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Distributions associated with simultaneous multiple hypothesis testing
Journal of Statistical Distributions and Applications Pub Date : 2020-10-19 , DOI: 10.1186/s40488-020-00109-6
Chang Yu , Daniel Zelterman

We develop the distribution for the number of hypotheses found to be statistically significant using the rule from Simes (Biometrika 73: 751–754, 1986) for controlling the family-wise error rate (FWER). We find the distribution of the number of statistically significant p-values under the null hypothesis and show this follows a normal distribution under the alternative. We propose a parametric distribution ΨI(·) to model the marginal distribution of p-values sampled from a mixture of null uniform and non-uniform distributions under different alternative hypotheses. The ΨI distribution is useful when there are many different alternative hypotheses and these are not individually well understood. We fit ΨI to data from three cancer studies and use it to illustrate the distribution of the number of notable hypotheses observed in these examples. We model dependence in sampled p-values using a latent variable. These methods can be combined to illustrate a power analysis in planning a larger study on the basis of a smaller pilot experiment.

中文翻译:

与同时进行的多个假设检验相关的分布

我们使用Simes(Biometrika 73:751–754,1986)的规则来控制家庭错误率(FWER),从而开发出具有统计学意义的假设数量分布。我们在原假设下找到了统计上显着的p值数量的分布,并显示了在替代条件下这遵循正态分布。我们提出了一个参数分布ΨI(·)来建模在不同的替代假设下,从零个均匀分布和非均匀分布的混合物中采样的p值的边际分布。当存在许多不同的假设并且这些假设没有被很好地理解时,I分布很有用。我们将threeI拟合为来自三项癌症研究的数据,并用它来说明在这些例子中观察到的著名假设数量的分布。我们使用潜在变量对采样p值中的依赖关系进行建模。可以将这些方法组合起来,以在较小的试验实验的基础上规划较大的研究中说明功效分析。
更新日期:2020-10-21
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