Convergence of Nonparametric Long-Memory Phase I Designs

Details Convergence of Nonparametric Long-Memory Phase I Designs Convergence of Nonparametric Long-Memory Phase I Designs

2009-08-18

arxiv.org/abs/0908.2616v2

International Journal of Biostatistics, Volume 7, Issue 1, Article 39, 2011

Statistics

Methodology

New version uploaded. Lemma added that proves convergence of running point estimates based on martingale theory. Also simulati

Scientific paper

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.

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