非参数长记忆阶段I设计的收敛性
Convergence of Nonparametric Long-Memory Phase I Designs
摘要：
我们研究了非参数剂量发现设计，使用毒性估计的基础上，所有可用的数据，在每个剂量分配的决定。我们证明，这样的设计家族，这里称为“间隔设计”，收敛几乎肯定的最大耐受剂量（MTD），如果MTD是唯一的剂量水平，其毒性率落在预定的间隔内所需的目标率。另一个非参数族，称为“点设计”，具有不收敛的正概率。在一项数值敏感性研究中，随机生成了剂量-毒性情景的各种样本。在该示例中，“区间设计”收敛条件的满足频率远远高于单参数设计收敛条件（Shen-O 'Quigley条件），这表明区间设计条件的限制性较小。这些理论和数值结果的影响，小样本的设计行为，并为今后的研究，进行了讨论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
