  The keyboard design is a novel phase I dose-finding method that is simple and
has good operating characteristics. This paper studies theoretical properties
of the keyboard design, including the optimality of its decision rules,
coherence in dose transition, and convergence to the target dose. Establishing
these theoretical properties explains the mechanism of the design and provides
assurance to practitioners regarding the behavior of the keyboard design. We
further extend the keyboard design to dual-agent dose-finding trials, which
inherit the same statistical properties and simplicity as the single-agent
keyboard design. Extensive simulations are conducted to evaluate the
performance of the proposed keyboard drug-combination design using a novel,
random two-dimensional dose--toxicity scenario generating algorithm. The
simulation results confirm the desirable and competitive operating
characteristics of the keyboard design as established by the theoretical study.
An R Shiny application is developed to facilitate implementing the keyboard
combination design in practice.
