In this paper, we present novel methodologies that incorporate auxiliary variables for multiple hypotheses testing related to the main point of interest while effectively controlling the false discovery rate. When dealing with multiple tests concerning the primary variable of interest, researchers can use auxiliary variables to set preconditions for the significance of primary variables, thereby enhancing test efficacy. Depending on the auxiliary variable's role, we propose two approaches: one terminates testing of the primary variable if it does not meet predefined conditions, and the other adjusts the evaluation criteria based on the auxiliary variable. Employing the copula method, we elucidate the dependence between the auxiliary and primary variables by deriving their joint distribution from individual marginal distributions.Our numerical studies, compared with existing methods, demonstrate that the proposed methodologies effectively control the FDR and yield greater statistical power than previous approaches solely based on the primary variable. As an illustrative example, we apply our methods to the Set4$Δ$ mutant dataset. Our findings highlight the distinctions between our methodologies and traditional approaches, emphasising the potential advantages of our methods in introducing the auxiliary variable for selecting more genes.

翻译：本文提出了一种新颖的方法论，该方法在有效控制错误发现率的同时，结合辅助变量进行与主要关注点相关的多重假设检验。当处理与主要关注变量相关的多重检验时，研究者可利用辅助变量为原变量的显著性设定前提条件，从而提升检验效能。根据辅助变量的作用，我们提出了两种方法：一种是在主要变量不满足预设条件时终止其检验；另一种则是基于辅助变量调整评估标准。通过采用copula方法，我们从各自的边际分布推导出联合分布，从而阐明了辅助变量与主要变量之间的依赖关系。我们的数值研究，与现有方法相比，表明所提出的方法能有效控制FDR，并且比以往仅基于主要变量的方法具有更高的统计功效。作为一个示例，我们将我们的方法应用于Set4Δ突变体数据集。我们的研究结果凸显了我们的方法论与传统方法之间的区别，并强调了我们的方法在引入辅助变量以筛选更多基因方面的潜在优势。