. 2020 Dec 2;6:60. doi: 10.1038/s41522-020-00160-w

Table 3.

Summary of different normalization methods.

Method	Sampling fraction estimate
ANCOM-BC	$\log ({\hat{c}}_{j}^{ANCOM - BC}) = \frac{1}{m} \sum_{i = 1}^{m} (y_{ij} - x_{j}^{T} {\hat{β}}_{i})$
CSS	${\hat{c}}_{j}^{CSS} = \frac{s_{j}^{\hat{l}} + 1}{N}$
MED	${\hat{c}}_{j}^{MED} = {median}_{i : O_{i}^{R} \neq 0} \frac{O_{ij}}{O_{i}^{R}}$
UQ	${\hat{c}}_{j}^{UQ} = {UQ}_{i : O_{ij} > 0} (\frac{O_{ij}}{O_{\cdot j}})$
TMM	$\log_{2} ({\hat{c}}_{j}^{TMM}) = \frac{\sum_{i \in G } w_{ij} M_{ij}}{\sum_{i \in G } w_{ij}}$
Elib-UQ	${\hat{c}}_{j}^{Elib - UQ} = O_{\cdot j} {\hat{c}}_{j}^{UQ}$
Elib-TMM	${\hat{c}}_{j}^{Elib - TMM} = O_{\cdot j} {\hat{c}}_{j}^{TMM}$
Wrench	${\hat{c}}_{j}^{Wrench} = \frac{1}{m} \sum_{i = 1}^{m} b_{ij} \frac{r_{ij}}{{\bar{r}}_{i \cdot}}$
TSS	${\hat{c}}_{j}^{TSS} = O_{\cdot j}$

${\hat{β}}_{i}$ is obtained from ANCOM-BC algorithm.

N = an approximately chosen normalization constant.

$s_{j}^{\hat{l}} = \sum_{i : O_{ij} \leq q_{j}^{\hat{l}}} O_{ij}$ .

$q_{j}^{\hat{l}} = {\hat{l}}^{th}$ quantile of sample j.

$O_{i}^{R} = {(\prod_{j = 1}^{n} O_{ij})}^{\frac{1}{n}}$ .

UQ(X) denotes the upper quartile of X.

$M_{ij} = \log_{2} (\frac{O_{ij}}{O_{\cdot j}}) - \log_{2} (\frac{O_{i j^{'}}}{O_{\cdot j^{'}}})$ , where $j^{'}$ is the reference sample.

$w_{ij} = \frac{O_{\cdot j} - O_{ij}}{O_{\cdot j} O_{ij}} + \frac{O_{\cdot j^{'}} - O_{i j^{'}}}{O_{\cdot j^{'}} O_{i j^{'}}}$ , where $j^{'}$ is the reference sample.

G* represents a set of taxa that were not considered as extreme data for fold-change (M values) and average intensity (A values). Refer to Robinson and Oshlack⁴³ for details.

b_ij represents the taxon-specific weight. Refer to Kumar et al.⁴⁵ for details.