Performance Evaluation of Normalization Approaches for Metagenomic Compositional Data on Differential Abundance Analysis

Abstract

Background: In recent years, metagenomics, as a combination of research techniques without the process of cultivation, has become more and more popular in studying the genomic/genetic variation of microbes in environmental or clinical samples. Though generated from similar sequencing technologies, there is increasing evidence that metagenomic sequence data may not be treated as another variant of RNA-Seq count data, especially due to its compositional characteristics. While it is often of primary interest to compare taxonomic or functional profiles of microbial communities between conditions, normalization for library size is usually an inevitable step prior to a typical differential abundance analysis. Some methods have been proposed for such normalization. But the existing performance evaluation of normalization methods for metagenomic sequence data does not adequately consider the compositional characteristics.

Result: The normalization methods assessed in this chapter include Total Sum Scaling (TSS), Relative Log Expression (RLE), Trimmed Mean of M-value (TMM), Cumulative Sum Scaling (CSS), and Rarefying (RFY). In addition to compositional proportions, simulated data were generated with consideration of overdispersion, zero inflation, and under-sampling issue. The impact of normalization on subsequent differential abundance analysis was further studied.

Conclusion: Selection of a normalization method for metagenomic compositional data should be made on a case-by-case basis. Simulation using the parameters learned from the experimental data may be carried out to assist the selection.

Appendix

1.1 Supplementary Data Distribution

Negative Binomial Distribution. A NB distribution is defined as,

$$ \vspace*{-3pt}P\left(X=x\right)=\frac{\Gamma \left(x+r\right)}{\Gamma \left(\mathrm{r}\right)\mathrm{x}!}{p}^r{\left(1-p\right)}^x,\vspace*{-3pt} $$

where r and p are two parameters, and r is called size parameter. The mean of the NB distribution is,

$$ \vspace*{-3pt}\mu =\frac{r\left(1-p\right)}{p},\vspace*{-3pt} $$

and the variance is,

$$ \vspace*{-3pt}V=\frac{r\left(1-p\right)}{p^2}=\mu +\frac{1}{r}{\mu}^2.\vspace*{-3pt} $$

Thus, r indicates the level of overdispersion in the counts.

1.2 Supplementary Illustration of TMM and RLE with Compositional Dataset

For gene expression studies, there is a widely used assumption that the majority of genes do not express differentially between conditions. Many of RNA-Seq normalization methods were developed based on this assumption, including TMM and RLE. The “non-differential” in the assumption is implemented as non-differential absolute abundance after normalization. Subsequent differential analysis is also to compare the normalized counts between conditions, instead of comparing the relative abundances as it is for compositional data.

Focusing on the essence of a normalization procedure, the hypothetical datasets are made of the expectations of counts. For TMM approach, the logarithm function and the weighted sum are not applied since those are designed for reducing the effect of count variation. In Fig. 16.5, the relative abundance ratio, compared to the first sample, is first calculated from the raw counts, i.e., $\frac{y_{ij}/{\sum}_i{y}_{ij}}{y_{i1}/{\sum}_i{y}_{i1}}$. The trimmed mean of the ratios for each sample, after trimming the largest and smallest values, is used as the scale factor. The true scale factor is 2.6 (390/150), but the output from TMM is 1.73. Figure 16.5 shows a very likely situation for metagenomic compositional data, in which the relative abundances vary largely between conditions. TMM may not work well for such data since it merely relies on the assumption that after normalization most of features should share the same absolute abundance.

Fig. 16.5

TMM normalization on a hypothetical dataset

For RLE normalization, the geometric mean of the counts to each feature from all the samples is first calculated, see Fig. 16.6. Next, the ratio of a raw count over the mean count for the same feature is computed. The scale factor for a sample is obtained as the median of the ratios for the sample. For this hypothetic dataset, RLE approach does not suggest any normalization adjustment since all the scale factors equal to 1; however, the true library sizes are very different (e.g., 210 vs. 310). In Fig. 16.6, it is clear that the scale factor is determined by the absolute count of Feature 2, 3, 4, or 5, instead of the relative abundance of one of those features. A subsequently comparative analysis would reach the conclusion that there is no differential abundance for Feature 2, 3, 4, or 5 between the conditions. However, the relative abundances of the features have altered, for Feature 4 it is 14% and 10% under the two conditions, respectively.

Fig. 16.6

RLE normalization steps on a hypothetical dataset

1.3 Supplementary Example

Mouse stool metagenomic data. Fresh or frozen adult human fecal microbial communities were transplanted into guts of germ-free C57BL/6J mice. Here, germ-free environment is referred to as mice gut that does not previously expose to microbes. Following the transplanting, 12 recipient mice were fed with a standard low-fat, plant polysaccharide-rich diet for 4 weeks; after that, six mice were switched to take high-fat/high-sugar Western diet for another 6 weeks. Amplification and pyrosequencing of V2 region of 16S rRNA genes were performed periodically to record the changes of microbial community structure of fecal samples of the mice (Turnbaugh et al. 2009). There are 85 samples under condition one (associated to low-fat diet fed mice), and 54 samples under condition two (associated to Western diet fed mice). The bioinformatic tool RDP (Wang et al. 2007) was used to generate the count data, which is featured at species level. Together, there are 52 genera shown under both conditions, and the data is considered to represent low complex metagenomic data. Figure 16.7 demonstrates that RLE and RFY should not be recommended for normalization of the metagenomic data.

Fig. 16.7

Boxplots of coefficients of variation of counts in the raw data, and the normalized data for the mouse stool metagenomic data