Statistical report of test project test_edgeR_multi-pariwise:

pairwise analysis of conditions

with SARTools' edgeR library

Author: Upendra

Date: 2016-07-28

Table of contents

  1. Introduction
  2. Description of raw data
  3. Filtering low counts
  4. Variability within the experiment: data exploration
  5. Normalization
  6. Differential gene expression analysis
  7. R session information and parameters
  8. Bibliography

1 Introduction

The analyses reported in this document are part of the test_edgeR_multi-pariwise project. The aim is to find features that are differentially expressed between OP, LL and M. The statistical analysis process includes data normalization, graphical exploration of raw and normalized data, test for differential expression for each feature between the conditions, raw p-value adjustment and export of lists of features having a significant differential expression between the conditions. In this analysis, the cond effect will be taken into account in the statistical models.

The analysis is performed using the R software [R Core Team, 2014], Bioconductor [Gentleman, 2004] packages including edgeR [Robinson, 2010] and the SARTools package developed at PF2 - Institut Pasteur. Normalization and differential analysis are carried out according to the edgeR model and package. This report comes with additional tab-delimited text files that contain lists of differentially expressed features.

For more details about the edgeR methodology, please refer to its related publications [Robinson, 2007, 2008, 2010 and McCarthy, 2012].

2 Description of raw data

The count data files and associated biological conditions are listed in the following table.

Table 1: Data files and associated biological conditions.
label file group cond
5_OP_1 count3.txt OP 5
5_OP_2 count3.txt OP 5
5_OP_3 count3.txt OP 5
33_OP_1 count3.txt OP 33
33_OP_2 count3.txt OP 33
33_OP_3 count3.txt OP 33
5_LL_1 count3.txt LL 5
5_LL_2 count3.txt LL 5
5_LL_3 count3.txt LL 5
33_LL_1 count3.txt LL 33
33_LL_2 count3.txt LL 33
33_LL_3 count3.txt LL 33
5_M_1 count3.txt M 5
5_M_2 count3.txt M 5
5_M_3 count3.txt M 5
33_M_1 count3.txt M 33
33_M_2 count3.txt M 33
33_M_3 count3.txt M 33

After loading the data we first have a look at the raw data table itself. The data table contains one row per annotated feature and one column per sequenced sample. Row names of this table are feature IDs (unique identifiers). The table contains raw count values representing the number of reads that map onto the features. For this project, there are 8000 features in the count data table.

Table 2: Partial view of the count data table.
5_OP_1 5_OP_2 5_OP_3 33_OP_1 33_OP_2 33_OP_3 5_LL_1 5_LL_2 5_LL_3 33_LL_1 33_LL_2 33_LL_3 5_M_1 5_M_2 5_M_3 33_M_1 33_M_2 33_M_3
oystercontig_1 8 54 10 17 3 1 19 47 42 44 6 2 229 47 4 301 231 11
oystercontig_10 4 0 1 8 5 4 4 2 0 9 1 3 3 6 0 2 4 9
oystercontig_100 0 18 0 5 0 1 0 3 8 11 0 0 0 1 0 1 0 0
oystercontig_1000 0 12 1 13 1 3 17 17 32 18 8 0 2 9 0 6 24 1
oystercontig_1001 15 178 39 424 25 14 168 246 305 220 40 13 79 85 1 268 285 20
oystercontig_1002 3 0 0 0 0 0 1 1 5 0 0 1 0 0 1 0 3 0

Looking at the summary of the count table provides a basic description of these raw counts (min and max values, median, etc).

Table 3: Summary of the raw counts.
5_OP_1 5_OP_2 5_OP_3 33_OP_1 33_OP_2 33_OP_3 5_LL_1 5_LL_2 5_LL_3 33_LL_1 33_LL_2 33_LL_3 5_M_1 5_M_2 5_M_3 33_M_1 33_M_2 33_M_3
Min. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1st Qu. 1 3 1 4 1 1 2 6 5 6 0 1 3 5 0 4 7 1
Median 4 24 3 29 4 4 14 30 25 32 2 4 19 31 1 23 39 5
Mean 40 254 25 218 22 24 193 240 249 233 17 25 228 243 9 202 256 28
3rd Qu. 17 104 11 114 14 13 62 109 98 119 8 15 85 112 4 93 143 16
Max. 35277 231541 16026 161486 15647 20671 227239 214852 207549 274029 12538 20387 125872 189081 8332 157386 262174 21835

Figure 1 shows the total number of mapped reads for each sample. Reads that map on multiple locations on the transcriptome are counted more than once, as far as they are mapped on less than 50 different loci. We expect total read counts to be similar within conditions, they may be different across conditions. Total counts sometimes vary widely between replicates. This may happen for several reasons, including:

Barplot total counts
Figure 1: Number of mapped reads per sample. Colors refer to the biological condition of the sample.

Figure 2 shows the proportion of features with no read count in each sample. We expect this proportion to be similar within conditions. Features with null read counts in the 18 samples will not be taken into account for the analysis with edgeR. Here, 44 features (0.55%) are in this situation (dashed line).

Barplot null counts
Figure 2: Proportion of features with null read counts in each sample.

Figure 3 shows the distribution of read counts for each sample. For sake of readability, \(\text{log}_2(\text{counts}+1)\) are used instead of raw counts. Again we expect replicates to have similar distributions. In addition, this figure shows if read counts are preferably low, medium or high. This depends on the organisms as well as the biological conditions under consideration.

Estimated densities of raw counts
Figure 3: Density distribution of read counts.

It may happen that one or a few features capture a high proportion of reads (up to 20% or more). This phenomenon should not influence the normalization process. The edgeR normalization has proved to be robust to this situation [Dillies, 2012]. Anyway, we expect these high count features to be the same across replicates. They are not necessarily the same across conditions. Figure 4 illustrate the possible presence of such high count features in the data set.

Most represented sequences
Figure 4: Percentage of reads associated with the sequence having the highest count (provided in each box on the graph) for each sample.

We may wish to assess the similarity between samples across conditions. A pairwise scatter plot is produced (figure 5) to show how replicates and samples from different biological conditions are similar or different (\(\text{log}_2(\text{counts}+1)\) are used instead of raw count values). Moreover, as the Pearson correlation has been shown not to be relevant to measure the similarity between replicates, the SERE statistic has been proposed as a similarity index between RNA-Seq samples [Schulze, 2012]. It measures whether the variability between samples is random Poisson variability or higher. Pairwise SERE values are printed in the lower triangle of the pairwise scatter plot. The value of the SERE statistic is:

Pairwise scatter plot
Figure 5: Pairwise comparison of samples.

3 Filtering low counts

edgeR suggests to filter features with null or low counts because they do not supply much information. For this project, 199 features (2.49%) have been removed from the analysis because they did not satisfy the following condition: having at least 1 counts-per-million in at least 6 samples.

4 Variability within the experiment: data exploration

The main variability within the experiment is expected to come from biological differences between the samples. This can be checked in three ways. The first one is to perform a hierarchical clustering of the whole sample set. This is performed after a transformation of the count data as moderated log-counts-per-million. Figure 6 shows the dendrogram obtained from CPM data. An euclidean distance is computed between samples, and the dendrogram is built upon the Ward criterion. We expect this dendrogram to group replicates and separate biological conditions.

Clustering
Figure 6: Sample clustering based on normalized data.

The second method of visaulizing the experiment variability is to look at the heatmaps of the two conditions as show on figure 7. On this figure the x-axis represents the two conditions (along with the replicates) and the y-axis represent the top 20 genes with the top variance over all samples.

Heatmap
Figure 7: Heatmap based on normalized data.

Another way of visualizing the experiment variability is to look at the first two dimensions of a multidimensional scaling plot, as shown on figure 8. On this figure, the first dimension is expected to separate samples from the different biological conditions, meaning that the biological variability is the main source of variance in the data.

Multidimensional scaling plot
Figure 8: Multidimensional scaling plot of the samples.

For the statistical analysis, we need to take into account the effect of the cond parameter. Statistical models and tests will thus be adjusted on it.

5 Normalization

Normalization aims at correcting systematic technical biases in the data, in order to make read counts comparable across samples. The normalization proposed by edgeR is called Trimmed Mean of M-values (TMM) but it is also possible to use the RLE (DESeq) or upperquartile normalizations. It relies on the hypothesis that most features are not differentially expressed.

edgeR computes a factor for each sample. These normalization factors apply to the total number of counts and cannot be used to normalize read counts in a direct manner. Indeed, normalization factors are used to normalize total counts. These in turn are used to normalize read counts according to a total count normalization: if \(N_j\) is the total number of reads of the sample \(j\) and \(f_j\) its normalization factor, \(N'_j=f_j \times N_j\) is the normalized total number of reads. Then, let \(s_j=N'_j/\bar{N'}\) with \(\bar{N'}\) the mean of the \(N'_j\) s. Finally, the normalized counts of the sample \(j\) are defined as \(x'_{ij}=x_{ij}/s_j\) where \(i\) is the gene index.

Table 5: Normalization factors.
5_OP_1 5_OP_2 5_OP_3 33_OP_1 33_OP_2 33_OP_3 5_LL_1 5_LL_2 5_LL_3 33_LL_1 33_LL_2 33_LL_3 5_M_1 5_M_2 5_M_3 33_M_1 33_M_2 33_M_3
TMM normalization factors 1.00 0.77 1.03 1.01 1.44 1.26 0.65 0.90 0.77 1.02 1.20 1.31 0.71 0.91 1.08 0.92 1.10 1.34

Boxplots are often used to assess the quality of the normalization process, as they show how distributions are globally affected during this process. We expect normalization to stabilize distributions across samples. Figure 9 shows boxplots of raw (left) and normalized (right) data respectively.

Boxplots of raw and normalized counts
Figure 9: Boxplots of raw (left) and normalized (right) read counts.

6 Differential analysis

6.1 Modelization

edgeR aims at fitting one linear model per feature. For this project, the design used is ~ cond + group and the goal is to estimate the models' coefficients which can be interpreted as \(\log_2(\texttt{FC})\). These coefficients will then be tested to get p-values and adjusted p-values.

6.2 Dispersions estimation

The edgeR model assumes that the count data follow a negative binomial distribution which is a robust alternative to the Poisson law when data are over-dispersed (the variance is higher than the mean). The first step of the statistical procedure is to estimate the dispersion of the data.

Dispersions estimations
Figure 10: Dispersion estimates.

Figure 10 shows the result of the dispersion estimation step. The x- and y-axes represent the mean count value and the estimated dispersion respectively. Black dots represent empirical dispersion estimates for each feature (from the observed count values). The blue curve shows the relationship between the means of the counts and the dispersions modeled with splines. The red segment represents the common dispersion.

6.3 Statistical test for differential gene expression

Once the dispersion estimation and the model fitting have been done, edgeR can perform the statistical testing. Figure 11 shows the distributions of raw p-values computed by the statistical test for the comparison(s) done. This distribution is expected to be a mixture of a uniform distribution on \([0,1]\) and a peak around 0 corresponding to the differentially expressed features.

Histogram(s) of raw p-values
Figure 11: Distribution(s) of raw p-values.

6.4 Final results

A p-value adjustment is performed to take into account multiple testing and control the false positive rate to a chosen level \(\alpha\). For this analysis, a BH p-value adjustment was performed [Benjamini, 1995 and 2001] and the level of controlled false positive rate was set to 0.5.

Figure 12 represents the MA-plot of the data for the comparisons done, where differentially expressed features are highlighted in red. A MA-plot represents the log ratio of differential expression as a function of the mean intensity for each feature. Triangles correspond to features having a too low/high \(\log_2(\text{FC})\) to be displayed on the plot.

MA-plot(s)
Figure 12: MA-plot(s) of each comparison. Red dots represent significantly differentially expressed features.

Figure 13 shows the volcano plots for the comparisons performed and differentially expressed features are still highlighted in red. A volcano plot represents the log of the adjusted P value as a function of the log ratio of differential expression.

Volcano plot(s)
Figure 13: Volcano plot(s) of each comparison. Red dots represent significantly differentially expressed features.

Full results as well as lists of differentially expressed features are provided in the following text files which can be easily read in a spreadsheet. For each comparison:

These files contain the following columns:

7 R session information and parameters

The versions of the R software and Bioconductor packages used for this analysis are listed below. It is important to save them if one wants to re-perform the analysis in the same conditions.

Parameter values used for this analysis are:

8 Bibliography