Dose Response with Competing Failure Modes

Directed Walk Designs for Dose Response Problems with Competing Failure Modes

Janis Hardwick
EECS Department, University of Michigan

Mary C. Meyer
Statistics Department, University of Georgia

Quentin F. Stout
EECS Department, University of Michigan

Abstract: We examine adaptive sampling designs for the problem of determining the optimal therapeutic dose for subjects in a clinical trial, especially those trials known as phase I/II.

Suppose subjects arrive sequentially for treatment and may be assigned to any of D discrete dose levels. We assume two opposing failure modes, each of which is a function of treatment dose. A subject can fail due to nonresponse to treatment or due to a toxic reaction. Successful subjects will have both a positive response and no toxic side effects. Subject responses are binary with regard to both failure modes and the toxicity and efficacy response curves are assumed to be nondecreasing in dose level. The product of the non-toxicity and efficacy curves defines the ``success'' curve, which is the function we seek to maximize.

We are interested in sampling rules that perform well along several criteria, including the ethical criterion that, as often as possible, experimental subjects be treated at or close to the mode in question. Statistically, we wish to identify the optimum dose with high probability at the close of the experiment. We also wish to estimate subject response at this dose and its neighbors.

In this paper, we compare a previous random walk sampling rule (Durham, Flournoy and Li, 1998) with directed walk designs that utilize curve estimation. Parametric, nonparametric, Bayesian and frequentist designs are all evaluated, and it is found that the smoothed shape constrained approaches perform the best. When the success curve is unimodal, the proposed sampling designs have the property that the mode of the sampling distribution of the sequence of dose assignments converges to the mode of the underlying function.

Keywords: Bayesian, phase I/II clinical trial, convex-concave, CRM, efficiency, experimental design, isotonic, nonparametric, controlled clinical trial, random walk, sequential, unimodal, response adaptive sampling.

Complete paper. This appears in Biometrics 59 (2003), pp. 229-236.

Related Work: This paper assumes that one can observe both efficacy and toxicity outcomes for all patients. We have also developed efficient designs to locate the mode when one only knows whether or not the outcome was a success (non-toxic and efficacious).

More generally, here is an explanation of response adaptive sampling, and here are our relevant papers.