Quantitative comparison of microbial composition from different populations is a fundamental task in various microbiome studies. We consider two-sample testing for microbial compositional data by leveraging the phylogenetic tree information. Motivated by existing phylogenetic distances, we take a minimun-cost flow perspective to study such testing problems. We first show that multivariate analysis of variance with permutation using phylogenetic distances, one of the most commonly used methods in practice, is essentially a sum-of-squares type of tests and has better power for dense alternatives. However, empirical evidence from real data sets suggests that the phylogenetic microbial composition difference between two populations is usually sparse. Motivated by this observation, we propose a new maximum type test, Detector of Active Flow on a Tree, and investigate its properties. We show that the proposed method is particularly powerful against sparse phylogenetic composition difference and enjoys certain optimality. The practical merit of the proposed method is demonstrated by simulation studies and an application to a human intestinal biopsy microbiome data set on patients with ulcerative colitis. Hongzhe Li Department of Biostatistics and Statistics University of Pennsylvania

中文翻译：

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系统发育组成的假设检验：最低成本流动视角

来自不同种群的微生物组成的定量比较是各种微生物组研究中的一项基本任务。我们考虑通过利用系统发育树信息对微生物组成数据进行两样本测试。受现有系统发育距离的启发，我们采用最小成本流的视角来研究此类测试问题。我们首先表明，使用系统发育距离的多变量方差分析是实践中最常用的方法之一，它本质上是一种平方和类型的测试，并且对于密集的替代方案具有更好的功效。然而，来自真实数据集的经验证据表明，两个种群之间的系统发育微生物组成差异通常很少。受此观察的启发，我们提出了一种新的最大类型测试，即树上主动流检测器，并研究其性质。我们表明，所提出的方法对稀疏的系统发育组成差异特别有效，并且具有一定的最优性。通过模拟研究和对溃疡性结肠炎患者的人体肠道活检微生物组数据集的应用，证明了所提出方法的实际优点。李洪哲 宾夕法尼亚大学生物统计与统计系