  The Project Optimus initiative by the FDA's Oncology Center of Excellence is
widely viewed as a groundbreaking effort to change the $\textit{status quo}$ of
conventional dose-finding strategies in oncology. Unlike in other therapeutic
areas where multiple doses are evaluated thoroughly in dose ranging studies,
early-phase oncology dose-finding studies are characterized by the practice of
identifying a single dose, such as the maximum tolerated dose (MTD) or the
recommended phase 2 dose (RP2D). Following the spirit of Project Optimus, we
propose an Multi-Arm Two-Stage (MATS) design for proof-of-concept (PoC) and
dose optimization that allows the evaluation of two selected doses from a
dose-escalation trial. The design assess the higher dose first across multiple
indications in the first stage, and adaptively enters the second stage for an
indication if the higher dose exhibits promising anti-tumor activities. In the
second stage, a randomized comparison between the higher and lower doses is
conducted to achieve proof-of-concept (PoC) and dose optimization. A Bayesian
hierarchical model governs the statistical inference and decision making by
borrowing information across doses, indications, and stages. Our simulation
studies show that the proposed MATS design yield desirable performance. An R
Shiny application has been developed and made available at
https://matsdesign.shinyapps.io/mats/.
