文章：Statistical Methods for Detecting Differentially Abundant Features in Clinical Metagenomic Samples

杂志：PLoS Comput Biol.

年份：2009

原始数据：

   数据格式如下，其中具体的值可以是任何要分析的值。原文描述是the relative abundance of specific features within each sample。可以是number of 16S rRNA clones assigned to a specific taxon，或者某条pathway上mapping reads数目。应当是每个group都会生成这样的表格，行表示特征，列表示样本！

Data normalization：

   表内的值用每个样品中的相对含量表示，where the cell in the ith row and the jthcolumn (which we shall denote fij) is the proportion of taxon i observed in individual j.

Analysis of differential abundance，丰度的差异计算：

   针对每个group，可以针对各菌计算其平均值和标准差值。

   然后计算t值检验差异情况

显著性的评估，Assessing significance:

   通过计算t值得到p-value去判断是否存在差异，但是这个依赖于分布是符合正态的！在此并不假定符合正态分布，而是通过permutation的方法去模拟，We do not make this assumption, but rather estimate the null distribution of ti non-parametrically using a permutation method。This procedure, also known as the nonparametric t-test has been shown to provide accurate estimates of significance when the underlying distributions are non-normal。

   进行permutation的操作，we randomly permute the treatment labels of the columns of the abundance matrix and recalculate the t statistics. Note that the permutation maintains that there are n1 replicates for treatment 1 and n2 replicates for treatment 2. Repeating this procedure for B trials, we obtain B sets of t statistics: t10b, …, tM0b, b = 1, …, B, where M is the number of rows in the matrix. For each row (feature), the p-value associated with the observed t statistic is calculated as the fraction of permuted tests with a t statistic greater than or equal to the observed ti:

   当样品量比较少时，This approach is inadequate for small sample sizes in which there are a limited number of possible permutations of all columns. As a heuristic, if less than 8 subjects are used in either treatment, we pool all permuted t statistics together into one null distribution and estimate p-values as:

   选择8这个界限是根据实验的经验设置的，Note that the choice of 8 for the cutoff is simply heuristic based on experiments during the implementation of our method. 当样品量比较少时，Our approach is specifically targeted at datasets comprising multiple subjects — for small data-sets approaches such as that proposed by Rodriguez-Brito et. al. might be more appropriate.

   在本软件中用的是1000次permutations, permutations和显著性阈值有一定关系，在一定情况下，permutations和p值之间是一种转换关系。Unless explicitly stated, all experiments described below used 1000 permutations. In general, the number of permutations should be chosen as a function of the significance threshold used in the experiment. Specifically, a permutation test with B permutations can only estimate p-values as low as 1/B (in our case 10−3).

p值校正，Multiple hypothesis testing correction：

   在文中没有用Bonferroni correction，而是利用FDR（false discoverty rata）。In this context, the significance of a test is measured by a q-value, an individual measure of the FDR for each test.

Given an ordered list of p-values, p(1)≤p(2)≤…≤p(m), (where m is the total number of features), and a range of values λ = 0, 0.01, 0.02, …, 0.90.Next, we fit with a cubic spline with 3 degrees of freedom, which we denote , and let .最后，q-value的计算：we estimate the q-value corresponding to each ordered p-value. First, . Then for i = m-1, m-2, …, 1。

the hypothesis test with p-value has a corresponding q-value of . Note that this method yields conservative estimates of the true q-values, i.e. . Our software provides users with the option to use either p-value or q-value thresholds, irrespective of the complexity of the data.

对于一些特殊特征的处理，Handling sparse counts：

   利用费舍尔检验，We compare the differential abundance of sparsely-sampled (rare) features using Fisher's exact test.

   核心在于针对不同的特征分为t检验和Fish exact检验，t检验通过permutation去估算分布模型，从而计算p值，计算好的p值，利用FDR去判断存在显著差异的界限值。

   此软件主要针对两组之间的比较，兼顾考虑了物种中分布广泛的菌（t permutation的分析）和分布稀少的菌（卡方检验）。