Illumina’s HumanMethylation450 arrays provide the most cost-effective means of high-throughput DNA methylation analysis. As with other types of microarray platforms, technical artifacts are a concern, including background fluorescence, dye-bias from the use of two color channels, bias caused by type I/II probe design, and batch effects. Several approaches and pipelines have been developed, either targeting a single issue or designed to address multiple biases through a combination of methods. We evaluate the effect of combining separate approaches to improve signal processing.In this study nine processing methods, including both within- and between- array methods, are applied and compared in four datasets. For technical replicates, we found both within- and between-array methods did a comparable job in reducing variance across replicates. For evaluating biological differences, within-array processing always improved differential DNA methylation signal detection over no processing, and always benefitted from performing background correction first. Combinations of within-array procedures were always among the best performing methods, with a slight advantage appearing for the between-array method Funnorm when batch effects explained more variation in the data than the methylation alterations between cases and controls. However, when this occurred, RUVm, a new batch correction method noticeably improved reproducibility of differential methylation results over any of the signal-processing methods alone.The comparisons in our study provide valuable insights in preprocessing HumanMethylation450 BeadChip data. We found the within-array combination of Noob + BMIQ always improved signal sensitivity, and when combined with the RUVm batch-correction method, outperformed all other approaches in performing differential DNA methylation analysis. The effect of the data processing method, in any given data set, was a function of both the signal and noise.The online version of this article (doi:10.1186/s12864-016-2819-7) contains supplementary material, which is available to authorized users. DNA methylation, featured by the presence of 5-methylcytosine in the context of CpG dinucleotides, is the most studied form of epigenetic modification. It plays an important role in both physiological processes and disease states. For instance in cancers, alterations in DNA methylation landscapes include a global hypomethylation of the genome accompanied with CpG island hypermethylation . DNA metAlong with the widespread application of the HM450 array, a number of statistical approaches have arisen to address technical noise in the estimate of DNA methylation level. For a targeted cytosine, probes bind to methylated and unmethylated alleles and emit a fluorescence signal. The DNA methylation level, called Beta value, is estimated by the ratio of the methylated to the sum of methylated and unmethylated intensities. Issues encountered during probe design resulted in the implementation of two types of chemical assays, Infinium I and Infinium II, with different technical characteristics. The Infinium type I design utilizes two probes in the same color channel to quantify methylated and unmethylated alleles, the color channel determined by the nucleotide 5’ to the target cytosine (green for G/C and red for A/T); type I probes are more likely to target CpG-dense regions and in the body of the probes all CpGs are assumed to have the same methylation state as the target site. In contrast, the Infinium type II design utilizes one probe but two color channels for a single cytosine target, with green and red channel measuring methylated and unmethylated alleles, respectively; type II probes contain a degenerate base at the cytosine position for CpGs in the probe body. Technical noise is introduced by the variation in background fluorescence signal across arrays and color channel and the different average intensities in the red and green channels. Together, these can introduce additive and multiplicative errors to the signal intensity, reducing the dynamic range of the Beta value and skewing the values of Infinium II Beta values differentially across samples. Other studies showed type II Beta values have lower dynamic range than type I Beta values  and thatGiven the increasing popularity of the HM450 array and the biases observed due to platform design, several approaches and pipelines have been developed, either targeting a single issue or designed to address multiple biases within a complete framework. Recently, some systematic comparisons of preprocessing procedures have appeared –10, howeIn total we evaluate and compare nine preprocessing approaches based on the following within-array and between-array methods: (1) background correction and dye-bias equalization (Noob) ; (2) betn = 92,596 for Cy3 features and n = 178,406 for Cy5 features). These background-corrected intensities are then normalized for variation in average intensity in the red and green channel via a multiplicative scale factor computed using the average intensities of the positive control probes.Briefly, Noob performs within-array normalization correcting for background fluorescence and dye bias. It fits a normal-exponential convolution model to estimate the true signal conditional on the observed intensities, capitalizing on the unique design of the Infinium I probe pairs to estimate non-specific signal from the ‘out-of-band’ intensities, the wavelength in the opposite color channel to their design  beta mixture model for the type I and type II probes separately, with probes assigned to the state with maximum probability. Beta values for the type II features are normalized by state to the distributions of the same estimated in type I features. Like Noob, it is a within-array method.SWAN is also a within-array normalization method for probe type design, but unlike BMIQ, it starts from methylated and unmethylated intensities. SWAN is based on the assumption that probes with the same number of CpGs in the probe body should have similar intensity distributions . For the methylated and unmethylated intensities separately, a random subset of type I and II probes matched on underlying CpG number are selected and quantile normalized. The intensities of the remaining probes are adjusted by linear interpolation. Consequently, the intensity distributions between two probe types are identical in each subset, while the difference in overall distributions between two probe types still remains.In contrast to the first three methods, the Dasen method is a between-sample normalization method, and like Noob and SWAN, it adjusts the raw intensities instead of Beta values. The background of type I probes is adjusted to match that of the type II and standard quantile normalization applied to methylated and unmethylated intensities separately by probe type (I or II).SQN is another between-sample normalization method for methylated and unmethylated intensities that also involves within-sample normalization of type I and II probes. Type II intensities are normalized across arrays, and within arrays, type I intensities are normalized to the type II distributions within four feature subsets  . The stm = 2 principle components of the summarized measures chosen as covariates for intensity adjustment. Adjustment is performed separately in methylated and unmethylated intensities, and in type I and II probes. For probes mapped to X and Y chromosomes, males and females are processed separately, with ordinary quantile normalization used for probes on the Y chromosome because of the small number of probes (N = 416). By default the functional normalization is applied after Noob in the current version of minfi package (version 1.6.0).Funnorm is a between-sample  normalization method that attempts to remove unwanted variation by adjusting for covariates estimated from a control probe matrix. Briefly, 42 summary measures are estimated from the combined 848 control probes and type I ‘out-of-band’ intensities, with the first The summary of data preprocessing methods used in this study is shown in Additional file Five datasets are used to evaluate the different processing methods. One contains six technical replicates from human peripheral blood lymphocytes (PBLs), and is used to investigate how the processing methods reduce technical variances. These samples were commercially bought, pooled human PBLs, and are the same as used in . The secAll samples are analyzed using the Infinium HumanMethylation450 BeadChip, and DNA methylation levels are reported as Beta (β) values, the proportion of methylation intensity to the total intensity, ranging from 0 to 1. The samples from the last three studies are divided into discovery and validation datasets for evaluating reproducibility of testing differential DNA methylation. Each processing method is performed in the discovery and validation set separately. The separate processing will not affect the Beta values for individual samples processed using within-array methods , but can affect the Beta values when using between-array processing methods . The details for defining discovery and validation data sets are described below, and summarized in Additional file We use the identical samples and study design implemented by Fortin et al. . In totaA total of 321 COAD (colon adenocarcinoma) samples (284 tumor/37 non-tumor colon) are included in this study. These samples are selected by plate to create discovery and validation datasets. No substantial plate-to-plate variation was observed in COAD dataset  and 161 are from controls, frequency matched by age and sex. Once more, discovery and validation data sets are created selecting samples by plate. A total of 180 samples across the first four plates are assigned to the discovery set (102 diseased and 78 controls) and 196 samples from the latter four plates to the validation set (113 diseased and 83 controls). These data were generated at the University of Southern California.p-values using concordance plots and ROC curves. Second, we assess overlap of differentially methylated positions (DMPs) applying the Benjamini-Yekutieli method [p <0.05). Benjamini-Yekutieli allows for correlation in test results and results in many fewer significant test results than methods that ignore correlation between test statistics.Improved measures of DNA methylation should increase our power to detect biological associations. However, evaluating our ability to detect true signals in real data is complicated by the fact that we do not know which signals are genuine. However, we can study the reproducibility of differential methylation results between different data sets. Higher reproducibility would reflect more potential for a method in revealing true signals, while poorer agreement indicates the results are more likely due to chance. We assess differential methylation by disease status for the case-control data by applying two-sample t-tests separately in discovery and validation sets. The data are analyzed on the Beta-value scale and tests are two-sided. Several tests of reproducibility are performed. First, result reproducibility is evaluated from the lists of (ranked) i method  to contrIn a concordance plot, the overlap percentage is plotted against feature list size for lists of size one to k, where the overlap percentage is defined by the proportion of features ranked in the top k in both the discovery and validation set. The processing approach with higher overlap percentages across different list sizes indicates higher reproducibility. If the data set is underpowered and the results are not reproducible, the overlap percentage follows a diagonal line through the origin, with slope equal to the inverse of the number of features. This approach has connections with the change of correspondence plot proposed for the irreproducibility rate framework .p values in the discovery subset are defined as “true signal”. For the brain data, we anticipate small differences and only select the top 100 in the discovery set as “true signals”. These same list sizes are used in [ROC curves are used to quantify, for a known gold standard, the true positive and false-positive results using all possible threshold values of a quantitative marker. Although the genuine gold standard is unknown, we use the results from the discovery subset, samples selected because they reflected lower technical variation between plates, to define the ‘gold standard’, and pick the number of true signals from a list size with high overlap percentage from the concordance plots. Specifically, for the TCGA KIRC and COAD data sets, the features from the top 100,000 ranked  used in  for evalA total of 485,512 cytosines are queried by the HM450 BeadChip array. For method evaluation, we filter probes with missing Beta values across samples. For the TCGA and brain data sets we also exclude probes mapped to the X or Y chromosomes, containing a common SNP  within 10 bp of the target cytosine, or map to multiple regions of the genome. This filtering results in 485,110 features in the PBL dataset, 371370 in KIRC, 384470 in COAD, and 360894 in the brain data set.p values are used for determining missing Beta values; the detection p-value reports the quantile from the distribution of 600 negative control probes (from the same color channel) for the larger of the methylated or unmethylated intensity. Then, the Beta value will be assigned missing if the corresponding detection p-value is more than 0.05 (not above background). This can result in a much larger number of missing Beta values than assigned in the minfi package. We use missing values assigned by the methylumi package.It is worth noting that the minfi and methylumi packages in R have different criteria in assigning missing to Beta values. In minfi, missing values (“NAs”) are assigned when both the raw methylated and unmethylated intensities are zero. Although this catches all features with failed probes that do not fluoresce, it allows features fluorescing at background levels for both M and U probes to have Beta values near 0.5. We favor the additional assignment of ‘NA’ to features that do not have at least one of the M and U intensities fluoresce above background. Such masking is applied in the methylumi package, where the detection We assess the ability of preprocessing methods to reduce technical variance and adjust type I/II bias using six technical replicates from commercially available pooled human male peripheral blood lymphoctytes (PBLs) assayed as part of a larger experiment  and prevFigure Figure We used five lung adenocarcinoma (LUAD) samples from TCGA to benchmark the post-processing HM450 Beta value estimates to estimates from WGBS. The number of features available for cross-platform comparison ranged from 110,962 to 199,441 after restricting to cytosines with a minimum sequencing depth of 10. Loess curves summarizing the relationship between the Beta values from the two platforms showed Noob + BMIQ estimates were most similar to WGBS Fig. . The Peath dimension that the cumulative proportion of variance exceeds 50 %. Case-control differences are not apparent until the 10th dimension (t-test p = 0.002)  Fig. . Figure Grey lines in Fig. We use concordance plots to present the overlap in the top ranking DMPs as a function of list size when applying the different processing methods. Combining the methods Noob with BMIQ or SWAN always showed higher reproducibility than any of the three methods alone so the results for the individual methods are not shown. For the two cancer data sets, all within-array combination methods show similar performance to one another and all show higher concordance compared to the raw data Fig.  and c. TWe note that for each of these two cancer datasets, the concordance after processing nears 85 %. However, the concordance of discoveries is above 70 % even for the raw data at a list size of 15,000 features. The overlap percentage for the raw COAD data is over 80 % for the top 50,000 features. These results are not surprising given that the separate clustering of cancer and non-cancer samples in the MDS plots reflects substantial variation in DNA methylation between groups with genuine signals very likely to be detected and reproduced. The higher homogeneity of colon control samples and their homogeneity relative to cancer samples might explain the higher reproducibility of DMPs in the COAD study see Fig. .Reproducibility for the Brain data is much lower than for the cancer data, which was not surprising either based on the earlier MDS figures. This time, the fraction of overlapping discoveries from the analysis of the raw data appears essentially random Fig. ; howeverRUVm improved result reproducibility, outperforming both SVA and ComBat. In fact ComBat showed a minor loss in reproducibility over no batch correction, suggesting there was confounding between samples and BeadChips. Applying RUVm to Noob + BMIQ processed brain data resulted in a nearly 30 % improvement in overlap percentage, achieving a max 63 % overlap in the brain data set, up from 36 % observed using normalization methods alone Fig. . The resLastly, we investigated whether our results are sensitive to the single split of the data into discovery and validation sets. We resampled the brain data ten times into new discovery and validation sets, each time computing the AUC for the raw data, the data processed with Noob + BMIQ, and the data processed with Noob + BMIQ + RUVm. There was very little overlap in distributions, with AUC interquartile ranges (IQR) 0.65-0.68 for the raw data, 0.7-0.82 for Noob + BMIQ and 0.95-0.97 for Noob + BMIQ + RUVm. This order of results held their rank, and suggested that one data split was representative, and the performance does not change with repeated sampling.In this study nine preprocessing methods for Illumina HM450 array data are applied and compared, using combinations of three within-array and three between-array methods. Since different normalization methods address different technical effects in the data, we take advantage of this diversity of approaches and combine methods addressing different mechanisms.et al. found Noob + BMIQ performed best in reducing differences between Beta values in intra-plate duplicates [a priori background correction and dye-bias normalization using Noob improved both bias and variance over type I/type II correction methods alone (BMIQ and SWAN). Analysis of paired HM450 and WGBS data showed the highest Pearson correlations after using Noob + BMIQ to process the HM450 data.Analysis of technical replicates showed that different methods optimized different assessment criterion. The within-array methods Noob + BMIQ and Noob + SWAN were favored at removing type I/type II bias, while the between-array methods Funnorm, SQN and Dasen, reduced between-sample variability the best. However, a recent paper by Lemire plicates . SQN, a et al. [When evaluation focused on detecting reproducible DMPs across different disease data sets, within-array normalization and between-array methods that relied only on control features consistently displayed the highest reproducibility. The performance of between-array methods that utilized biological features for normalization depended on the characteristics of the data set. When disease state was not associated with the principal scaling dimension, between-array methods tended to improve sensitivity of reproduced signals. Still, they never outperformed the best within-array methods. Furthermore, when the biological signal was strong, they had the potential to behave worse than no processing at all. This was the case for the COAD data set for which the first two principal scaling dimensions were both associated with disease status. It also agreed with the separate finding of a lower validation rate after SQN by Wu et al. . OverallWe evaluated three batch-correction methods capable of removing additional variation not accounted for by data processing , to see whether they could improve the low reproducibility of DMPs in the brain data. Both RUVm and SVA improved reproducibility, however using ComBat to adjust for BeadChip effects reduced it. This suggested that there was confounding of case-control comparisons by BeadChip. Application of RUVm increased DMP reproducibility in the brain data the most, and interestingly, a large variation in performance appeared depending on the preprocessing method applied; Noob + BMIQ turned in substantially superior reproducibility compared to competing approaches.Finally, Beta regression has been proposed as a more powerful test of differential DNA methylation than t-tests . HoweverThis study provides a comprehensive comparison of the currently popular normalization methods in processing HM450 array data. Combinations of methods are applied and compared in five data sets, ranging from cancer data to Alzheimer’s brain data, and showing distinctly different variation in DNA methylation. We find that the combination of Noob + BMIQ, a within-array method, performs well in reducing technical variance, adjusting typeI/II bias, and gaining reproducibility in differential methylation analysis. At the same time, the between-array normalization methods might hurt the data when there are global methylation alterations. For differential DNA methylation analysis RUVm was the most powerful batch correction method, and it performed best on data first processed with Noob + BMIQ. The combination of methods and comprehensive comparisons in our study provide valuable insights in processing HM450 BeadChip data.


DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression. The DESeq2 package is available at http://www.bioconductor.org/packages/release/bioc/html/DESeq2.html.In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-seq, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present The online version of this article (doi:10.1186/s13059-014-0550-8) contains supplementary material, which is available to authorized users. The rapid adoption of high-throughput sequencing (HTS) technologies for genomic studies has resulted in a need for statistical methods to assess quantitative differences between experiments. An important task here is the analysis of RNA sequencing (RNA-seq) data with the aim of finding genes that are differentially expressed across groups of samples. This task is general: methods for it are typically also applicable for other comparative HTS assays, including chromatin immunoprecipitation sequencing, chromosome conformation capture, or counting observed taxa in metagenomic studies.Besides the need to account for the specifics of count data, such as non-normality and a dependence of the variance on the mean, a core challenge is the small number of samples in typical HTS experiments – often as few as two or three replicates per condition. Inferential methods that treat each gene separately suffer here from lack of power, due to the high uncertainty of within-group variance estimates. In high-throughput assays, this limitation can be overcome by pooling information across genes, specifically, by exploiting assumptions about the similarity of the variances of different genes measured in the same experiment .edgeR DESeq2 peS [EBSeq . Other m package  and the  package . For theffdiff 2  method orocedure .Sensitivity and precision We simulated datasets of 10,000 genes with negative binomial distributed counts. To simulate data with realistic moments, the mean and dispersions were drawn from the joint distribution of means and gene-wise dispersion estimates from the Pickrell et al. data, fitting only an intercept term. These datasets were of varying total sample size , and the samples were split into two equal-sized groups; 80% of the simulated genes had no true differential expression, while for 20% of the genes, true fold changes of 2, 3 and 4 were used to generate counts across the two groups, with the direction of fold change chosen randomly. The simulated differentially expressed genes were chosen uniformly at random among all the genes, throughout the range of mean counts. MA-plots of the true fold changes used in the simulation and the observed fold changes induced by the simulation for one of the simulation settings are shown in Additional file P value <0.1 among the genes with true differences between group means. The precision was calculated as the fraction of genes with true differences between group means among those with adjusted P value <0.1. The sensitivity is plotted over 1−precision, or the FDR, in Figure DESeq2, and also edgeR, often had the highest sensitivity of the algorithms that controlled type-I error in the sense that the actual FDR was at or below 0.1, the threshold for adjusted P values used for calling differentially expressed genes. DESeq2 had higher sensitivity compared to the other algorithms, particularly for small fold change (2 or 3), as was also found in benchmarks performed by Zhou et al. [Algorithms’ performance in the simulation benchmark was assessed by their sensitivity and precision. The sensitivity was calculated as the fraction of genes with adjusted u et al. . For larDESeq tool can be observed, with reduced sensitivity compared to the other algorithms and an actual FDR less than the nominal value of 0.1. We note that EBSeq version 1.4.0 by default removes low-count genes – whose 75% quantile of normalized counts is less than ten – before calling differential expression. The sensitivity of algorithms on the simulated data across a range of the mean of counts are more closely compared in Additional file The overly conservative calling of the old Outlier sensitivity We used simulations to compare the sensitivity and specificity of DESeq2’s outlier handling approach to that of edgeR, which was recently added to the software and published while this manuscript was under review. edgeR now includes an optional method to handle outliers by iteratively refitting the GLM after down-weighting potential outlier counts [edgeR-robust had slightly higher actual than nominal FDR, as seen in Additional file r counts . The simPrecision of fold change estimates We benchmarked the DESeq2 approach of using an empirical prior to achieve shrinkage of LFC estimates against two competing approaches: the GFOLD method, which can analyze experiments without replication [edgeR package, which provides a pseudocount-based shrinkage termed predictive LFCs. Results are summarized in Additional file DESeq2 had consistently low root-mean-square error and mean absolute error across a range of sample sizes and models for a distribution of true LFCs. GFOLD had similarly low error to DESeq2 over all genes; however, when focusing on differentially expressed genes, it performed worse for larger sample sizes. edgeR with default settings had similarly low error to DESeq2 when focusing only on the differentially expressed genes, but had higher error over all genes.lication  and can Clustering We compared the performance of the rlog transformation against other methods of transformation or distance calculation in the recovery of simulated clusters. The adjusted Rand index [PoiClaClu package [plotMDS function of edgeR . The results, shown in Additional file nd index  was used package , and a dWhile simulation is useful to verify how well an algorithm behaves with idealized theoretical data, and hence can verify that the algorithm performs as expected under its own assumptions, simulations cannot inform us how well the theory fits reality. With RNA-seq data, there is the complication of not knowing fully or directly the underlying truth; however, we can work around this limitation by using more indirect inference, explained below.In the following benchmarks, we considered three performance metrics for differential expression calling: the false positive rate (or 1 minus the specificity), sensitivity and precision. We can obtain meaningful estimates of specificity from looking at datasets where we believe all genes fall under the null hypothesis of no differential expression . SensitiFalse positive rate To evaluate the false positive rate of the algorithms, we considered mock comparisons from a dataset with many samples and no known condition dividing the samples into distinct groups. We used the RNA-seq data of Pickrell et al. [P values less than 0.01 by the total number of tests; genes with zero sum of read counts across samples were excluded. The results over the 30 replications, summarized in Figure DESeq (old) and Cuffdiff 2 appeared overly conservative in this analysis, not using up their type-I error budget.l et al.  for lympSensitivity To obtain an impression of the sensitivity of the algorithms, we considered the Bottomly et al. [DESeq (old), DESeq2, DSS, edgeR or voom algorithms, which can accommodate complex experimental designs, to have comparable calls across all algorithms.y et al.  dataset,P value <0.1 in the larger verification set, as diagrammed in Additional file We rotated though each algorithm to determine the calls of the verification set. For a given algorithm’s verification set calls, we tested the evaluation set calls of every algorithm. We used this approach rather than a consensus-based method, as we did not want to favor or disfavor any particular algorithm or group of algorithms. Sensitivity was calculated as in the simulation benchmark, now with true differential expression defined by an adjusted DESeq2 had comparable sensitivity to edgeR and voom though less than DSS. The median sensitivity estimates were typically between 0.2 and 0.4 for all algorithms. That all algorithms had relatively low median sensitivity can be explained by the small sample size of the evaluation set and the fact that increasing the sample size in the verification set increases power. It was expected that the permutation-based SAMseq method would rarely produce adjusted P value <0.1 in the evaluation set, because the three vs three comparison does not enable enough permutations.The ranking of algorithms was generally consistent regardless of which algorithm was chosen to determine calls in the verification set. Precision Another important consideration from the perspective of an investigator is the precision, or fraction of true positives in the set of genes which pass the adjusted P value threshold. This can also be reported as 1−FDR. Again, ‘true’ differential expression was defined by an adjusted P value <0.1 in the larger verification set. The estimates of precision are displayed in Figure DESeq2 often had the second highest median precision, behind DESeq (old). We can also see that algorithms with higher median sensitivity, e.g., DSS, were generally associated here with lower median precision. The rankings differed significantly when Cuffdiff 2 was used to determine the verification set calls. This is likely due to the additional steps Cuffdiff 2 performed to deconvolve changes in isoform-level abundance from gene-level abundance, which apparently came at the cost of lower precision when compared against its own verification set calls.P values . Having thus calibrated each algorithm to a target FDR, we evaluated the sensitivity of calling, as shown in Additional file DESeq2 often was among the top algorithms by median sensitivity, though the variability across random replicates was larger than the differences between algorithms.To compare the sensitivity and precision results further, we calculated the precision of algorithms along a grid of nominal adjusted  FDR = 0.. Having The absolute number of calls for the evaluation and verification sets can be seen in Additional file DESeq2 effectively controlled type-I errors, maintaining a median false positive rate just below the chosen critical value in a mock comparison of groups of samples randomly chosen from a larger pool. For both simulation and analysis of real data, DESeq2 often achieved the highest sensitivity of those algorithms that controlled the FDR.In summary, the benchmarking tests showed that DESeq2 offers a comprehensive and general solution for gene-level analysis of RNA-seq data. Shrinkage estimators substantially improve the stability and reproducibility of analysis results compared to maximum-likelihood-based solutions. Empirical Bayes priors provide automatic control of the amount of shrinkage based on the amount of information for the estimated quantity available in the data. This allows DESeq2 to offer consistent performance over a large range of data types and makes it applicable for small studies with few replicates as well as for large observational studies. DESeq2’s heuristics for outlier detection help to recognize genes for which the modeling assumptions are unsuitable and so avoids type-I errors caused by these. The embedding of these strategies in the framework of GLMs enables the treatment of both simple and complex designs.A critical advance is the shrinkage estimator for fold changes for differential expression analysis, which offers a sound and statistically well-founded solution to the practically relevant problem of comparing fold change across the wide dynamic range of RNA-seq experiments. This is of value for many downstream analysis tasks, including the ranking of genes for follow-up studies and association of fold changes with other variables of interest. In addition, the rlog transformation, which implements shrinkage of fold changes on a per-sample basis, facilitates visualization of differences, for example in heat maps, and enables the application of a wide range of techniques that require homoskedastic input data, including machine-learning or ordination techniques such as principal component analysis and clustering.DESeq2 hence offers to practitioners a wide set of features with state-of-the-art inferential power. Its use cases are not limited to RNA-seq data or other transcriptomics assays; rather, many kinds of high-throughput count data can be used. Other areas for which DESeq or DESeq2 have been used include chromatin immunoprecipitation sequencing assays , bar package ), metage package ), riboso package  and CRIS package . Finallytructure  and comeA summary of the notation used in the following section is provided in Additional file Kij for gene i in sample j is described with a GLM of the negative binomial family with a logarithmic link:The read count DESeq2 software reports estimated model coefficients and their estimated standard errors on the log2 scale.For notational simplicity, the equations here use the natural logarithm as the link function, though the sij are considered constant within a sample, sij=sj, and are estimated with the median-of-ratios method previously described and used in DESeq [DEXSeq [By default, the normalization constants in DESeq  and DEXS [DEXSeq :\documesij calculated using other methods , which R statistical language. In linear modeling, a categorical variable or factor can take on two or more values or levels. In standard design matrices, one of the values is chosen as a reference value or base level and absorbed into the intercept. In standard GLMs, the choice of base level does not influence the values of contrasts (LFCs). This, however, is no longer the case in our approach using ridge-regression-like shrinkage on the coefficients (described below), when factors with more than two levels are present in the design matrix, because the base level will not undergo shrinkage while the other levels do.For consistency with our software’s documentation, in the following text we will use the terminology of the DESeq2 uses expanded design matrices, which include an indicator variable for each level of each factor, in addition to an intercept column . While such a design matrix no longer has full rank, a unique solution exists because the zero-centered prior distribution (see below) provides regularization. For dispersion estimation and for estimating the width of the LFC prior, standard design matrices are used.To recover the desirable symmetry between all levels, Contrasts between levels and standard errors of such contrasts can be calculated as they would in the standard design matrix case, i.e., using:where αi follows a log-normal prior distribution that is centered around a trend that depends on the gene’s mean normalized read count:We assume the dispersion parameter αtr is a function of the gene’s mean normalized count,σd is the width of the prior, a hyperparameter describing how much the individual genes’ true dispersions scatter around the trend. For the trend function, we use the same parametrization as we used for DEXSeq [Here, r DEXSeq , namely,αtr. Finally, we combine the likelihood with the trended prior to get maximum a posteriori (MAP) values as final dispersion estimates. Details for the three steps follow.We get final dispersion estimates from this model in three steps, which implement a computationally fast approximation to a full empirical Bayes treatment. We first use the count data for each gene separately to get preliminary gene-wise dispersion estimates Gene-wise dispersion estimates To get a gene-wise dispersion estimate for a gene i, we start by fitting a negative binomial GLM without an LFC prior for the design matrix X to the gene’s count data. This GLM uses a rough method-of-moments estimate of dispersion, based on the within-group variances and means. The initial GLM is necessary to obtain an initial set of fitted values, fNB is the probability mass function of the negative binomial distribution with mean μ and dispersion α, and the second term provides the Cox–Reid bias adjustment [edgeR, corrects for the negative bias of dispersion estimates from using the MLEs for the fitted values XtWX), where W is the diagonal weight matrix from the standard iteratively reweighted least-squares algorithm. As the GLM’s link function is g(μ)= log(μ) and its variance function is V=μ+αμ2, the elements of the diagonal matrix Wi are given by:where justment . This adjustment  and thenjustment  in edgeRils, see , Sectionα using a backtracking line search with accepted proposals that satisfy Armijo conditions [The optimization in Equation  is perfonditions .Dispersion trend A parametric curve of the form .μ and dispersion α. Its variance v=μ+αμ2 has two components, v=vP+vD, the Poisson component vP=μ independent of α, and the overdispersion component vD=αμ2. When μ is small, μ≲1/α .where mad stands for the median absolute deviation, divided as usual by the scaling factor Three or less residuals degrees of freedom When there are three or less residual degrees of freedom (number of samples minus number of parameters to estimate), the estimation of the prior variance m−p) to account for the scaling of the χ2 distribution. We repeat the simulation over a grid of values for Final dispersion estimate We form a logarithmic posterior for the dispersion from the Cox–Reid adjusted logarithmic likelihood , above For such genes, the gene-wise estimate βir of model (βi0):To incorporate empirical Bayes shrinkage of LFCs, we postulate a zero-centered normal prior for the coefficients of model  that repDESeq2’s approach can be seen as an extension of these approaches for stable estimation of gene-expression fold changes to count data.As was observed with differential expression analysis using microarrays, genes with low intensity values tend to suffer from a small signal-to-noise ratio. Alternative estimators can be found that are more stable than the standard calculation of fold change as the ratio of average observed values for each condition -55. DESeEmpirical prior estimate To obtain values for the empirical prior widths σr for the model coefficients, we again approximate a full empirical Bayes approach, as with the estimation of dispersion prior, though here we do not subtract the expected sampling variance from the observed variance of maximum likelihood estimates. The estimate of the LFC prior width is calculated as follows. We use the standard iteratively reweighted least-squares algorithm [r of the design matrix (except for the intercept), a zero-centered normal distribution to the empirical distribution of MLE fold change estimates lgorithm  for eachσr is chosen such that the (1−p) empirical quantile of the absolute value of the observed LFCs, p/2) theoretical quantile of the prior, p is set by default to 0.05. If we write the theoretical upper quantile of a normal distribution as QN(1−p) and the empirical upper quantile of the MLE LFCs as To make the fit robust against outliers with very high absolute LFC values, we use quantile matching: the width σr will be independent of the choice of base level, the estimates from the quantile matching procedure are averaged for each factor over all possible contrasts of factor levels. When determining the empirical upper quantile, extreme LFC values , i.e., the logarithm of the density of the normal prior (up to an additive constant), can be read as a ridge penalty term, and therefore, we perform the optimization using the iteratively reweighted ridge regression algorithm [weighted updates [The term lgorithm , also kn updates . SpecifiFisher information. The effect of the zero-centered normal prior can be understood as shrinking the MAP LFC estimates based on the amount of information the experiment provides for this coefficient, and we briefly elaborate on this here. Specifically, for a given gene i, the shrinkage for an LFC βir depends on the observed Fisher information, given byβir. For a negative binomial GLM, the observed Fisher information, or peakedness of the logarithm of the profile likelihood, is influenced by a number of factors including the degrees of freedom, the estimated mean counts μij, and the gene’s dispersion estimate αi. The prior influences the MAP estimate when the density of the likelihood and the prior are multiplied to calculate the posterior. Genes with low estimated mean values μij or high dispersion estimates αi have flatter profile likelihoods, as do datasets with few residual degrees of freedom, and therefore in these cases the zero-centered prior pulls the MAP estimate from a high-uncertainty MLE closer toward zero.βir divided by its estimated standard error SE(βir) to a standard normal distribution. The estimated standard errors are the square root of the diagonal elements of the estimated covariance matrix, Σi, for the coefficients, i.e., P values from the subset of genes that pass the independent filtering step are adjusted for multiple testing using the procedure of Benjamini and Hochberg [The Wald test compares the beta estimate cs using  and 4)..βir diviHochberg .under the null hypothesis [DESeq2 is the mean of normalized counts for a gene, while the test statistic is p, the P value from the Wald test. We first consider the case where the size factors are equal and where the gene-wise dispersion estimates are used for each gene, i.e. without dispersion shrinkage. The distribution family for the negative binomial is parameterized by θ=. Aside from discreteness of p due to low counts, for a given μ, the distribution of p is Uniform under the null hypothesis, so p is an ancillary statistic. The sample mean of counts for gene i, μ. Then from Basu’s theorem, p are independent.Independent filtering does not compromise type-I error control as long as the distribution of the test statistic is marginally independent of the filter statistic pothesis , and we p under the null hypothesis, DESeq2 does not use the distribution of p in its estimation procedure – for example, DESeq2 does not estimate the proportion of null genes using the distribution of p – so this kind of dependence of p on μ does not lead to increased type-I error.While for very low counts, one can observe discreteness and non-uniformity of normalized counts should also provide uniformly distributed p as with conditioning on the mean of counts, p, as one condition could have positive counts and the other condition often zero counts. This could lead to non-uniformity of p under the null hypothesis; however, such a pathological case would pose problems for many statistical tests of differences in mean.If the size factors are not equal across samples, but not correlated with condition, conditioning on the mean of p across the range of mean normalized counts. Despite spikes in the distribution for the genes with the lowest mean counts due to discreteness of the data, these densities were nearly uniform across the range of average expression strength.We used simulation to demonstrate that the independence of the null distribution of the test statistic from the filter statistic still holds for dispersion shrinkage. Additional file DESeq2 offers tests for composite null hypotheses of the form θ>0. The composite null hypothesis is replaced by two simple null hypotheses: P values are generated by integrating a normal distribution centered on θ with standard deviation SE(βir) from |βir| toward ∞. The value of the integral is then multiplied by 2 and thresholded at 1. This procedure controls type-I error even when βir=±θ, and is equivalent to the standard DESeq2P value when θ=0.P value is constructed as the maximum of two one-sided tests of the simple null hypotheses: P values are generated by integrating a normal distribution centered on θ with standard deviation SE(βir) from βir toward −∞, and integrating a normal distribution centered on −θ with standard deviation SE(βir) from βir toward ∞.Conversely, when searching for genes whose absolute LFC is significantly below a threshold, i.e., when testing the null hypothesis DESeq2 requires that no prior has been used when testing the null hypothesis of large LFCs, so that the data alone must provide evidence against the null hypothesis.Note that while a zero-centered prior on LFCs is consistent with testing the null hypothesis of small LFCs, it should not be used when testing the null hypothesis of large LFCs, because the prior would then favor the alternative hypothesis. DESeq2 LFC estimation steps are used for experimental designs with interaction terms. First, when any interaction terms are included in the design, the LFC prior width for main effect terms is not estimated from the data, but set to a wide value  of the normalized counts plus a pseudocount of The rlog transformation is calculated as follows. The experimental design matrix quations  and 2)  X is subi and sample j, Cook’s distance for GLMs is given by [Rij is the Pearson residual of sample j, τ is an overdispersion parameter , p is the number of parameters including the intercept, and hjj is the jth diagonal element of the hat matrix H:The MLE of given by :\documeRij are calculated asμij is estimated by the negative binomial GLM without the LFC prior, and using the variance function V(μ)=μ+αμ2. A method-of-moments estimate Pearson residuals DESeq2 is implemented as a package for the R statistical environment and is available [SummarizedExperiment class of the GenomicRanges package [SummarizedExperiment objects containing count matrices can be easily generated using the summarizeOverlaps function of the GenomicAlignments package [htseq-count script [easyRNASeq [featureCount [vailable  as part vailable . The cou package . Summari package . This wot script  and the syRNASeq  and featureCount .DESeq2 package comes with a detailed vignette, which works through a number of example differential expression analyses on real datasets, and the use of the rlog transformation for quality assessment and visualization. A single function, called DESeq, is used to run the default analysis, while lower-level functions are also available for advanced users.The summarizeOverlaps function of the GenomicRanges package [et al. [Homo sapiens reference sequence GRCh37 downloaded in March 2013 from Illumina iGenomes. Reads were counted in the genes defined by the Ensembl GTF file, release 70, contained in the Illumina iGenome. The sequence read archive fastq files of the Bottomly et al. [Mus musculus reference sequence NCBIM37 downloaded in March 2013 from Illumina iGenomes. Reads were counted in the genes defined by the Ensembl GTF file, release 66, contained in the Illumina iGenome.Reads were aligned using the TopHat2 aligner , and ass package . The seq [et al.  dataset y et al.  dataset DESeq2paper [Sweave vignettes for reproducing all figures and tables in this paper, including data objects for the experiments mentioned, and code for aligning reads and for benchmarking, can be found in a package eq2paper .


We describe a new signature definition and analysis method to be used as biomarker for early cancer detection. Our new approach is based on the construction of a reference map of transcriptional signatures of both healthy and cancer affected individuals using circulating miRNA from a large number of subjects. Once such a map is available, the diagnosis for a new patient can be performed by observing the relative position on the map of his/her transcriptional signature. To demonstrate its efficacy for this specific application we report the results of the application of our method to published datasets of circulating miRNA, and we quantify its performance compared to current state-of-the-art methods. A number of additional features make this method an ideal candidate for large-scale use, for example, as a mass screening tool for early cancer detection or for at-home diagnostics. Specifically, our method is minimally invasive (because it works well with circulating miRNA), it is robust with respect to lab-to-lab protocol variability and batch effects , and it is scalable to a large number of subjects. Finally we discuss the need for HPC capability in a widespread application of our or similar methods. A growing body of evidence is pointing to the potential role of microRNA (miRNA) profiles as biomarkers for the early detection, classification, and/or prognosis of a growing list of cancer types . The Our signature generation and analysis method is part of a class of algorithms based on the ranking of the expression values obtained for each sample  and on tThe rank-based signature method is quite general and can be applied to any phenomenon that produces a differential transcriptional signature of detectable magnitude. In a previous work we have detailed the advantages of this approach when applied to the definition and analysis of diagnostic signatures . SpecifiThese benefits are particularly valuable in the analysis of circulating miRNA as biomarkers for cancer, given that the role and degree of involvement of most miRNA's in pathogenesis is still unclear and that the search for accurate biomarkers is still open for many types of pathologies. The robustness to differences in lab protocols and batch effects makes it particularly suitable for a clinical use in which such sources of confounding signals are often unavoidable.In this paper we present a new application of our method and make a case for its suitability for large-scale use, for example, as a mass screening tool for early cancer detection or for at-home diagnostics. The novelties with respect to previous works are in (i) the application of the method , (ii) the type of diagnosis to be performed (early detection of cancer), and (iii) the type of data used as input (circulating miRNA). These aspects are all connected. For example, in the case of mass screenings for the early detection of cancer, the tool needs to be minimally invasive (hence the use of circulating miRNA), must have demonstrated efficacy for this specific application , and must be scalable to a large number of subjects .The conceptual novelty that we introduce is a notion of sample-specific signature, coupled with a metric to quantify the degree of similarity between any two such signatures. Contrary to current practices, instead of evaluating expression profiles by means of a common yardstick (a single list of highly discriminating RNA species), our method first seeks to summarize the characteristics of each sample employing a specific signature, and then it performs a systematic, all-to-all signature comparison. The expected result is the emergence of a partitioning of the set of samples in separate groups on the basis of signature similarity. The classification problem is then reduced to the simpler task of identifying the phenotype associated with each of the resulting groups, in what we call the labeling step. In order to facilitate the partitioning step, a similarity map of the samples is constructed in the form of an undirected graph, in which samples are represented as nodes and sample-to-sample edges are drawn with a length inversely proportional to the degree of mutual similarity. After applying our method to a large number of expression profile sets, we have indeed observed a marked tendency of nodes to spontaneously cluster into clearly visible groups. The relatively simple final labeling step can be carried out using one of many possible empirical methods, for example, by noting the membership of a few additional samples whose classification is known a priori.n1 and the last n2 miRNA species IDs (or probe IDs) in the ranking; in other words, our composite signature is composed by the identity of the n1 most expressed and n2 least expressed genes. The values of n1 and n2 are two input parameters of our method . Interestingly, this preselection step was not required with early generation miRNA microarrays containing 400–700 probes but has become a necessity with current generation arrays having typically in excess of ~1000 probes. Since our method has been shown to work well with the 20 K+ probes of typical DNA microarrays without any preselection, we attribute the need for this extra step to the diluting effect of the large percentage of control probes added in latest generation miRNA microarrays.As a second step, we perform what is called a feature selection operation on the list of miRNA species, using a relatively low threshold . In other words, we apply our method not to all the probes in the array, but only to the subset of those showing statistically significant differences between control and affected groups, as determined by a Mann-Whitney The pseudocode, reported in top + ESbottom)/2).The distance between each pair of samples is computed by (i) finding the enrichment score (ES)  of the sN% of distances are selected and thus represented as edges of corresponding length in the map; typically, the N = 10% shortest distances are sufficient to produce a clear map.In the map construction step, the resulting distances are employed to draw a map of the testing set samples with the help of a tool such as Cytoscape . The mapn1, n2, N, in order to increase the cluster separation in the resulting map. Once a satisfactory partitioning is achieved, the relatively simple step of assigning a control/affected phenotype label to each cluster can be performed according to a number of empirical methods, for example, by adding a few labeled samples from the training dataset or inspecting the sign of the expression change of disease genes, that is, genes known from the literature to be associated with the condition under study. The overall procedure is illustrated by the diagram in The analysis of the resulting map represents the last and crucial step of the method. Most of the time this map can be easily partitioned in clusters or modules  by hand; if however the clusters are not easily delineated, the partitioning can be performed with the help of one of the many unsupervised community identification algorithms described in the literature . AdditiP < 0.05 constrained by at least twofold expression change as selection criteria, they found that 31 miRNAs were differentially expressed in CA study subjects (17 up and 14 down) and 18 miRNAs were differentially expressed in AA study subjects (9 up and 9 down). Interestingly, only 2 differentially expressed miRNAs overlapped between CA and AA study subjects.A necessary condition for the use of any transcriptional signature as biomarker for cancer is that the healthy versus cancer miRNA transcriptional profiles are sufficiently divergent to produce a map of practically relevant discriminatory value. A number of recent results have examined the validity of this hypothesis for a number of cancer types. The work by Zhao et al.  providesWhile the work by Zhao et al. is a genome-wide study, it focuses on identifying single miRNAs as biomarkers. Our work instead is based on a complex signature as a biomarker and, in this respect, is closer to the work by Boeri et al.  on circuP_value = 0.1) selected 184 species for the AA group and 316 species for the CA group. Using our method, we measured the reciprocal distances between the twenty samples in each group and then we drew a map based on such distances. The values of the signature size that gave the best results in terms of separation of the two groups in the final graph were n1 = n2 = 25 for AA and n1 = n2 = 50 for CA. For the sake of clarity we only represented distances falling below a suitably chosen threshold , as large distances are obviously less interesting. The map is in the form of undirected graph and was drawn using Cytoscape; the layout is the one produced by Cytoscape with the force-directed method (force is interpreted as 1-distance).We analysed the expression data described in the Zhao et al. paper (GEO accession GSE22981); as done in the Zhao paper, we analysed the AA and the CA group separately. The profiles in the dataset were obtained with the Illumina Human v2 MicroRNA Expression BeadChips platform, were used as downloaded from the GEO repository, and included 1134 miRNA species after removing those with missing values. Of these, the feature selection step . The profiles included 141 miRNA species, of which 51 were selected in the feature selection step. In the Bianchi et al. paper the dataset was divided in two subsets, used for training and testing, respectively; we treated the profiles as a single set. The resulting map is shown in In order to quantify the predictive power of our method as biomarker of early cancer we tested it on the dataset from the paper of Bianchi et al. . In suchAs described before, the diagnosis for a new subject can be obtained by adding his/her profile to the input dataset and noticing in which group the new node is going to fall. The one shown in Our new approach to biomarker definition has been recently validated in an open international competition, the SBV IMPROVER Diagnostic Biomarker Challenge, organized by IBM Research and Philip Morris International to evaluate and compare state-of-the-art approaches to the identification of diagnostic biomarkers based on gene expression profiles . In the One major advantage of diagnostic signatures based on expression profiles with respect to existing practices is that a test based on circulating miRNA biomarkers is inherently much less invasive than a mammography or a colonoscopy. Furthermore the method described here for blood miRNA is also being tested on urine and saliva miRNA, making it not only even less invasive, but also potentially suitable for self-administration once a suitable simplified quantification/profiling technology has been developed. The twist is that the result of a test, in the form of a miRNA profile for a certain individual, needs to be interpreted by comparing it with a number of other (known) profiles in order to produce a diagnosis. Therefore, it is easy to envision a scenario in which dedicated on-line repositories maintain both the clinical and the transcriptomic data of millions of individuals. Such repository would provide the real-time interpretation of newly produced miRNA profiles as a service, while ensuring compliance with the current privacy regulations on the handling of sensitive data. The necessity of an HPC capability to provide such service is compound by the fact that expression profiles might be compared to several reference datasets , each relative to a type of cancer or of other disease, and that such datasets will be dynamically updated based on advances of our understanding of subtypes of cancer, their treatment, histological classification, and so forth.The signature definition and analysis algorithm presented here is not particularly computationally intensive as long as the analysis is restricted to a modest number of samples . The execution times for the datasets described in the previous sections (~40 profiles of ~1 K miRNA species) are on the order of 10 seconds, using GNU Octave 3.6.4  on a Win3 to 106), times (ii) the collection of certified profiles used for the reference map (102 to 103), times (iii) the types of cancers to be tested for (100 to 102), times (iv) the number of times an individual will be tested in his/her lifetime (101 to 102). The HPC platform selected for the task would have to meet not only the computational requirements but also the storage requirements needed for holding and making available online the large body of reference datasets plus the individual medical data. Such levels of hardware performance are comparable to those currently achieved by large search engines like Google and therefore might adopt the same large-scale server farm architecture [However, the possibility of using the algorithm as a part of a mass screening program for the early detection of cancer would require scaling up its execution capability by several orders of magnitude. Such scaling up would be needed to accommodate (i) the potential number of subjects tested , it would be advisable to periodically perform a diagnostic test like the one described here, generalizing the preventive approach already being implemented in current screening campaigns for the early detection of breast and colon cancers.


Regression Analysis of Combined Expression Regulation), which fits the mRNA expression as response using as explanatory variables, the TF data from ENCODE, and CNV, DM, miRNA expression signals from TCGA. Briefly, RACER first infers the sample-specific regulatory activities by TFs and miRNAs, which are then used as inputs to infer specific TF/miRNA-gene interactions. Such a two-stage regression framework circumvents a common difficulty in integrating ENCODE data measured in generic cell-line with the sample-specific TCGA measurements. As a case study, we integrated Acute Myeloid Leukemia (AML) data from TCGA and the related TF binding data measured in K562 from ENCODE. As a proof-of-concept, we first verified our model formalism by 10-fold cross-validation on predicting gene expression. We next evaluated RACER on recovering known regulatory interactions, and demonstrated its superior statistical power over existing methods in detecting known miRNA/TF targets. Additionally, we developed a feature selection procedure, which identified 18 regulators, whose activities clustered consistently with cytogenetic risk groups. One of the selected regulators is miR-548p, whose inferred targets were significantly enriched for leukemia-related pathway, implicating its novel role in AML pathogenesis. Moreover, survival analysis using the inferred activities identified C-Fos as a potential AML prognostic marker. Together, we provided a novel framework that successfully integrated the TCGA and ENCODE data in revealing AML-specific regulatory program at global level.Gene expression is a combinatorial function of genetic/epigenetic factors such as copy number variation (CNV), DNA methylation (DM), transcription factors (TF) occupancy, and microRNA (miRNA) post-transcriptional regulation. At the maturity of microarray/sequencing technologies, large amounts of data measuring the genome-wide signals of those factors became available from Encyclopedia of DNA Elements (ENCODE) and The Cancer Genome Atlas (TCGA). However, there is a lack of an integrative model to take full advantage of these rich yet heterogeneous data. To this end, we developed RACER ( Recent studies from The Cancer Genome Atlas (TCGA) showed that most Acute Myeloid Leukemia (AML) patients lack DNA mutations, which can potentially explain the tumorigenesis, and motivated a systematic approach to elucidate aberrant molecular signatures at the transcriptional and epigenetic levels. Using recently available data from two large consortia namely Encyclopedia of DNA Elements and TCGA, we developed a novel computational model to infer the regulatory activities of the expression regulators and their target genes in AML samples. Our analysis revealed 18 regulators whose dysregulation contributed significantly to explaining the global mRNA expression changes. Encouragingly, the inferred activities of these regulatory features followed a consistent pattern with cytogenetic phenotypes of the AML patients. Among these regulators, we identified microRNA hsa-miR-548p, whose regulatory relationships with leukemia-related genes including YY1 suggest its novel role in AML pathogenesis. Additionally, we discovered that the inferred activities of transcription factor C-Fos can be used as a prognostic marker to characterize survival rate of the AML patients. Together, we demonstrated an effective model that can integrate useful information from a large amount of heterogeneous data to dissect regulatory effects. Furthermore, the novel biological findings from this study may be constructive to future experimental research in AML. One of the most intriguing questions in molecular biology is to decipher condition-specific transcription programs in complex organisms such as human At the maturity of several high-throughput technologies, large-scale expression profiling of long and small RNAs by microarray or RNA-sequencing (RNA-seq) across hundreds of human samples as well as genome-wide interrogation of TF occupancy by chromatin immunoprecipitation sequencing (ChIP-seq) have become increasingly permissive. In particular, two major consortia namely Encyclopedia of DNA Elements (ENCODE) With the availability of these huge amount of the data, there is an urgent need of developing computational models to effectively integrate heterogeneous data from multiple platforms and provide insightful directions for further focused research. Using ENCODE ChIP-seq data, Recently, Regression Analysis of Combined Expression Regulation), lies in its ability to infer sample-specific TF activities using ENCODE TF binding data derived from a generic cell-line and then using the estimated regulatory activities to infer miRNA/TF-gene regulatory relationships across samples. As a case study, we choose Acute Myeloid Leukemia (AML) for the following reasons. Various high quality genome-wide measurements  of a large cohort of 173 AML patients have very recently become available from TCGA (2013), providing a unique opportunity to study one of the most prevalent cancers In this study, we propose a novel two-stage regression framework that integrates data from both TCGA and ENCODE. The novelty of our model, named RACER  and their cognate mRNA targets. To this end, we took a reverse engineering approach in attempt to explain the gene expression by integrating transcriptional regulators, whose genome-wide measurements have recently become available from TCGA sample-specific TF and miRNA activities  that is specifically designed to integrate the above-mentioned explanatory variables to tackle this problem. Suppose there are In the AML data, To justify our model formalism, we compared the full RACER model with the models excluding one of the variables in terms of their abilities to explain expression changes in AML. Specifically, we performed a 10-fold cross-validation (CV) by training the full or reduced models on 90% of the genes and tested their predictions on the held-out 10%. The CV was carried out per sample-basis. After each CV run, we obtained the Spearman rank correlation bove 60% . Becausegenes within each sample samples for each gene relative performance gained by the full model comparing with the reduced models, which is remarkably consistent at both regression stages.The above correlation is based on the results after stage 1 regression (Eq 1). We also performed a similar model comparison using the predicted gene expression after stage 2 regression (Eq 2) and obtained consistent results . Notablya points . Due to a points . NonetheFinally, we further compared four alternative models each using copy number and DNA methylation data but different in using the remaining input data as follows:TRANSFAC + TargetScanTRANSFAC + TargetScan * miRNA.exprsENCODE + TargetScanENCODE + TargetScan * miRNA.exprs (the full RACER model)in vivo ChIP-seq measurements in K562 are perhaps more consistent with the actual TF occupancies in the AML patient samples than the TF binding signals from the motif database. Although we observed no significant improvement by weighting the target site counts with the miRNA expression, we decided to still use the full RACER model (with miRNA expression) to more realistically recapitulate the regulatory relationships. Presumably, miRNAs with low or no expression  should assume lower or no regulatory power than the highly expressed ones and vice versa.Here, “TRANSFAC” represents the integer counts of the putative TF binding sites from TRANSFAC database (version 7.4) GATA2 knockdown study in K562 cell line We examined how well our model can be used to predict miRNA-mRNA and TF-gene regulatory relationships using  GENMIR; , LASSO w GENMIR;  (Materink test)  and achink test) . For TF-n-recall . Togethep-value was then calculated by To determine the most predominant TF/miRNA regulators in regulating gene expression in AML, we developed a feature selection procedure. Specifically, we performed the same regression analysis as described above but leaving out one of the TF/miRNA regulators, regulatorX, from the regression formula. We then compared the residual sum of squared , the most significant regulator we found is PHF8, which is a histone demethylase that is specifically recruited by PML-RARa fusions. PHF8 enzymatic function is critical to the mechanism of all-trans retinoic acid treatment in acute promyelocytic leukemia Hoxa9, a Hox-containing transcription factor that is required for normal hematopoiesis and strongly stimulates myeloid cell proliferation EGR-1 locus is a recurrent genotype in patients with myelodysplastic syndrome and AML Moreover, PU1 was ranked at the fifth among the 18 regulators with FDR Furthermore, C/EBPFor miRNA regulators, we first examined the statistics of those previously identified leukemia-related miRNAs, and found that they exhibited modestly significant statistics based on our analysis. For instance, previous studies showed that silencing of miR-145 in mouse hematopoietic stem/progenitor cells induced transition into a myeloid-like leukemia To examine whether the miRNAs regulatory powers were overshadowed by the TF influence, we performed the same feature selection procedure without TF binding scores and compared the distributions of the l (cyan) . We founficients  and the atistics . Despiteatistics . AdditioIntriguingly, however, we identified hsa-miR-548p, a recently identified and poorly characterized miRNA  highly accessible to non-computational researchers. While the LASSO approach minimizes the squared error + L1-norm to obtain point estimates of the regulatory activities, the Bayesian model in ISMARA infers the posterior distribution of the regulator activities by combining the Gaussian likelihood with the Gaussian priors for the activities. Since we do not have a gold-standard for the true regulatory activities in AML, it is difficult to directly compare the performance between ISMARA and RACER. As mentioned by Balwierz et. al. (2014), however, the LASSO approaches can be interpreted as a Bayesian model using Laplacian priors instead of Gaussian priors in the regression framework and remain as a popular alternative since they induce a sparse solution  in the high dimensional feature space During the preparation of this manuscript, Importantly, our regression analysis coupled with feature selection provided two novel biological findings involving a recently discovered miRNA hsa-miR-548p and a TF regulator C-Fos. Specifically, we observed that miR-548p not only conferred significant explanatory power to mRNA expression changes in AML but also targets a large number of leukemia-related genes. Moreover, our network analysis identified miR-548p as a master regulator that regulates another selected regulator and also a prominent AML-related TF YY1 While C-Fos exhibited ectopic expression in various clinical tumour tissues, the predictive power of C-Fos mRNA expression as prognostic marker is often inconsistent among different studies individual effects  post-translational modification despite its low expression variance across AML patients. Notably, we can infer the regulatory activities of the proposed regulators in a single sample without borrowing information across multiple samples, which is cost-effective for future screening of unknown cases in a prognostic setting. In conclusion, our proposed approach provides a novel strategy and, to the best of our knowledge, the first framework that successfully integrates TCGA and ENCODE data to study AML at a comprehensive system level.Although our analyses identified several AML-related TFs such as PU1, C-Fos, YY1, some of the other AML-related TF regulators such as p300 and C-Myc Genome-wide measurements including mRNA/miRNA expression profiles, DNA methylation (DM), and copy number variation (CNV) and clinical information for Acute Myeloid Leukemia (AML) were downloaded from TCGA Data Portal The TF-binding data were retrieved from the ENCODE data portal For each mRNA-miRNA pair that has measured expression in the TCGA data, we obtained their conserved target sites from TargetScanHuman 6.2 database glmnet with For miRNA target predictions, experimentally validated miRNA-mRNA pairs were downloaded from MirTarBase ROCR package In addition, we constructed a confidence positive target list for miR-34a using the published data from GATA2 knockdown in K562 using the published data from For TF target predictions, we used the motif-based TF-target relationships from TRANSFAC (version 7.4) biomaRtWe examined whether the predicted miRNA/TF targets of the selected regulators are biologically meaningful via functional enrichment analysis. Specifically, we downloaded the Gene Ontology (GO) terms in Biological Processes (BP) (GO-BP) using getBM function from R package ClassDiscovery). Additionally, we performed Kaplan-Meier survival analysis using R package survival to examine the prognostic power of the identified feature using either their inferred activities or mi/mRNA expression level. The resulting p-values from log-rank test were then adjusted for multiple testings with BH-method Clinical data for each of the 173 patients were obtained from TCGA data portal. We first performed a hierarchical clustering (hclust in R) using the feature activities or mi/mRNA expression profiles. In all cases, the distance and clustering method were set to 1 - Pearson correlation and average-linkage, respectively. We then examined how well each molecular signature can cluster the four cytogenetic risk groups. Specifically, we cut the dendrogram of each clustering assignments into 4 groups using cutree function from R and compared the resulting groups with cytogenetic assignments quantitatively using Rand index  was performed using Figure S1Model comparison. Boxplot of coefficients of determination between the predicted and the actual held-out genes in 10-fold cross-validation (CV). Please refer to (EPS)Click here for additional data file.Figure S2Model comparison in regression step 1 and 2.A. In regression step 1, correlation was calculated between predicted and observed gene expression within each sample by training on 90% of the genes and testing on 10% of the remaining genes in a 10-fold cross-validation (CV). B. In step 2 regression, we applied a similar 10-fold CV for each gene by training on 90% of the samples and testing on the remaining 10%. For each gene, we averaged Spearman correlation over the 10 runs, and compared the distributions of the correlation among the full, reduced, and random models. Please refer to (EPS)Click here for additional data file.Figure S3Comparison of four alternative models. Each model used copy number and DNA methylation data but different in using the remaining input data as indicated in the figure legend above. We compared the four models in terms of the Spearman correlation between the predicted and observed mRNA target expression signals via 10-fold cross-validation. The indicated p-value was derived from the comparison between the ENCODE-based models and the TRANSFAC-based models using Wilcoxon signed rank test.(EPS)Click here for additional data file.Figure S4Comparison of miRNA explanatory powers in the full (red) and reduced RACER model excluding TF effects (cyan).A. Comparison of F-statistic distributions of the miRNAs derived from the feature selection procedure applied to the full data (red) and the data excluding TF binding scores. B & C. Comparison of the activities and F-statistic of CNV and DNA methylation (DM), respectively. D. F-statistics of selected miRNAs for the full (red) and reduced RACER model with TF effects excluded from the linear equation (cyan). False discover rates (FDR) corresponding to the adjusted p-value of the F-statistic were indicated on the top of each bar.(EPS)Click here for additional data file.Figure S5Expression correlation between AML averaged sample and K562 from ENCODE. To compare the expression between AML samples and K562 (cell line derived from a CML patient), we obtained the mRNA expression (in RPKM based on Gencode V7) in K562 from the ENCODE Data Portal. Only expression in cytosol were used. Expression in replicates were averaged and logarithmically transformed with 0.05 as pseudo-count to stabilize variance Click here for additional data file.Table S1Summary statistics in regression step 1 and 2.(PDF)Click here for additional data file.Table S2Feature selection results for the TF/miRNA regulators.(XLSX)Click here for additional data file.Table S3Functional enrichments of predicted targets from the 18 selected regulators.(XLSX)Click here for additional data file.


The high-throughput sequencing technology, RNA-Seq, has been widely used to quantify gene and isoform expression in the study of transcriptome in recent years. Accurate expression measurement from the millions or billions of short generated reads is obstructed by difficulties. One is ambiguous mapping of reads to reference transcriptome caused by alternative splicing. This increases the uncertainty in estimating isoform expression. The other is non-uniformity of read distribution along the reference transcriptome due to positional, sequencing, mappability and other undiscovered sources of biases. This violates the uniform assumption of read distribution for many expression calculation approaches, such as the direct RPKM calculation and Poisson-based models. Many methods have been proposed to address these difficulties. Some approaches employ latent variable models to discover the underlying pattern of read sequencing. However, most of these methods make bias correction based on surrounding sequence contents and share the bias models by all genes. They therefore cannot estimate gene- and isoform-specific biases as revealed by recent studies.We propose a latent variable model, NLDMseq, to estimate gene and isoform expression. Our method adopts latent variables to model the unknown isoforms, from which reads originate, and the underlying percentage of multiple spliced variants. The isoform- and exon-specific read sequencing biases are modeled to account for the non-uniformity of read distribution, and are identified by utilizing the replicate information of multiple lanes of a single library run. We employ simulation and real data to verify the performance of our method in terms of accuracy in the calculation of gene and isoform expression. Results show that NLDMseq obtains competitive gene and isoform expression compared to popular alternatives. Finally, the proposed method is applied to the detection of differential expression (DE) to show its usefulness in the downstream analysis.https://github.com/PUGEA/NLDMseq.The proposed NLDMseq method provides an approach to accurately estimate gene and isoform expression from RNA-Seq data by modeling the isoform- and exon-specific read sequencing biases. It makes use of a latent variable model to discover the hidden pattern of read sequencing. We have shown that it works well in both simulations and real datasets, and has competitive performance compared to popular methods. The method has been implemented as a freely available software which can be found at The online version of this article (doi:10.1186/s12859-015-0750-6) contains supplementary material, which is available to authorized users. RNA-Seq, based on high-throughput sequencing technology, is nowadays a commonly used method to study transcriptome. An RNA-Seq experiment typically produces millions or billions of short sequenced reads. By counting the reads aligned to a reference transcriptome, the expression of the related transcripts can be calculated . As alteAs read counts are proportional to the mRNA fragment abundance of a gene, the reads per kilobase of transcript per million mapped reads (RPKM) has been commonly used to represent gene expression . Due to In addition to read mapping ambiguity, another difficulty of expression calculation from RNA-Seq data is the non-uniformity of read distribution along the reference genome and transcriptome due to positional, sequencing, mappability and other undiscovered sources of biases . The nonIn this paper, we propose a latent variable model, NLDMseq , to estimate gene and isoform expression. Given known annotations, this model introduces latent variables to represent the unknown isoforms, from which reads originate, and the proportion of multiple spliced isoforms. The isoform- and exon-specific read sequencing rates are modeled as parameters which can be estimated from data. We utilize the replicate information of multiple lanes for a single library to identify read sequencing rates. NLDMseq benefits from the latent variable model that would help to discover the hidden pattern of read sequencing. Another advantage of NLDMseq is that it models normalized read counts for each exon rather than each individual read as many latent variable models do –8. ThereIt has been found by previous studies that there exist similarities among the patterns of count variation for many genes or isoforms among samples , 15. TheE exons and K isoforms for a given gene. Let ni represent the number of fragments that fall in the ith exon, where 1≤i≤E. We also consider the exon junctions and treat them as individual exons in order to obtain more information of alternative splicing in the data. Let L represent the length of reads. We construct special junction exons by combining the sequence with length L−1 at the end of the exon ahead and the sequence with the same length at forepart of the next exon  for each gene is assumed as follows,θl once for lane l, θl∼Dirichlet(α).Generate l, generate tln, tln∼Multinomial.For lane eln given tln, Generate exon With the above assumptions and notations, we adopt the Dirichlet-Multinomial Bayesian model as that in the latent Dirichlet allocation . The date is the observed data, θ and t are latent variables, and the K-vector α and the K×E matrix β are hyperparameters, where αk>0, βt is the kth row of β corresponding to isoform t. We can see that under our model assumption the parameter βt is isoform-specific and each entry indicates the average sequencing rate for an exon. For those exons which are not used in isoform t, the corresponding entries in βt are constrained to zero. Here, we consider to model the data for each individual lane in order to make use of this technical replicate information to have better estimation of the distribution of θ and the isoform- and exon-specific read sequencing rate β. A graphical representation of our model is shown in Fig. By repeating steps 2 and 3, all exon data can be generated for each lane. In our model, β across samples as Sequgio in case that biological variation may violate the conserved read count distribution for some genes. Biological samples are therefore processed individually with our approach. We aim to provide accurate expression measurements at this stage and intend to handle the biological replicate noise in the downstream analysis  which indicates the underlying fraction of isoform abundances. Unfortunately, this distribution is intractable to compute when we apply Bayes’ rule. We employ the variational EM algorithm proposed in [θl} and {tln}, the posterior of {θl} and {tln} can be approximated by a set of Dirichlet distributions with parameters {ηl} and a set of multinomial distributions with parameters {λln}, respectively. Initially, we set unbiased values for the hyperparameters α and β, indicating that no preference is set for any isoform and exon. At the E-step, the variational parameters are updated as follows,Our purpose is to infer the hidden generative process which most likely produces the observed normalized exon counts {posed in  to work q denotes the variational distribution of θl. We omit the variational parameters of q distribution for simplification. The Eqs. (where < · > represents expectation and The Eqs.  and 2)  q denoteα and β,At the M-step, the following function is maximized with respect to whereβ can be worked out in a closed form as follows,The hyperparameter k includes exon j, βkj is updated using Eq.  implies the percentage of multiple isoform abundance for each lane, we use the generative distribution p(θ|α) with the estimated α to represent the underlying fraction of isoform abundance. The expectation of θk isSince kth isoform, fk, can be expressed asThe fragments mapped to each exon are allocated to the corresponding isoforms according to the fraction in Eq. . Using tNs is the total number of fragments obtained for this sample. Gene expression can be represented by M samples from the distribution p(θ|α) and calculate isoform and gene expression for each sample θm, where 1≤m≤M. Thus, we have M estimates for each isoform and gene expression. Using these samples, we can obtain the variance of the estimated expression which can be propagated into downstream analysis to obtain improved results. For single-isoform genes, the expression is calculated directly using FPKM assuming the uniform distribution of the reads.where https://github.com/PUGEA/NLDMseq, for public use. Any aligner that can align the raw experimental reads to reference transcriptome can be used for the preprocess of RNA-seq data for NLDMseq. We use Bowtie 2 [We have implemented NLDMseq in a free Python/C tool, which is available from Bowtie 2  throughoBowtie 2  and MMSEBowtie 2 . After tWe use the well-studied Microarray Quality Control (MAQC) dataset  to validA real study on molecular injury in response to tobacco smoke exposure and lung cancer pathogenesis (SELC)  is used We also use a publicly available human breast cancer (HBC) dataset  to verifθl from tln from Multinomial. Next, given the generated tln generate exon eln from eln for a single-end read. To generate a pair of paired-end reads, we sample the length of the sequenced fragment from N and then uniformly sample the starting position of this fragment along exon eln. With the sampled fragment position and length, the paired reads for both ends can be simulated.We generated simulated data using our model based on the calculated parameters from the MAQC dataset. We select all 1,604 multi-isoform genes and 12,064 isoforms of chromosome 1 from Ensembl human genome assembly GRCh37/hg19 and simulate two samples with single-end and paired-end data respectively. For the single-end data, we generate 3,673,804 single-end reads with seven lanes using parameters We compare NLDMseq with other three popular alternatives, Cufflinks v2.2.0 , RSEM v1We evaluate the proposed approach, NLDMseq, on the estimation of gene and isoform expression in terms of accuracy using three real datasets and considering both single-end and paired-end data.j of isoform k is represented by βkj. The subplots a ∼e in Fig. βkj for each isoform. We can see that the sequencing rates for different exons of the same isoform are really different. From subplot f in Fig. αk. For each exon, we summarize the sequencing rates contributed from all isoforms, βkj and αk, are consistent with the observed data. In order to consider reads caused by noise or undiscovered isoforms, we include a special isoform which contains all exons of this gene. We observe that the fraction of this special isoform is as low as 9 %, which is not greater than the fraction of known isoforms in this example, showing that most sequenced fragments are useful and few are credited to noise and undiscovered isoforms.One advantage of NLDMseq is that it is able to model the isoform- and exon-specific read sequencing rate which is thought to be the main reason for the non-uniformity of read distribution in RNA-Seq data. Before evaluating the accuracy of expression calculation, we use a randomly selected example from the MAQC dataset as shown in Fig. We first use the well-studied MAQC dataset to justify the accuracy of NLDMseq on gene expression estimation. Each sample in this dataset contains multiple lanes. NLDMseq processes multi-lane data automatically and obtain the intrinsic fraction of multi-isoform abundance based on multi-lane information. We also apply Cufflinks, RSEM and MMSEQ to data coming from each individual lane and calculate the average gene expression for each sample. The Pearson correlation coefficients of gene expression estimation with the qRT-PCR measurements for the 740 qRT-PCR validated genes in the three samples are calculated as shown in Table We next use the real SELC data with qRT-PCR validation to further verify the performance of NLDMseq on gene expression calculation. Table We use the HBC dataset to justify the isoform expression obtained from NLDMseq and compare it with Cufflinks, RSEM and MMSEQ. We used the UCSC knownGene transcriptome annotation (NCBI36/hg18) for obtaining all the annotation information for the eight qRT-PCR validated isoforms related to genes TRAP1, ZNF581, WISP2 and HIST1H2BD. We apply NLDMseq, Cufflinks, RSEM and MMSEQ to this dataset and calculate the expression of the eight qRT-PCR validated isoforms. The log-ratios obtained from different methods for the 16 regulations of the eight qRT-PCR validated isoforms are shown in Table We find the regulations between isoforms of genes TRAP1 and HIST1H2BD under cell lines HME and MCF-7  curves to show the performance of various DE approaches. The higher the curve, the better performance of the examined method. Accordingly, a higher value of area under the ROC curve (AUC) indicates higher accuracy of the method. We plot the ROC curves for different DE approaches as shown in Fig. Finally, we use the data of NC phenotype in the SELC data to compare the computation efficiency of various approaches. This data contain 22 million paired-end reads. The expression computation time of the four methods are shown in Table In this contribution, we have presented a latent variable model, NLDMseq, to accurately estimate gene and isoform expression from RNA-Seq data given a known annotation. NLDMseq handles the two major difficulties in expression calculation in RNA-Seq data analysis, read mapping ambiguity and non-uniformity of read distribution, by adopting a latent model to discover the hidden pattern of read sequencing and modeling the isoform- and exon-specific read sequencing rates. Unlike many latent variable models which simulate the sequencing of each individual read, NLDMseq models normalized read counts for each exon without dealing with nucleotide constitution of each read. This significantly reduces the computation load of the model. We have used the replicate information of multiple lanes for a single library run to achieve read sequencing rate for each isoform-specific exon which shows the particular sequencing bias for this exon. We have constructed junction-exons to deal with reads mapped to the region of exon junction. For accommodation of noise reads and reads mapped to undiscovered isoforms, we have considered a special isoform which contains all the exons of a gene. We have found that the fraction of this special isoform is usually lower than that of known isoforms indicating that most reads are useful in calculation of expression for known isoforms and there are few reads which are due to noise and undiscovered isoforms.We have employed simulation and qRT-PCR validated real data to verify the performance of our method in terms of accuracy in the calculation of gene and isoform expression. Results have shown that NLDMseq is comparable to and in some cases outperforms the other competing methods. We have also applied NLDMseq to DE analysis by combining a previously designed DE analysis method, PPLR, which has been successfully applied to microarray analysis. This DE analysis approach was tested on a well-studied qRT-PCR validated benchmark. Results have shown that our approach have presented competitive performance compared with other popular methods. We also used a dataset to examine the running time of our approach. The comparison results indicate that our approach is computationally efficient compared with the other alternatives.One advantage of our method is that isoform- and exon-specific sequencing rate can be estimated to account for different sequencing bias for each isoform-specific exon. However, we find the distribution of the observed read counts is over-dispersed compared with the obtained sequencing rates as shown in subplots θl}, obtained from the variational EM estimation, it is also possible to detect differential isoform usage, where multiple isoforms of a single gene are expressed, but at different proportions between two groups of samples. This also provides a possibility of identifying alternative splicing.We have used an example of detecting DE genes to show the application of NLDMseq to DE analysis. As for the detection of differential alternative splicing, NLDMseq can also be combined with available DE analysis method, such as PPLR, to find DE isoforms by using the isoform expression calculated in Eq. . Moreove