This paper introduces a method which conditions on the number of events that occur in the control group to determine rejection regions and power for comparative Poisson trials with multiple experimental treatment arms that are each compared to one control arm. This leads to the negative multinomial as the statistical distribution used for testing. For one experimental treatment and one control with curtailed sampling, this is equivalent to Gail's (1974) approach. We provide formulas to calculate exact one‐sided overall Type I error and pointwise power for tests of treatment superiority and inferiority (vs the control). Tables of trial design parameters for combinations of one‐sided overall Type I error = 0.05, 0.01 and pointwise power = 0.90, 0.80 are provided. Curtailment approaches are presented to stop follow‐up of experimental treatment arms or to stop the study entirely once the final outcomes for each arm are known.

中文翻译：

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使用负多项分布的多个实验治疗与单个对照的比较泊松临床试验

本文介绍了一种方法，该方法以对照组中发生的事件数量为条件，以确定拒绝区域和功率，用于具有多个实验治疗臂的比较泊松试验，每个治疗臂与一个控制臂进行比较。这导致负多项式作为用于测试的统计分布。对于一种实验处理和一种减少抽样的控制，这相当于 Gail (1974) 的方法。我们提供了公式来计算精确的单边总体 I 型误差和逐点功效，以用于检验治疗优劣（与对照组相比）。提供了单边总体 I 型错误 = 0.05、0.01 和逐点功效 = 0.90、0.80 组合的试验设计参数表。