses in Phase III) is yet investigated. This paper provides the analytical conditions under which FWER is controlled with the graphical approach in such a 2-in-1 design. It also provides the numeric explorations of FWER control for such design with group sequential interim analyses in Phase III, as a direct Phase III design normally would have. As a result, our work helps lower the hurdle of the application of the 2-in-1 design and pave the way for its wider application.