ABSTRACT Unconditional exact tests are increasingly used in practice for categorical data to increase the power of a study and to make the data analysis approach being consistent with the study design. In a two-arm study with a binary endpoint, p-value based on the exact unconditional Barnard test is computed by maximizing the tail probability over a nuisance parameter with a range from 0 to 1. The traditional grid search method is able to find an approximate maximum with a partition of the parameter space, but it is not accurate and this approach becomes computationally intensive for a study beyond two groups. We propose using a polynomial method to rewrite the tail probability as a polynomial. The solutions from the derivative of the polynomial contain the solution for the global maximum of the tail probability. We use an example from a double-blind randomized Phase II cancer clinical trial to illustrate the application of the proposed polynomial method to achieve an accurate p-value. We also compare the performance of the proposed method and the traditional grid search method under various conditions. We would recommend using this new polynomial method in computing accurate exact unconditional p-values.

中文翻译：

---

具有二元终点的双臂研究的准确无条件 p 值

摘要 无条件精确检验在实践中越来越多地用于分类数据，以增加研究的效力并使数据分析方法与研究设计保持一致。在具有二元终点的双臂研究中，通过最大化范围为 0 到 1 的有害参数的尾部概率来计算基于精确无条件 Barnard 检验的 p 值。传统的网格搜索方法能够找到一个使用参数空间的分区近似最大值，但它不准确，并且对于超过两个组的研究，这种方法变得计算密集。我们建议使用多项式方法将尾概率重写为多项式。多项式导数的解包含尾部概率的全局最大值的解。我们使用一个来自双盲随机 II 期癌症临床试验的例子来说明所提出的多项式方法的应用，以获得准确的 p 值。我们还比较了所提出的方法和传统网格搜索方法在各种条件下的性能。我们建议使用这种新的多项式方法来计算准确的无条件 p 值。