Up-and-Down Designs for Selecting the Dose with Maximum Success Probability

Abstract

Assume that the probability of success is unimodal as a function of dose, such as may be the case when too much of a drug is toxic and too little is ineffective. We characterize a class of up-and-down designs, that is, treatment allocation methodologies, for identifying the dose that maximizes the patients' success probability. These designs are constructed to use accruing information to limit the number of patients that are exposed to doses with high probabilities of failure. This treatment allocation procedure is motivated by Kiefer-Wolfowitz's stochastic approximation procedure. However, we take the response to be binary and the possible treatment space to be a lattice. The procedure is shown to allocate treatments to pairs of subjects in a way that causes the treatment distribution to center around the treatment with maximum success probability. The procedure defines a nonhomogeneous random walk, so well-known theory is used to explicitly characterize the treatment distribution. As an estimator of the best dose, the mode of the empirical treatment distribution is shown to converge faster than does the last dose allocated, which is used as an estimator of the optimal dose in stochastic approximation procedures.

STEIN: A simple toxicity and efficacy interval design for seamless phase I/II clinical trials

“…Hunsberger et al developed a slope sign design, which mimics the traditional 3+3 design. Kpamegan and Flournoy optimized the up‐and‐down design for phase I/II trials under the assumption that the dose‐response curve is unimodal. However, the aforementioned phase I/II dose‐finding designs are relatively inefficient, as each dose assignment in these designs solely depends on the observed data from the most recent subject.…”

A Novel Strategy for Solving the Stochastic Point Location Problem Using a Hierarchical Searching Scheme

“…One should also observe that the proof and the concepts are almost the same as in the first proposed solution to the SPL [36]. It should also be mentioned that Kpamegan and Flournoy [19] suggest that the problem can be solved, as alluded to earlier, using stochastic optimization methods.…”

“…Rather, we have chosen to not resort to the latter schemes because applying them in modern-day research does not involve either novelty or scientific risk. It is extremely pertinent and interesting to mention that the SPL, almost exactly as it is described by us and in [19], has been precisely the model used in selecting doses in clinical practice and experiments. The problem has been referred to as "The Design of Up and Down Clinical Trials" and is cited in [19].…”

“…It is extremely pertinent and interesting to mention that the SPL, almost exactly as it is described by us and in [19], has been precisely the model used in selecting doses in clinical practice and experiments. The problem has been referred to as "The Design of Up and Down Clinical Trials" and is cited in [19]. The model is essentially the same as ours except that the solution scheme allows the algorithm to also stay at the same state at the next time instant.…”

“…Finally, as stated above, the SPL in its virgin form, has been precisely the model used in selecting doses in clinical practice and experiments to resolve the problem of designing up and down clinical trials [19].…”