单指标调制多次测试
Single-index modulated multiple testing
摘要：
在大规模多重检验中，假设往往伴随着一定的先验信息。在本文中，我们提出了一个单指数调制（SIM）的多重检验程序，它保持控制的错误发现率，同时将先验信息，通过假设的二元$p$ -值，$(p_1,p_2)$，为每个假设，其中$p_1$是一个初步的$p$ -值从先验信息和$p_2$是主要的$p$ -值的最终分析的可用性。为了找到二元$p$ -值的最佳拒绝区域，我们提出了一个基于真空和非空情况下$(p_1,p_2)$的概率密度函数之比的准则。二元正态设置中的该标准进一步促使我们将二元$p$值投影到单指标$p(θ)$，用于广泛的方向$θ$。通过参数和非参数方法估计$p(θ)$的真零分布，导致两个程序估计和控制错误发现率。为了得到最优投影方向$θ$，我们提出了一种新的方法，基于功率比较，这是进一步证明了在一些温和的条件下是一致的。仿真结果表明，SIM多重检测过程在控制错误发现率的同时，显著提高了检测能力。将说明对真实数据集的分析。
英文摘要：
In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this paper, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate $p$-value, $(p_1,p_2)$, for each hypothesis, where $p_1$ is a preliminary $p$-value from prior information and $p_2$ is the primary $p$-value for the ultimate analysis. To find the optimal rejection region for the bivariate $p$-value, we propose a criteria based on the ratio of probability density functions of $(p_1,p_2)$ under the true null and nonnull. This criteria in the bivariate normal setting further motivates us to project the bivariate $p$-value to a single-index, $p(θ)$, for a wide range of directions $θ$. The true null distribution of $p(θ)$ is estimated via parametric and nonparametric approaches, leading to two procedures for estimating and controlling the false discovery rate. To derive the optimal projection direction $θ$, we propose a new approach based on power comparison, which is further shown to be consistent under some mild conditions. Simulation evaluations indicate that the SIM multiple testing procedure improves the detection power significantly while controlling the false discovery rate. Analysis of a real dataset will be illustrated.
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