Convergence of Nonparametric Long-Memory Phase I Designs

TL;DR

This paper proves that the interval design in nonparametric dose-finding converges almost surely to the MTD under certain conditions, and shows it is more reliable than point design in various scenarios.

Contribution

It establishes convergence properties of the interval design and compares its robustness to the point design in dose-finding studies.

Findings

Interval design converges almost surely to the MTD under specified conditions.

Interval design conditions are less restrictive than Shen-O'Quigley conditions.

Numerical studies show higher likelihood of convergence for interval design.

Abstract

We examine nonparametric dose-finding designs that use toxicity estimates based on all available data at each dose allocation decision. We prove that one such design family, called here "interval design", converges almost surely to the maximum tolerated dose (MTD), if the MTD is the only dose level whose toxicity rate falls within the pre-specified interval around the desired target rate. Another nonparametric family, called "point design", has a positive probability of not converging. In a numerical sensitivity study, a diverse sample of dose-toxicity scenarios was randomly generated. On this sample, the "interval design" convergence conditions are met far more often than the conditions for one-parameter design convergence (the Shen-O'Quigley conditions), suggesting that the interval-design conditions are less restrictive. Implications of these theoretical and numerical results for small-sample behavior of the designs, and for future research, are discussed.