  We propose a rule-based statistical design for combination dose-finding
trials with two agents. The Ci3+3 design is an extension of the i3+3 design
with simple decision rules comparing the observed toxicity rates and
equivalence intervals that define the maximum tolerated dose combination. Ci3+3
consists of two stages to allow fast and efficient exploration of the
dose-combination space. Statistical inference is restricted to a beta-binomial
model for dose evaluation, and the entire design is built upon a set of fixed
rules. We show via simulation studies that the Ci3+3 design exhibits similar
and comparable operating characteristics to more complex designs utilizing
model-based inferences. We believe that the Ci3+3 design may provide an
alternative choice to help simplify the design and conduct of combination
dose-finding trials in practice.
