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Statistica Sinica 32 (2022), 1983-2005

SEMIPARAMETRIC DOSE FINDING METHODS FOR
PARTIALLY ORDERED DRUG COMBINATIONS

Matthieu Clertant, Nolan A. Wages and John O'Quigley

Université Sorbonne Paris Nord, University of Virginia
and University College London

Abstract: We investigate a statistical framework for Phase I clinical trials that test the safety of two or more agents in combination. For such studies, the traditional assumption of a simple monotonic relation between the dose and the probability of an adverse event no longer holds. Nonetheless, the dose toxicity (adverse event) relationship does obey an assumption of partial ordering in that there will be pairs of combinations for which the ordering of the toxicity probabilities is known. Some authors have considered how to best estimate the maximum tolerated dose (a dose providing a rate of toxicity as close as possible to some target rate) in this setting. A related and equally interesting problem is to partition the two-dimensional dose space into two sub-regions: doses with probabilities of toxicity lower and greater than the target. We carry out a detailed investigation of this problem, using the recently presented semiparametric dose finding method as the theoretical framework. This results in a number of proposals, one of which can be viewed as an extension of the product of independent beta probabilities escalation (PIPE) method. We derive useful asymptotic properties, which also apply to the PIPE method when it is seen as a special case of the more general method given here. Simulation studies provide added confidence concerning the good behavior of the operating characteristics.

Key words and phrases: Bayesian method, dose-finding design, partial ordering, phase I clinical trials, semiparametric method.

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