A comparison of methods for differential expression analysis of RNAseq data
 Charlotte Soneson^{1}Email author and
 Mauro Delorenzi^{1, 2}
https://doi.org/10.1186/147121051491
© Soneson and Delorenzi; licensee BioMed Central Ltd. 2013
Received: 2 October 2012
Accepted: 1 March 2013
Published: 9 March 2013
Abstract
Background
Finding genes that are differentially expressed between conditions is an integral part of understanding the molecular basis of phenotypic variation. In the past decades, DNA microarrays have been used extensively to quantify the abundance of mRNA corresponding to different genes, and more recently highthroughput sequencing of cDNA (RNAseq) has emerged as a powerful competitor. As the cost of sequencing decreases, it is conceivable that the use of RNAseq for differential expression analysis will increase rapidly. To exploit the possibilities and address the challenges posed by this relatively new type of data, a number of software packages have been developed especially for differential expression analysis of RNAseq data.
Results
We conducted an extensive comparison of eleven methods for differential expression analysis of RNAseq data. All methods are freely available within the R framework and take as input a matrix of counts, i.e. the number of reads mapping to each genomic feature of interest in each of a number of samples. We evaluate the methods based on both simulated data and real RNAseq data.
Conclusions
Very small sample sizes, which are still common in RNAseq experiments, impose problems for all evaluated methods and any results obtained under such conditions should be interpreted with caution. For larger sample sizes, the methods combining a variancestabilizing transformation with the ‘limma’ method for differential expression analysis perform well under many different conditions, as does the nonparametric SAMseq method.
Keywords
Background
Transcriptome analysis is an important tool for characterization and understanding of the molecular basis of phenotypic variation in biology, including diseases. During the past decades microarrays have been the most important and widely used approach for such analyses, but recently highthroughput sequencing of cDNA (RNAseq) has emerged as a powerful alternative [1] and it has already found numerous applications [2]. RNAseq uses nextgeneration sequencing (NGS) methods to sequence cDNA that has been derived from an RNA sample, and hence produces millions of short reads. These reads are then typically mapped to a reference genome and the number of reads mapping within a genomic feature of interest (such as a gene or an exon) is used as a measure of the abundance of the feature in the analyzed sample [3].
Arguably the most common use of transcriptome profiling is in the search for differentially expressed (DE) genes, that is, genes that show differences in expression level between conditions or in other ways are associated with given predictors or responses. RNAseq offers several advantages over microarrays for differential expression analysis, such as an increased dynamic range and a lower background level, and the ability to detect and quantify the expression of previously unknown transcripts and isoforms [35]. The analysis of RNAseq data is, however, not without difficulties. Some of these difficulties are inherent to nextgeneration sequencing procedures. For example, the variation in nucleotide composition between genomic regions implies that the read coverage may not be uniform along the genome. Further, more reads will map to longer genes than to shorter ones with the same expression level. In differential expression analysis, where the genes are tested individually for expression differences between conditions, such ‘withinsample’ biases are usually ignored since they are assumed to affect all samples similarly [3].
Other types of nonuniformities are seen between samples in an RNAseq experiment. First, the sequencing depths or library sizes (the total number of mapped reads) are typically different for different samples, which means that the observed counts are not directly comparable between samples. Indeed, even in the absence of any true differential expression, if one sample is sequenced to twice the depth of another we expect all the genes to obtain twice as high count in the first sample compared to the second, and we do not want to confuse such effects with true differential expression. The most straightforward way of approaching the different library sizes is to simply rescale or resample the read counts to obtain equal library sizes for all samples. However, such a normalization is generally not enough. The reason is that even if the library sizes are indeed identical, RNAseq counts inherently represent relative abundances of the genes. A few highly expressed genes may contribute a very large part of the sequenced reads in an experiment, leaving only few reads to be distributed among the remaining genes [6]. The presence of the few highly expressed genes thus represses the counts for all other genes, and in comparison to a sample where the reads are more evenly distributed, the latter group of genes may, perhaps incorrectly, seem to have a lower expression which can lead to a lot of genes being falsely called differentially expressed. To account for this difficulty and attempt to make the counts comparable across samples, more complex normalization schemes have been proposed [68]. In addition to the library sizes, these procedures also include the estimation of samplespecific normalization factors that are used to rescale the observed counts. Using these normalization methods, the sum of the normalized counts across all genes are therefore not necessarily equal between samples (as it would be if only the library sizes were used for normalization), but the goal is instead to make the normalized counts for nondifferentially expressed genes similar between the samples. In this study, we use the TMM normalization (trimmed mean of Mvalues [8]) and the normalization provided in the DESeq package [7]. A comprehensive evaluation of seven different normalization methods was recently performed [9], in which these two methods were shown to perform similarly, and they were also the only ones providing satisfactory results with respect to all metrics used in that evaluation. Still, it is important to keep in mind that even these methods are based on an assumption that most genes are equivalently expressed in the samples, and that the differentially expressed genes are divided more or less equally between up and downregulation [9].
Microarrays have been used routinely for differential expression analysis for over a decade, and there are wellestablished methods available for this purpose (such as limma [10]). These methods are not immediately transferable to analysis of RNAseq data [11], since these are somewhat different from the data obtained from microarrays. The intensities recorded from microarrays are treated as continuous measurements, commonly assumed to follow a lognormal distribution, while the counts from an RNAseq experiment are nonnegative integers and thus inherently follow a discrete distribution. In the methods explicitly developed for differential expression analysis of this type of count data, the Poisson distribution and the Negative Binomial (NB) distribution are the two most commonly used models [7, 1215]. Other distributions, such as the betabinomial [16], have also been proposed. The Poisson distribution has the advantage of simplicity and has only one parameter, but it constrains the variance of the modeled variable to be equal to the mean. The Negative Binomial distribution has two parameters, encoding the mean and the dispersion, and hence allows modeling of more general meanvariance relationships. For RNAseq, it has been suggested that the Poisson distribution is well suited for analysis of technical replicates, whereas the higher variability between biological replicates necessitates a distribution incorporating overdispersion, such as the Negative Binomial [6, 17]. Instead of using integer counts directly, some software packages represent RNAseq data by transformed quantities such as RPKM (Reads Per Kilobase per Million mapped reads) [1] or the related FPKM (Fragments Per Kilobase per Million mapped reads) [18]. The goal of such transformations is to normalize the counts with respect to the differing library sizes and with respect to the length of the transcripts, since a long transcript is expected to obtain more reads than a short transcript with the same expression level. Other normalization strategies can be employed to handle other biases, arising for example from the variable GC content of the reads. After transformations such as these, the resulting values are no longer integer counts, which means that they should not be plugged into countbased methods for differential expression analysis. Among the methods evaluated in this study, only the nonparametric ones would thus be suitable also for RPKM values. Other software, such as Cufflinks/Cuffdiff [18], provide an integrated analysis pipeline from the aligned reads to the differential expression results, where the inference is based on FPKM values.
The field of differential expression analysis of RNAseq data is still in its infancy and new methods are continuously being presented. So far, there is no general consensus regarding which method performs best in a given situation and few extensive comparisons between the proposed methods have been published. In a recent paper [19], four parametric methods were compared in terms of their ability to discriminate between truly differentially expressed (DE) and truly nonDE genes, under different simulation conditions. The authors also compared the overlap between the sets of DE genes found by the different methods in a real data set. Another recent study [20] evaluated the impact of increasing sequencing depth on the ability to detect DE genes and contrasted this with the benefits of increasing the sample size, and the latter were found to be considerably larger. In [21], the authors presented a case study on Saccharomyces cerevisiae, comparing the results obtained by several differential expression analysis methods for RNAseq with each other and with results obtained from microarrays, and reported a generally good agreement between the different methods.
In the present paper we conduct a comparison of eleven methods, developed for differential expression analysis of RNAseq data, under different experimental conditions. Among the eleven methods, nine model the count data directly, while the remaining two transform the counts before applying a traditional method for differential expression analysis of microarray data. The study is confined to methods that are implemented and available within the R framework [22] and that are applicable to count matrices (containing the count for each of a number of genes or other genomic features of interest in each of a number of samples). Several methods for obtaining such a matrix from the raw sequence data exist, but a comprehensive evaluation of these are outside the scope of the present study. We further focus on finding genes that are differentially expressed between two conditions only, since this is arguably the most commonly encountered application. Moreover, it is supported by all evaluated methods, although most methods allow also more complex experimental designs (see further in the Materials and Methods section).
Results and discussion
Eleven methods for differential expression analysis of RNAseq data were evaluated in this study. Nine of them work on the count data directly: DESeq [7], edgeR [23], NBPSeq [15], TSPM [13], baySeq [14], EBSeq [24], NOISeq [25], SAMseq [26] and ShrinkSeq [27]. The remaining two combine a data transformation with limma [10] for differential expression analysis, and we will refer to them as voom(+limma) [10] and vst(+limma) [7, 10]. More detailed descriptions of the methods can be found in the Materials and Methods section and in the respective original publications.
The methods were evaluated mainly based on synthetic data, where we could control the settings and the true differential expression status of each gene. Details regarding the different simulation studies can be found in the Materials and Methods section. As the baseline (simulation studies abbreviated ‘B’), we simulated all counts using Negative Binomial distributions, with mean and dispersion parameters estimated from real data. In these simulations, the dispersions in both conditions were assumed to be identical. Note that this does not imply that the variances are the same in the two conditions, since the variance depends also on the mean. We also evaluated the robustness of the methods against variations in the distribution of the input data, by instead imposing a Poisson distribution for the counts for some of the genes (simulation studies denoted ‘P’), or including outliers with abnormally high counts (simulation studies denoted ‘S’ and ‘R’). The outliers were introduced in two different ways. For the ‘single’ outlier simulation studies (denoted ‘S’), we selected 10% of the genes, and for each of these genes we selected a single sample for which we multiplied the observed count with a randomly generated factor between 5 and 10. For the ‘random’ outlier simulation studies (denoted ‘R’), we considered each observed count independently, and with probability 0.05 we multiplied it with a randomly generated factor between 5 and 10.
The total number of genes in each simulated data set was 12,500, and the number of differentially expressed (DE) genes was set to either 0, 1,250 or 4,000. We also varied the composition of the DE genes, that is, the fraction of DE genes that were up and downregulated, respectively, in one condition compared to the other. Finally, we evaluated the effect of varying the sample size, from 2 to 5 or 10 samples per condition. These sample sizes were chosen to reflect a wide range of experimental settings. Since, however, most current RNAseq experiments exhibit small sample sizes and the choice in the experimental design is often between two or three samples per condition, we also performed some comparisons with 3 samples per condition. These comparisons, contrasted with the results from 2 and 5 samples per condition, are given in the supplementary material (Additional file 1). In the supplementary material we also present some results obtained for data sets where the dispersion parameters were different between the two conditions.
In addition to the simulated data, we compared the methods based on their performance for three real RNAseq data set. The results from one of these data sets are shown in the main article, and the remaining two are discussed in the supplementary material (Additional file 1).
Using the synthetic data, we studied the following aspects of the methods under different experimental conditions:

The ability to rank truly DE genes ahead of nonDE genes. This was evaluated in terms of the area under a Receiver Operating Characteristic (ROC) curve (AUC), as well as in terms of false discovery curves, depicting the number of false detections encountered while going through the list of genes ranked according to the evidence for differential expression.

The ability to control type I error rate and false discovery rate at an imposed level. This was evaluated by computing the observed type I error and the true false discovery rate, respectively, among the genes called differentially expressed at given significance levels.

The computational time requirement for running the differential expression analysis. These results are given in the supplementary material (Additional file 1).
For the real RNAseq data we compared the collections of genes called DE by the different methods, both in terms of their individual cardinalities and in terms of their overlaps. We also studied the concordance of the gene rankings obtained by the different methods.
Discrimination between DE and nonDE genes
We first evaluated to what extent the eleven considered methods were able to discriminate between truly DE genes and truly nonDE ones. We computed a score for each gene and each method, which allowed us to rank the genes in order of significance or evidence for differential expression between the two conditions. For the six methods providing nominal pvalues (edgeR, DESeq, NBPSeq, TSPM, voom+limma, vst+limma), we defined the score as 1  p_{ nom }. For SAMseq we used the absolute value of the averaged Wilcoxon statistic as the ranking score, and for baySeq, EBSeq and ShrinkSeq we used the estimated posterior probability of differential expression or, equivalently in terms of ranking, 1  BFDR, where BFDR denotes the estimated Bayesian False Discovery Rate [28] (see Materials and Methods for more information about the different methods). For NOISeq, we used the statistic q_{ NOISeq } (see Materials and Methods). All these scores are twosided, that is, they are not affected by the direction of differential expression between the two conditions. Given a threshold value for such a score, we may thus choose to call all genes with scores exceeding the threshold DE, and correspondingly all genes with scores below the threshold are called nonDE. Considering the genes that were simulated to be DE as the true positive group and the remaining genes as the true negative group, we computed the false positive rate and the true positive rate for all possible score thresholds and constructed a ROC (Receiver Operating Characteristic) curve for each method. The area under the ROC curve (AUC) was used as a measure of the overall discriminative performance of a method, that is, the overall ability to rank truly DE genes ahead of truly nonDE ones.
For the largest sample sizes (5 or 10 samples per condition) and when there were both up and downregulated genes, all methods performed similarly in terms of the AUC. All methods performed better for large sample sizes. TSPM and EBSeq showed the strongest sample size dependencies among the methods, followed by SAMseq and baySeq. For the smallest sample size (2 samples per condition), the best results were generally obtained by DESeq, edgeR, NBPSeq, voom+limma and vst+limma.
When all DE genes were upregulated in condition S_{2} compared to condition S_{1} (Figures 1A and 1C), we saw a high variability in the results obtained by baySeq. This variability was reduced when the DE genes were regulated in different directions (Figures 1B and 1D).
We chose to evaluate the effect of introducing nonoverdispersed genes or outliers under the settings of simulation study ${B}_{625}^{625}$ (Figure 1B). When the fraction of genes following a Poisson distribution was increased from 0 to 50% (simulation study ${P}_{625}^{625}$) the AUC increased, especially for the smallest sample size (Additional file 1: Figure S17, compare to Figure 1B). Outliers with abnormally high counts reduced the AUC slightly for all methods, but less for the transformationbased methods (vst+limma and voom+limma) and SAMseq than for the other methods (Figures 1E and 1F).
Larger sample sizes led to considerably fewer false positives found among the topranked genes (compare Figure 2 to Additional file 1: Figures S18 and S19). Actually, as seen by comparing Additional file 1: Figure S18 to Additional file 1: Figures S10(b) and 11(b), already increasing the number of samples per condition from 2 to 3 provided a tangible improvement.
Control of type I error rate
The results stayed largely similar when we let the counts for half of the genes be Poisson distributed (simulation study ${P}_{0}^{0}$, Figure 3B), but for the smallest sample size we noted a reduction of the type I error rate for TSPM and an increase of the type I error rate for the transformationbased methods and NBPSeq. Introducing ‘single’ outliers (simulation study ${S}_{0}^{0}$) had a considerable effect on the type I error of the three methods that are explicitly modeling the counts using a Negative Binomial distribution (edgeR, DESeq and NBPSeq). Under these conditions, the type I error rates of NBPSeq and edgeR increased substantially, while DESeq instead became even more conservative (Figure 3C). The type I error rates of the transformationbased methods and the TSPM were less affected, but tended to decrease rather than increase following the introduction of outliers. Similar effects, but even more pronounced, were noted when we instead introduced ‘random’ outliers (simulation study ${R}_{0}^{0}$) Figure 3D, see the Materials and Methods section for a more extensive explanation of the different types of outliers). If these outliers were instead introduced by dividing the counts by a random factor between 5 and 10 (instead of multiplying with this factor), the results were largely similar to those from the baseline study (without outliers), except for a slight reduction of the type I error rate for NBPSeq and edgeR (data not shown). In Additional file 1 (Additional file 1: Figures S20 and S21), we show representative pvalue distributions under the different simulation settings. In these figures, we note that even when all null hypotheses are true, the pvalues are not always uniformly distributed. Specifically, some methods (edgeR, DESeq and NBPSeq) exhibit an excess of large pvalues. This has been observed also in previous studies and has been attributed to the use of exact tests based on discrete probability distributions [20]. Since the total number of reads mapping to the different genes is very different, the null distribution of pvalues will be a mixture of a large number of different discrete distributions [29].
Control of the false discovery rate
Next, we examined whether setting a significance threshold for the adjusted pvalue (or an FDR threshold) indeed controlled the false discovery rate at the desired level. We put the FDR threshold at 0.05, and calculated the true false discovery rate as the fraction of the genes called significant at this level that were indeed false discoveries. Since NOISeq does not return a statistic that is recommended to use as an adjusted pvalue or FDR estimate, it was excluded from this evaluation. For baySeq, EBSeq and ShrinkSeq, we imposed the desired threshold on the Bayesian FDR [28].
When the DE genes were regulated in different directions, increasing the number of DE genes from 1,250 to 4,000 improved the ability to control the FDR (simulation study ${B}_{2000}^{2000}$ Figure 4D, compare to Figure 4B). Conversely, when all DE genes were regulated in the same direction, increasing the number of DE genes impaired the ability to control the FDR especially for the largest sample sizes (simulation study ${B}_{0}^{4000}$, Figure 4C, compare to Figure 4A). When outliers with extremely high counts were introduced (simulation studies ${S}_{625}^{625}$ and ${R}_{625}^{625}$ the FDRs of baySeq, NBPSeq and edgeR, which are all based on a Negative Binomial distribution, were considerably increased. The transformationbased methods were less affected and controlled the FDR under these conditions as well (Figures 4E and 4F). Also the FDRs of SAMseq and TSPM were largely unaffected by the inclusion of outliers.
In a practical situation, we are not only interested in keeping the rate of false discoveries low, but also to actually be able to find the true positives. Therefore, we also computed the true positive rate (the fraction of truly DE genes that were found to be significant) among the genes that were called significant at a FDR threshold of 0.05. In general, DESeq and baySeq tended to give the lowest number of true positives (Additional file 1: Figure S22). This should be viewed in relation to Figure 4, where it was shown that these methods often also gave low fractions of false discoveries. The other two methods that are based on the NB model, edgeR and NBPSeq, as well as ShrinkSeq, in which we used a zeroinflated NB model, returned more true positives but at the price of a higher false discovery rate. The nonparametric SAMseq method gave high true positive rates across all simulation settings, seemingly without an accompanying high false discovery rate. However, for the smallest sample sizes this method did not find any significantly differentially expressed genes at all which is not surprising due to its nonparametric nature and reliance on sample permutations. The true positive rate of EBSeq was largely unaffected by the sample size, but the false discovery rate decreased as sample size increased.
As expected, increasing the expression difference between the two conditions (w_{ g }, see Materials and Methods) improved the ability to detect truly DE genes and reduced the observed false discovery rate, in a concordant manner for all methods (data not shown). When the dispersions in the two conditions were different, we observed an increased FDR for the majority of the methods (Additional file 1: Figure S12(c), compare to Figure 4B).
Real RNAseq data from two mouse strains
In addition to the synthetic data set, we also analyzed an RNAseq data set from 21 mice, 10 of the C57BL/6J strain and 11 of the DBA/2J strain [30]. After filtering out genes for which the total count across the 21 mice was less than 10, the data set contained 11,870 genes. We applied the eleven methods to find genes that showed differential expression between the two mouse strains. All genes found to be DE at a FDR or Bayesian FDR threshold of 0.05 were considered significantly DE. It is not clear how to set a threshold for the qvalue returned by NOISeq to be comparable with the FDR estimate or adjusted pvalue from the other methods, and hence NOISeq was excluded from most of the subsequent analysis.
The number of shared differentially expressed genes found by the different methods for the Bottomly data set
ShrinkSeq  DESeq  edgeR  NBPSeq  TSPM  voom  vst  baySeq  EBSeq  SAMseq  

ShrinkSeq  3259  583  1125  985  1075  971  1049  192  803  1821 
DESeq  583  598  598  567  588  589  587  191  523  592 
edgeR  1125  598  1160  877  886  942  1013  194  753  1099 
NBPSeq  985  567  877  1082  695  753  797  194  612  924 
TSPM  1075  588  886  695  1161  891  907  191  794  1014 
voom  971  589  942  753  891  1009  971  194  752  991 
vst  1049  587  1013  797  907  971  1095  194  752  1061 
baySeq  192  191  194  194  191  194  194  195  175  194 
EBSeq  803  523  753  612  794  752  752  175  819  801 
SAMseq  1821  592  1099  924  1014  991  1061  194  801  1860 
In Additional file 1: Figures S24S28, we show the normalized counts (normalized using the normalization factors provided by the TMM method [8] together with the library sizes) across all samples for some of the genes found to be DE by only a single method. DESeq, edgeR, voom+limma, baySeq and EBSeq did not find any unique DE genes and hence there are no figures corresponding to these methods. From Additional file 1: Figures S24S28, we noted that the DE genes found uniquely by ShrinkSeq, and to some extent for those found uniquely by SAMseq, tended to be reasonably highly expressed and consistently expressed across the samples from both conditions while for many of the other methods, the unique DE genes exhibited highly inconsistent counts even within conditions. The two genes found exclusively by vst+limma both had very low counts in all samples, as was the case for most genes found uniquely by TSPM.
In Additional file 1: Figure S29 we compare the gene ranking scores obtained by the different methods for the Bottomly data set (the scores were computed as described previously, recall that high scores correspond to genes considered DE). From this figure, we noted that edgeR, DESeq, voom+limma, vst+limma, TSPM and SAMseq tended to rank the genes similarly, while the rankings obtained by NBPSeq were less similar to these. The rankings obtained by baySeq and EBSeq were considerably different from the other rankings.
To further evaluate the performance of the methods, we applied them to the data set consisting of only the mice from the C57BL/6J strain, within which we defined two arbitrary sample classes of 5 samples each. The analysis was repeated five times for different arbitrary divisions. Under these conditions, we expect that no genes are truly DE. Nevertheless, most methods found differentially expressed genes in at least one instance. TSPM found by far the largest number of DE genes (Figure 5D), which supports our previous observation that this method may be too liberal. By studying the genes called DE in the five instances, we noted that the DE genes found by edgeR often overlapped with the DE genes found by NBPSeq, while only few of the DE genes called by TSPM overlapped with those found by the other methods. Also EBSeq tended to call unique genes, that were not found by any of the other methods. The lack of consensus among the DE genes found by the different methods may be a further indication that they are indeed false positives, and that the different methods tend to favor different types of patterns.
Conclusions
Summary of the main observations
DESeq   Conservative with default settings. Becomes more conservative when outliers are introduced. 
 Generally low TPR.  
 Poor FDR control with 2 samples/condition, good FDR control for larger sample sizes, also with outliers.  
 Medium computational time requirement, increases slightly with sample size.  
edgeR   Slightly liberal for small sample sizes with default settings. Becomes more liberal when outliers are introduced. 
 Generally high TPR.  
 Poor FDR control in many cases, worse with outliers.  
 Medium computational time requirement, largely independent of sample size.  
NBPSeq   Liberal for all sample sizes. Becomes more liberal when outliers are introduced. 
 Medium TPR.  
 Poor FDR control, worse with outliers. Often truly nonDE genes are among those with smallest pvalues.  
 Medium computational time requirement, increases slightly with sample size.  
TSPM   Overall highly samplesize dependent performance. 
 Liberal for small sample sizes, largely unaffected by outliers.  
 Very poor FDR control for small sample sizes, improves rapidly with increasing sample size. Largely unaffected by outliers.  
 When all genes are overdispersed, many truly nonDE genes are among the ones with smallest pvalues. Remedied when the counts for some genes are Poisson distributed.  
 Medium computational time requirement, largely independent of sample size.  
voom / vst   Good type I error control, becomes more conservative when outliers are introduced. 
 Low power for small sample sizes. Medium TPR for larger sample sizes.  
 Good FDR control except for simulation study ${B}_{0}^{4000}$. Largely unaffected by introduction of outliers.  
 Computationally fast.  
baySeq   Highly variable results when all DE genes are regulated in the same direction. Less variability when the DE genes are regulated in different directions. 
 Low TPR. Largely unaffected by outliers.  
 Poor FDR control with 2 samples/condition, good for larger sample sizes in the absence of outliers. Poor FDR control in the presence of outliers.  
 Computationally slow, but allows parallelization.  
EBSeq   TPR relatively independent of sample size and presence of outliers. 
 Poor FDR control in most situations, relatively unaffected by outliers.  
 Medium computational time requirement, increases slightly with sample size.  
NOISeq   Not clear how to set the threshold for q_{ NOISeq } to correspond to a given FDR threshold. 
 Performs well, in terms of false discovery curves, when the dispersion is different between the conditions (see supplementary material).  
 Computational time requirement highly dependent on sample size.  
SAMseq   Low power for small sample sizes. High TPR for large enough sample sizes. 
 Performs well also for simulation study ${B}_{0}^{4000}$.  
 Largely unaffected by introduction of outliers.  
 Computational time requirement highly dependent on sample size.  
ShrinkSeq   Often poor FDR control, but allows the user to use also a fold change threshold in the inference procedure. 
 High TPR.  
 Computationally slow, but allows parallelization. 
Small sample sizes (2 samples per condition) imposed problems also for the methods that were indeed able to find differentially expressed genes, there leading to false discovery rates sometimes widely exceeding the desired threshold implied by the FDR cutoff. For the parametric methods this may be due to inaccuracies in the estimation of the mean and dispersion parameters. In our study, TSPM stood out as the method being most affected by the sample size, potentially due to the use of asymptotic statistics. Even though the development goes towards large sample sizes, and barcoding and multiplexing create opportunities to analyze more samples at a fixed cost, as of today RNAseq experiments are often too expensive to allow extensive replication. The results conveyed in this study strongly suggest that the differentially expressed genes found between small collections of samples need to be interpreted with caution and that the true FDR may be several times higher than the selected FDR threshold.
DESeq, edgeR and NBPSeq are based on similar principles and showed, overall, relatively similar accuracy with respect to gene ranking. However, the sets of significantly differentially expressed genes at a prespecified FDR threshold varied considerably between the methods, due to the different ways of estimating the dispersion parameters. With default settings and for reasonably large sample sizes, DESeq was often overly conservative, while edgeR and in particular NBPSeq often were too liberal and called a larger number of false (and true) DE genes. In the supplementary material (Additional file 1) we show that varying the parameters of edgeR and DESeq can have large effects on the results of the differential expression analysis, both in terms of the ability to control type I error rates and false discovery rates and in terms of the ability to detect the truly DE genes. These results also show that the recommended parameters (that are used in the main paper) are indeed well chosen and often provide the best results.
EBSeq, baySeq and ShrinkSeq use a different inferential approach, and estimate the posterior probability of being differentially expressed, for each gene. baySeq performed well under some conditions but the results were highly variable, especially when all DE genes were upregulated in one condition compared to the other. In the presence of outliers, EBSeq found a lower fraction of false positives than baySeq for large sample sizes, while the opposite was true for small sample sizes.
Methods
In the following section we give a brief overview of the eleven methods for differential expression analysis that are evaluated and compared in the present paper. For more elaborate descriptions we refer to the original publications. All methods take their starting point in a count matrix, containing the number of reads mapping to each gene in each of the samples in the experiment. Nine of the methods work directly on the count data, while the remaining two transform the counts and feed the transformed values into the R package limma [10], which was originally developed for differential expression analysis of microarray data.
The methods working directly on the count data can be broadly divided into parametric (baySeq [14], EBSeq[24], ShrinkSeq [27], edgeR [23], DESeq [7], NBPSeq [15] and TSPM [13]) and nonparametric methods (NOISeq [25] and SAMseq [26]). The twostage Poisson model (TSPM) proposed in [13] is based on a Poisson model for the counts, which is extended via a quasilikelihood approach to allow for overdispersion if there is enough evidence for it in the data. Hence, the first step is to test each gene individually for evidence of overdispersion, in order to decide which of the two models to use for the differential expression analysis. The tests for differential expression are based on asymptotic statistics, which implies that the total count for each gene, across all samples, must not be too small. The authors therefore recommend that genes with a total count less than 10 are removed from the analysis. They also note that for the TSPM to work well, it may be important that there are indeed some genes for which there is no overdispersion.
Most of the remaining parametric models (baySeq, DESeq, EBSeq, edgeR and NBPSeq) use instead a Negative Binomial (NB) model to account for the overdispersion, while ShrinkSeq allows the user to select among a number of different distributions, including the NB and a zeroinflated NB distribution. DESeq, edgeR and NBPSeq take a classical hypothesis testing approach, while baySeq, EBSeq and ShrinkSeq instead are cast within a Bayesian framework. It is acknowledged that a crucial part of the inference procedure is to obtain a reliable estimate of the dispersion parameter for each gene, and hence considerable effort is put into this estimation. Due to the small sample size in most RNAseq experiments it is difficult to estimate the genewise dispersion parameters reliably, which motivates information sharing across all genes in the data set in order to obtain more accurate estimates. Both DESeq, edgeR and NBPSeq incorporate information sharing in the dispersion estimation, and the way that this information sharing is done accounts for the main difference between the three methods. The first suggestion [12] was to assume that all genes had the same dispersion parameter. This could then be estimated from all the available data using a conditional maximum likelihood approach. A common dispersion for all genes may however be a too restrictive assumption, and so this procedure was developed further to allow for genewise dispersion estimates, but where the individual estimates were squeezed towards the common one using a weighted likelihood approach [31]. This method is used by edgeR. In contrast, DESeq and NBPSeq obtain the dispersion estimates by modeling the observed meanvariance (or the meandispersion) relationship for the genes in the data set using either parametric or local regression. After having obtained the fitted values, DESeq takes a conservative approach by defining the dispersion of a gene as the largest of the value obtained from the fitting and the individual dispersion estimate for the gene. NBPSeq does not take the same type of conservative approach as DESeq, and uses the fitted dispersion values only. After obtaining an estimate of the mean and the dispersion parameter for each gene, edgeR, DESeq and NBPSeq test for significant differential expression using either a variant of an exact test (for twogroup comparisons) or a generalized linear model (allowing more complex experimental designs).
The approach used by baySeq and EBSeq is similar to the three previously mentioned methods in terms of the underlying NB model, but differs in terms of the inference procedure. For baySeq, the user defines a collection of models, each of which is essentially a partitioning of the samples into groups, where samples in the same group are assumed to share the same parameters of the underlying distribution. Within an empirical Bayes framework, baySeq then estimates the posterior probability of each model for each of the genes in the data set. Information from the entire set of genes is used to form an empirical prior distribution for the parameters in the NB model. EBSeq uses a similar approach, but assumes a parametric form of the prior distribution of the parameters, with hyperparameters that are shared between all the genes and estimated from the data.
ShrinkSeq, which also takes a Bayesian perspective, supports a number of different count models, including the NB and a zeroinflated NB. It provides shrinkage of the dispersion parameter, but also of other parameters such as the regression coefficients that are of interest for the inference. Furthermore, it incorporates a step for refining the priors, and subsequently the posteriors, nonparametrically after fitting the model for each feature.
The two nonparametric methods evaluated here, NOISeq and SAMseq, do not assume any particular distribution for the data. SAMseq is based on a Wilcoxon statistic, averaged over several resamplings of the data, and uses a sample permutation strategy to estimate a false discovery rate for different cutoff values for this statistic. These estimates are then used to define a qvalue for each gene. NOISeq explores the distribution of foldchanges and absolute expression differences between the two contrasted conditions for the observed data, and compares this distribution to the corresponding distribution obtained by comparing pairs of samples belonging to the same condition (this is called the “noise distribution”). Briefly, NOISeq computes, for each gene, a statistic (here denoted q_{ NOISeq }) defined as the fraction of points from the noise distribution that correspond to a lower fold change and a lower absolute expression difference than those of the gene of interest in the original data.
Finally, the two transformation approaches (the variance stabilizing transformation provided in the DESeq R package and the voom transformation from the limma R package) aim to find a transformation of the counts to make them more amenable to analysis by traditional methods developed for differential expression analysis in the microarray context. The variancestabilizing transformation provided in the DESeq R package (here denoted ‘vst’) explicitly computes the transformation by assuming a NB distribution and using dispersion estimates obtained as for DESeq. The ‘voom’ transformation from the limma R package essentially logtransforms the normalized counts and uses the meanvariance relationship for the transformed data to compute gene weights, which are then used by limma during the differential expression analysis.
In the present study, we focus on twogroup comparisons only, since this is arguably the most common situation in practice. However, most of the evaluated methods support also more complex experimental designs. Most methods (edgeR, DESeq, NBPSeq, TSPM) achieve this through a generalized linear model (GLM) framework, where the user can specify desired contrasts to test. The limma package offers similarly flexible design options for the transformed data. The Bayesian methods (baySeq and EBSeq) allow the user to provide models defining collections of samples that are supposed to share the same distributional parameters, and return the posterior likelihood of each model thus defined. ShrinkSeq is based on the general framework of Gaussian latent models through the INLA approach [32], which allows very flexible experimental designs, including also random effects. It is also possible to impose a fold change threshold in the estimation of the posterior probabilities of differential expression. SAMseq provides nonparametric tests for various situations, such as paired and unpaired twogroup comparisons, multigroup comparisons and survival analysis. NOISeq, in its current implementation, allows only twogroup comparisons.
Parameter choices
Many of the methods that are compared in this paper allow the user to select the value of certain parameters, that can affect the results in various ways. We have mostly used the default values provided in the implementations, but in the supplementary material (Additional file 1) we also provide some comparisons of the performances for different choices of the parameter values. This section summarizes the parameter values that were used for the evaluations in the main paper. For more detailed information about the meaning of the different parameters, we refer to the original publications describing the respective methods.
For edgeR, we used the TMM method (Trimmed Mean of Mvalues [8]) to calculate normalization factors between samples. We used tagwise dispersion estimates, squeezed towards a trended estimate computed by the ‘moving average’ approach. We performed an exact test to find genes that were differentially expressed between two conditions.
For DESeq, we computed a pooled estimate of the dispersion parameter for each gene. We used local regression to find the meanvariance relationship and employed the conservative approach of selecting the largest among the fitted value and the individual dispersion estimate for each gene. Also here, we used the implemented exact test to find DE genes. The local regression approach was also used in the variancestabilizing transformation provided by the DESeq package (denoted ‘vst’). Here, we used instead the ‘blind’ option for the dispersion estimation.
Also for TSPM, baySeq, voom and NBPSeq we used the TMM method to compute normalization factors. For NOISeq, we normalized the counts using the TMM method before feeding the data into the differential expression analysis. Furthermore, for NBPSeq we used the ‘NBP’ parametrization of the Negative Binomial distribution. For baySeq, we assumed a Negative Binomial distribution and used the quasilikelihood approach to estimate priors. We used a sample size of 5,000 to estimate the priors. Furthermore, we assumed equal dispersion for a gene in the two sample groups and used the ‘BIC’ option for the prior reestimation step. For EBSeq, we used the default ‘median’ normalization method, that is, the normalization provided with DESeq [7].
Before applying ShrinkSeq, we normalized the counts using TMM normalization factors. Within ShrinkSeq we then employed a zeroinflated Negative Binomial distribution, and applied shrinkage to the dispersion parameter as well as the regression coefficient of interest in the inference procedure. To make the results from ShrinkSeq comparable to those from the other methods, we did not impose a nonzero fold change threshold when estimating the false discovery rates.
Data sets
Most of the evaluations in this paper are based on synthetic data, where we could control the settings and the true differential expression status of each gene. We generated the counts for each gene from a Negative Binomial distribution, with mean and dispersion parameters estimated from real RNAseq data, following the same approach as in [20]. We refer to the supplementary material (Additional file 1) for more detailed information about how the parameters were estimated. All methods were run on the same data sets.
We let G = {g_{1}, …, g_{G}} denote the set of genes in our data set. In the synthetic data sets, we took G=12,500. Similarly, we let S = {s_{1}, …, s_{S}} denote the set of samples, and assumed that these were partitioned into two subsets S_{1} and S_{2}. In our experiments, we let S_{1}=S_{2} and we thought of S_{1} as the “control” group of samples and S_{2} as a group of samples with an abnormal phenotype. We let ${G}_{\mathit{DE}}^{\mathit{up}}\subseteq G$ denote the set of genes that were differentially expressed between the two sample groups, and which were upregulated in S_{2}. Similarly, ${G}_{\mathit{DE}}^{\mathit{down}}\subseteq G$ denoted the set of genes that were downregulated in S_{2} compared to S_{1}.
where M_{ s } is the sequencing depth for sample s, which we defined as M_{ s } = 10^{7}U_{ s } for U_{ s } ~ Unif [0.7, 1.4], and c(s) ∈ {S_{1}, S_{2}} denoted the condition for sample s. We let the dispersion parameter φ_{gs} be the same in the two sample groups, that is, φ_{gs} = φ_{g} for all s.
The parameter w_{ g } denoted the lower bound on the differential expression between the two groups. In our simulations, we let w_{ g } = 1.5 for all g.
Summary of the parameters used to generate the synthetic data sets
Sim. study  ${\mathit{G}}_{\mathit{DE}}^{\mathit{up}}$  ${\mathit{G}}_{\mathit{DE}}^{\mathit{down}}$  {g; ϕ_{ g } = 0}  ‘Single’ outlier fraction  ‘Random’ outlier fraction 

${B}_{0}^{0}$  0  0  0  0  0 
${B}_{0}^{1250}$  1,250  0  0  0  0 
${B}_{625}^{625}$  625  625  0  0  0 
${B}_{0}^{4000}$  4,000  0  0  0  0 
${B}_{2000}^{2000}$  2,000  2,000  0  0  0 
${P}_{0}^{0}$  0  0  6,250  0  0 
${P}_{625}^{625}$  625  625  6,250  0  0 
${S}_{0}^{0}$  0  0  0  10%  0 
${S}_{625}^{625}$  625  625  0  10%  0 
${R}_{0}^{0}$  0  0  0  0  5% 
${R}_{625}^{625}$  625  625  0  0  5% 
In addition to the synthetic data, we also considered a real RNAseq data set [30] that we downloaded from http://bowtiebio.sourceforge.net/recount/. The data set contained RNAseq data taken from 21 samples from two different mouse strains. Also for this data set we filtered out all genes for which the total count across the 21 samples did not exceed 10, which left 11,870 genes in the data set. In the supplementary material, we analyse two other real data sets [33, 34], downloaded from the same source.
Declarations
Authors’ Affiliations
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