距离辅助递归测试
Distance Assisted Recursive Testing
摘要：
在许多应用中，收集大量特征的目的是识别一些重要的特征。有时，这些特征位于具有已知距离矩阵的度量空间中，这部分地反映了它们的共同重要性模式。正确使用距离矩阵将提高识别重要特征的能力。因此，我们开发了一个新的多重检验框架命名为距离辅助递归测试（DART）。DART有两个阶段。在第一阶段，我们将距离矩阵转换为聚合树，其中每个节点表示一组特征。在第二阶段，基于聚合树建立动态节点假设，并对聚合树进行多重检验。所有拒绝都映射回特征。在适度的假设下，DART的错误发现比例以高概率收敛到1的方式收敛到期望水平。我们通过理论和仿真说明，DART具有优越的性能，在各种模型下相比，现有的方法。我们将DART应用于异基因干细胞移植研究中的临床试验，以确定其丰度将受到移植后护理影响的肠道微生物群。
英文摘要：
In many applications, a large number of features are collected with the goal to identify a few important ones. Sometimes, these features lie in a metric space with a known distance matrix, which partially reflects their co-importance pattern. Proper use of the distance matrix will boost the power of identifying important features. Hence, we develop a new multiple testing framework named the Distance Assisted Recursive Testing (DART). DART has two stages. In stage 1, we transform the distance matrix into an aggregation tree, where each node represents a set of features. In stage 2, based on the aggregation tree, we set up dynamic node hypotheses and perform multiple testing on the tree. All rejections are mapped back to the features. Under mild assumptions, the false discovery proportion of DART converges to the desired level in high probability converging to one. We illustrate by theory and simulations that DART has superior performance under various models compared to the existing methods. We applied DART to a clinical trial in the allogeneic stem cell transplantation study to identify the gut microbiota whose abundance will be impacted by the after-transplant care.
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