Ivanova Anastasia, Montazer-Haghighi Aliakbar, Mohanty Sri Gopal, Durham Stephen D
Department of Biostatistics, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420, USA.
Stat Med. 2003 Jan 15;22(1):69-82. doi: 10.1002/sim.1336.
We consider several designs from the family of up-and-down rules for the sequential allocation of dose levels to subjects in a dose-response study. We show that an up-and-down design can be improved by using more information than the most recent response. For example, the k-in-a-row rule uses up to the k most recent responses. We introduce a new design, the Narayana rule, which uses a local estimate of the probability of toxicity calculated from all previous responses. For the Narayana rule, as the sample size gets large, the probability of assignment goes to zero for dose levels not among the two (or three) closest to the target. Different estimators of the target dose are compared. We find that the isotonic regression estimator is superior to other estimators for small to moderate sample sizes.
在剂量反应研究中，我们考虑了几种来自上下规则族的设计，用于将剂量水平依次分配给受试者。我们表明，通过使用比最近一次反应更多的信息，可以改进上下设计。例如，连续k次规则使用多达最近的k次反应。我们引入了一种新的设计，即纳拉亚纳规则，它使用根据所有先前反应计算出的毒性概率的局部估计。对于纳拉亚纳规则，随着样本量变大，对于不在最接近目标的两个（或三个）剂量水平之中的剂量水平，分配概率趋近于零。我们比较了目标剂量的不同估计量。我们发现，对于中小样本量，保序回归估计量优于其他估计量。
