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

TL;DR

This paper applies approximate dynamic programming to optimize Phase I cancer trial designs, balancing treatment safety and learning efficiency, resulting in a practical, convex combination approach validated through simulations.

Contribution

It introduces a novel Bayesian optimal design framework combining treatment and learning strategies using approximate dynamic programming.

Findings

The proposed design outperforms traditional methods in simulations.

It offers a flexible approach that can include cautious dose escalation.

The design is intuitive and suitable for clinical implementation.

Abstract

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.