Statistical Science

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

Jay Bartroff and Tze Leung Lai

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Optimal design of a Phase I cancer trial can be formulated as a stochastic optimization problem. By making use of recent advances in approximate dynamic programming to tackle the problem, we develop an approximation of the Bayesian optimal 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, thus directly addressing the treatment versus experimentation dilemma inherent in Phase I trials and providing a simple and intuitive design for clinical use. Computational details are given and the proposed design is compared to existing designs in a simulation study. The design can also be readily modified to include a first stage that cautiously escalates doses similarly to traditional nonparametric step-up/down schemes, while validating the Bayesian parametric model for the efficient model-based design in the second stage.

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Statist. Sci. Volume 25, Number 2 (2010), 245-257.

First available in Project Euclid: 19 November 2010

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Dynamic programming maximum tolerated dose Monte Carlo rollout stochastic optimization


Bartroff, Jay; Lai, Tze Leung. Approximate Dynamic Programming and Its Applications to the Design of Phase I Cancer Trials. Statist. Sci. 25 (2010), no. 2, 245--257. doi:10.1214/10-STS317.

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