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Optimal design of a Phase I cancer trial can be formulated as a stochasticoptimization problem. By making use of recent advances in approximate dynamicprogramming to tackle the problem, we develop an approximation of the Bayesianoptimal design. The resulting design is a convex combination of a "treatment"design, such as Babb et al.'s (1998) escalation with overdose control, and a"learning" design, such as Haines et al.'s (2003) $c$-optimal design, thusdirectly addressing the treatment versus experimentation dilemma inherent inPhase I trials and providing a simple and intuitive design for clinical use.Computational details are given and the proposed design is compared to existingdesigns in a simulation study. The design can also be readily modified toinclude a first stage that cautiously escalates doses similarly to traditionalnonparametric step-up/down schemes, while validating the Bayesian parametricmodel for the efficient model-based design in the second stage.

Approximate Dynamic Programming and Its Applications to the Design of Phase I Cancer Trials