The amount of publicly available cancer-related “omics” data is constantly growing and can potentially be used to gain insights into the tumour biology of new cancer patients, their diagnosis and suitable treatment options. However, the integration of different datasets is not straightforward and requires specialized approaches to deal with heterogeneity at technical and biological levels.Here we present a method that can overcome technical biases, predict clinically relevant outcomes and identify tumour-related biological processes in patients using previously collected large discovery datasets. The approach is based on independent component analysis (ICA) – an unsupervised method of signal deconvolution. We developed parallel consensus ICA that robustly decomposes transcriptomics datasets into expression profiles with minimal mutual dependency.By applying the method to a small cohort of primary melanoma and control samples combined with a large discovery melanoma dataset, we demonstrate that our method distinguishes cell-type specific signals from technical biases and allows to predict clinically relevant patient characteristics. We showed the potential of the method to predict cancer subtypes and estimate the activity of key tumour-related processes such as immune response, angiogenesis and cell proliferation. ICA-based risk score was proposed and its connection to patient survival was validated with an independent cohort of patients. Additionally, through integration of components identified for mRNA and miRNA data, the proposed method helped deducing biological functions of miRNAs, which would otherwise not be possible.We present a method that can be used to map new transcriptomic data from cancer patient samples onto large discovery datasets. The method corrects technical biases, helps characterizing activity of biological processes or cell types in the new samples and provides the prognosis of patient survival. Now, the question arises if these resources can also be used to support clinicians in making rapid and accurate assessments leading to tailored treatments for individual cancer patients. Integrating this information still poses a considerable obstacle as genomic and transcriptomic data from cancer patients are characterised by significant heterogeneity at three levels. First, results are generally collected using different sample preparation protocols and transcriptome analysis platforms and are then interrogated by constantly changing techniques. Although these techniques have improved on accuracy, sensitivity or genome coverage, they restrain backward compatibility, e.g., expression level analysis has evolved from qPCR through microarrays toward NGS sequencing in the last 15 years. Second, the data are collected for various layers of “omics”: genome, transcriptome, miRNome, proteome etc. Integration of data from these layers is not trivial especially when genomically unconnected entities should be integrated, like microRNA and their target mRNAs. Third, collected patient samples are intrinsically heterogeneous at tissue and cellular levels. Bulk analysis of transcriptomes can mask different types of heterogeneity in the sample as tumour biopsies contain many cell types that are mixed in different proportions [Genomic and transcriptomic research has accumulated a vast collection of publicly available cancer related data. Data have been continuously collected using massive financial and scientific efforts. For example, The Cancer Genome Atlas  and the concomitant genetic heterogeneity make it difficult to distinguish true cancer driver genes from noise in bulk samples using current technologies , 17. NevIn this study, we used the skin cutaneous melanoma (SKCM) TCGA cohort with over 470 patients diagnosed with cutaneous melanoma as the discovery dataset. Two layers of “omics” data were considered and integrated: mRNA and microRNA (miRNA). The investigation dataset included a small cohort of three primary melanoma tumours and two controls: matched cancer patient-derived normal skin and normal melanocytes. First, for the discovery cohort, we demonstrated that ICA deconvolution can be successfully applied to classify patients based on their tumour subtypes and to build the risk score that predicts patient survival. The risk score was then tested using an independent validation cohort of 44 patients, obtained by microarray gene expression technology. The strong technical differences between discovery RNA-seq data and microarray-derived validation datasets were resolved by our method. Next, the investigation dataset was studied in depth and key processes involved in cancer aetiology were detected and quantified: immune response and inflammation, angiogenesis, self-sufficient cell proliferation among others.We show here that consensus ICA can integrate data from different sources and platforms and predict clinically important characteristics of cancer in a bias-free, unsupervised and potentially automatable fashion, suggesting consensus ICA as a useful module of future clinical support systems.https://portal.gdc.cancer.gov/). Soft filtering as in [As a discovery dataset, we used two SKCM TCGA datasets: RNA-seq (472 samples) and miRNA-seq (452 samples) data from the Genomic Data Commons (GDC) data portal of the National Cancer Institute of the National Institutes of Health . We also added data of tumour subtype based on RNA-cluster  as it is relevant for prognosis . The extA validation gene expression dataset was taken from , availabThe investigation dataset, represented by RNA-seq and miRNA qPCR array data, originated from three primary tumour samples of melanoma patients  and two control samples: one matched normal skin P4NS and a healthy melanocyte cell line NHEM  and from the German Ethik-Kommission der Albert-Ludwigs-Universität Freiburg (EK-Freiburg 196/09). Histological examination and estimation of the percentage of tumour cells within the lesion was performed by two independent pathologists . Tissues from snap frozen biopsies were lysed in RLT buffer with a Qiagen TissueLyser . DNA and total RNA were extracted using the Qiagen’s AllPrep Mini Kit according to supplied protocols. Quality and quantity of samples were measured with Nanodrop, gel electrophoresis and Qubit High Sensitivity Kit. RNA integrity was determined using the Agilent Bioanalyzer Nano chip.RNA-seq data for these samples are available by GEO accession number GSE116111 and Ct-values for all quantified miRNAs are available in Additional file Enm the expression matrix of n genes or miRNAs measured in m bulk samples. ICA decomposed such a matrix into a product of k statistically independent transcriptional signals Snk (addressed as matrix of metagenes) and a weight or mixing matrix Mkm (matrix of metasamples) [ICA was applied to the combined discovery and investigation datasets for unsupervised separation of signals and feature extraction  .1\documS (metagenes) can be interpreted as the level of influence of the corresponding genes/miRNAs on the components and considered as “markers” of the component. Weights in rows of M show how the metagenes are mixed in the samples. In order to distinguish independent components obtained after ICA of mRNA and miRNA data, we introduce the terms RICs (mRNA) and MICs (miRNAs). Thus, each RIC and MIC is associated with two vectors: one showing the contribution of the genes into this component (a column of S); the second representing the weights of the component in the samples (a row of M). Unlike non-negative matrix factorization, both metagenes and weights can be positive or negative and ab initio the selection of the direction is random, depending on the initial estimation. ICA may also suffer from reduced reproducibility for at least some components. To mitigate these drawbacks, we ran the analysis multiple times  following [nt), a random sample was excluded from the expression matrix and ICA was performed on this reduced dataset. As a result, we obtained nt matrices M(1) and S(1).For the defined number of tries  and M(1). The squared correlation between corresponding metagenes was used as a measure of stability (R2).Consensus The values represented in the columns of ollowing . In briehttps://gitlab.com/biomodlih/consica.Multithreading was implemented in R code to speed-up calculations using the `foreach` package and either `doMC` (Linux) or `doSNOW` (MS Windows) packages available in R/Bioconductor. The script of the implemented consensus ICA and following analysis , and genes with an adjusted p-value  < 0.01 were reported as top-contributing  GO terms were investigated. In order to simplify the interpretation and to increase the robustness for runs on different datasets, we reoriented the components in order to have the most significantly enriched categories associated with positive top-contributing genes  as outputs. Each variable was analysed independently. First, leave-one-out cross-validation (LOOCV) was performed on the discovery set in order to address the ability of predicting sample classes and estimate the accuracy of prediction. Then the random forest, trained on all discovery data, was used to predict classes for the new clinical samples of the investigation dataset. To ensure accuracy and robustness of our approach to select the number of components, we performed a nested cross-validation, excluding 20% of the data and using the remaining 80% to estimate the optimal number of components and then train the classifier   and XPN M) were statistically linked to patient survival using Cox partial hazard regression implemented in the `survival` package of R [p-values of the log rank test were used to select significant components. However, the prognostic power of each individual component might not have been high enough to be applied to the patients from the new cohort. Therefore, we integrated weights of several components, calculating the risk score (RS) with an improved prognostic power. For each patient, its RS is the sum of the products of significant log-hazard ratios (LHR) of the univariable Cox regression, the component stability R2 and the standardised row of weight matrix M:Weights of the components  linked to survival and 0 for other. The applicability of the proposed score was checked using the independent validation dataset. This dataset was extracted from another study and was based on an independent cohort of the patients [where patients . In addihttps://zenodo.org/record/1250070). As enrichment of immune-related processes and functions was observed, we also correlated our metagenes to the immune cell type signature matrix named LM22 [Our strategy to investigate the biological relevance of the components is presented in Additional file med LM22  in ordermed LM22 . For miRPearson correlation between weights of the components was used to link the components found within mRNA and miRNA data. Here we hypothesized that if two components show significant correlation of the weights in all the samples, they should be functionally linked. Of note, these MICs have been linked to their respective RIC, purely based on the high absolute correlation of component weights, without considering any biological knowledge. Due to the lack of tools providing data with regard to biological functions or cell types for miRNAs, we performed literature mining, searching for all publications related to miRNAs-clusters and additional biologically relevant keywords. More detailed description of literature mining is given in Additional file The involvement or the weight of each component in the samples is not centred and scaled due to the nature of ICA. Therefore, to visualize the involvement of the components in the new samples, we replaced the weights of the components by a ranking score that changed from 0 to 1 (only discovery data were considered to define the ranking). If the weight of the considered component in a new sample was below (or above) the weights in the discovery set, such component automatically was assigned to a limiting value of 0 (or 1). Values of ranking score around 0.5 in the new sample suggest that the weight of the considered component was close to the median in the discovery set.R2 > 0.5). The values of R2 are provided in the Additional file p-value = 6e-3) but not for tumour subtype . At the same time, a much stronger effect was observed on the reproducibility of metagenes and gene signatures, associated with the components .The combined discovery/investigation dataset profiled by RNA-seq is presented in the space of two first principal components Fig. a and weip-value = 9.4e-4) while MIC9 was correlated with the skin-related signal of RIC5.An even stronger correction effect of ICA was observed for miRNA data, for which discovery data were obtained by miRNA-seq and investigation – by whole miRNome qPCR arrays. PCA showed strong differences between log2 transformed counts and inverted Ct values  and in-house clinical investigation data (5 samples). Analysis was run independently for both cases, and the identified components were re-ordered and renamed to obtain comparable results. Notably, the metagenes of the new decompositions were reproducible and strongly correlated with the metagenes from ICA of single discovery set.KRT5 and KRT14.Predicting patient gender showed a high accuracy of 0.977 in the validation data, with only one samples misclassified. Testing sample type (primary/metastatic) for this validation cohort resulted in 34 samples classified as metastatic and 10 – as primary . However, as the precise excision location of the tumours is unknown, we cannot exclude that some metastatic tissues were collected from skin. Indeed, 7 of 10 misclassified samples showed high expression of keratinocyte marker genes The investigation samples were classified as well and the results are presented in Table We also compared the ability of ICA-based features to predict patient classes in comparison with other dimensionality reduction method Fig. . The resp-value by log rank test for Cox regression < 0.05). Among them, 6 RICs and 2 MICs showed very high stability of R2 > 0.8 and 8 out or 11 RICs were linked to biological processes. The remaining 3 RICs did not have enough contributing genes to run successful enrichment analyses. However, their behaviour over the samples allowed us to link two of them (RIC74 and RIC79) to the immune cluster, as is described in the next section. Although these 11 RICs and 3 MICs were statistically linked to survival in our discovery set, the predictive power of any of them was not sufficient to predict survival of new patients. Therefore, we combined the weights of these components into a risk score (RS) as described in Methods. Combined RS showed high significance  for the TCGA dataset.Next, prognostic abilities of the ICA weights were examined by a Cox regression model. All components, their significance and log-hazard ratios (LHRs) are summarised in Additional file p-value< 0.05) on the discovery set were then used to compose RS for the validation data and also showed significant prognostic properties ; Kaplan-Meier plots are shown in Fig. In order to validate the proposed risk scoring approach on an independent cohort of patients, we applied it on the validation dataset. The components that showed a significant link to survival . This was in agreement with clinical observations, as patient P6 suffered from a very aggressive form of melanoma and deceased shortly after sample collection. From the quantitative results obtained from the validation dataset and qualitative differences observed for the investigation dataset, we concluded that weights of independent components can be combined into a risk score, suitable to predict patient survival.r2) between weights of corresponding components. Correlation maps are presented in Fig. The most challenging part of ICA is assigning components to specific biological processes, cell types and technical factors. The approach we have taken is outlined in Additional file p-value = 1.8e-4) and most probably originated from B cells . The metagenes of RIC2 were also correlated with the LM22 signatures for B cells , neutrophil degranulation , TNF-  and IL1-mediated signalling pathways ; RIC37 was connected to interferon signalling  whose metagenes were also reciprocally correlated with M5_INTERFERON of the Biton dataset [Functionally, RIC28 was linked to inflammatory responses to wounding . No specific cell type was associated with these components. RIC74 was, however, associated with positive and negative regulation of immune response and receptor-mediated endocytosis .Components RIC74 and RIC79 contained a very limited number of top-contributing genes, but both were significantly linked to survival . Among the top miRNAs in MIC20 were miR-155, miR-150, miR-342, miR-146b, and miR-142. MiR-155 is known to be a regulator of immune response in cancer cells [miR-150, miR-155 and miR-342 have been proposed as markers for melanoma patient survival [p-value = 7.3e-3).The weights of miRNA component MIC20 were positively correlated with the weights of RIC2, RIC25 and RIC27  and were positively linked with survival .The samples from the investigation cohort were characterised by the involvement of the above immune response-related components Fig. d. The rep-value 2e-26) and vasculature development . The component’s metagenes were strongly correlated with metagene M3_SMOOTH_MUSCLE of Biton et al. [p-value = 6e-24). Its most correlated single cell type was endothelial cells, which also form part of the tumour microenvironment. Thirteen of the positively contributing miRNAs from MIC22 were strongly concentrated in a narrow genomic region in chr14q32.2 . MiRNAs of MIC25 were significantly enriched in four cytogenetic locations: chr1q24.3, chr5q32, chr17p13.1 and chr21q21.1 .The second cluster of RICs was linked to the signals of stromal cells and showed enrichment in genes related to angiogenesis. It included four correlated components: RIC13, RIC49, MIC22 and MIC25  and keratinisation . Enrichr suggested that the signals of these components are specific to skin . The dataset contained 48 keratins and many of them were observed among the top-contributing genes: 20 for RIC5, 28 (RIC7), 30 (RIC19) and 13 (RIC31). RIC5 and RIC7 were negatively correlated with survival, which is in concordance with previous observations [miR-203 [p-value = 1.2e-5) and Enrichr linked these genes to melanocytes . RIC16 showed an inverse correlation of the weights with RIC4. Both components were linked to survival, but with an opposite effect: while RIC4 increased the risk , RIC16 increased the survival  .RIC5, RIC7, RIC19, RIC31 all showed an enrichment in GO terms related to processes of the skin including epidermis development .In the validation cohort we identified several patients with a strong skin signature  and the majority of the 383 genes positively associated to this component are known to be involved in cell cycle control with tumour cells contributing the most to cell division activities. Increased cell proliferation was linked to survival . In the investigated samples, the highest weight was observed for the most aggressive tumour P6PM and the lowest value for normal skin P4NS. In the validation samples this component was also linked to survival .Some components could be linked to transcriptional signals and regulation of cancer cells. For example, RIC55 captured the cell cycle process . This component was as well associated with patient survival . The component indicates the ability of melanoma cells to show expression patterns specific for cells of the neural crest of human embryos and can be linked to motility of malignant melanocytes.Several RICs showed linkage to neural tissue. As an example, both positive and negative top-contributing genes of RIC6 were linked to brain in the ARCHS4 tissue sets of Enrichr , suggesting two subgroups of melanoma patients with different prognosis. This component most probably was linked to regulation of epithelial-mesenchymal transition (EMT), as many miRNA positively or negatively influencing the component are known to be EMT regulators or linked to metastasis formation: miR-551, miR-206, miR-34a, miR-1269, miR-205, miR-876, miR-301b, and miR-365a. Based on our analysis of the discovery TCGA dataset, these miRNA listed in Additional file MiRNA component MIC1 showed an interesting bi-modal distribution in the discovery dataset  a large cohort of SKCM patients from TCGA used as discovery set; (b) an independent cohort of 44 patients with publicly available microarray mRNA data and (c) 5 in-house clinical investigation samples: 3 primary melanomas, a normal skin sample and a normal melanocyte cell line (NHEM). Both mRNA and miRNA datasets were obtained for the discovery and investigation samples. Despite the fact that different techniques were used for data acquisition, ICA was able to identify common signals in the datasets and properly allocate the new samples within the discovery set Fig. . This waS obtained from the discovery dataset in order to define the weights (M) for the samples forming the investigation dataset (1). However, in reality, the variability in the data requires recalculation of the components for the new investigated samples.The fact that ICA should be re-run for every series of new samples could be considered as a drawback of our approach. However, similarly to PCA, recalculation of the components does not require supervision and could be done automatically. In the case when investigation and discovery datasets come from the same distribution, one can use the matrix We demonstrate here that the weights of independent components can be used as predictive features of patient subgroups and can be linked to patient survival. We also propose a method to select the number of components, based on the required classification task  in the so-called imprinted DLK1-DIO3 region. Lower levels of this miRNA cluster have been described to favour neo-vascularisation [miR-379/miR-410 cluster was silenced in melanoma, which favoured tumorigenesis and metastasis [Another group of components were linked to tumour-stromal interactions and angiogenesis. One of them, MIC22, contained an almost complete miRNA mega cluster, risation  and showrisation , 49. Mosrisation . Moreovetastasis .Overall, we observed that ICA on miRNA expression data grouped together many miRNAs that belong to genetic clusters and by connecting MICs with genes (RICs), biological functions of miRNAs could be inferred. As an example, MIC11 represents a cluster on chrX q27.3 associated with early relapse in advanced stage ovarian cancer patients . In our The results for the ICA-derived biological networks implied that the combination of ICA with text mining  potentially uncovers two hidden connections: biological reasons for statistical correlations and detection of those genes actually responsible for the biological link between MICs and RICs. This in turn might give new insights into the significance of biological processes active in cancer in general or in certain cancer subtypes.Similarly to PCA or NMF, ICA could be integrated into standard analysis pipelines in the future. Unlike PCA, ICA could extract biologically-based signals. These signals are more stable than those obtained by NMF and can be further used to acquire clinically relevant information about new samples, thus helping patient diagnostics and prognostics.In conclusion, we used the consensus ICA method to combine transcriptomics data of melanoma patients with large public datasets. Here we showed successfully that the ICA-based decomposition separates true biologically relevant transcriptional signals from technical biases. The obtained ICA-based features were used to predict cancer subtypes and patient survival. We also showed how cellular composition and biological signals can be uncovered within new clinical samples. Transcriptional signals from immune cells, melanocytes, keratinocytes and stromal cells were identified and confirmed by comparison to published signatures. We demonstrated that some of the identified signals, including immune activity and cell proliferation, are linked to the aggressiveness of tumours and could influence patient survival. Finally, we were able to integrate miRNA and mRNA data, which allowed us to deduce biological functions of miRNAs.Additional file 1: Supplementary Methods detailed description of data acquisition and independent component analysis. (DOCX 45 kb)Additional file 2:. Supplementary Results automatic report generated for the discussed components by the presented consensus ICA tool (consICA). (PDF 1107 kb)Additional file 3: Fig. S1. Flow chart of post-processing of ICA results to determine biological relevance of components and networks. Fig. S2. Schematic workflow of ICA application to the discovery, validation and investigation datasets. Fig. S3. Performance of principal component and independent components as feature selection methods. Fig. S4. Similarity between the identified components improves with the increase of number of runs for consensus ICA. Fig. S5. Correlating components to profiles defined in the previous studies. Fig. S6. Pearson correlations between the metagenes of three immune components RIC2, RIC25, RIC57 and one angiogenic component RIC49 on one side, and averaged expression profiles of single cell sub-populations published by Tirosh et al. Fig. S7. Behavior of the important RICs in the validation dataset , RIC25 (B), RIC27 (C), RIC74 (D) metagenes, showing a significant protein interaction network  representing main players within immune response. Fig. S9. STRING networks based on overlapping: MIC22-target genes and RIC13 metagenes (A), MIC25-target genes and RIC13 metagenes (B), MIC25-target genes and RIC49 metagenes (C). Fig. S10. RNA-seq data preparation and metric selection based on discovery TCGA SKCM dataset. Fig. S11. (A) Number of significant positively (red) and negatively (blue) contributing genes in metagene of each of them RNA components before re-orientation. (PDF 2978 kb)Additional file 4: Table S1. Survival data of TCGA SKCM covering patient ID, age at diagnosis, year of diagnosis, disease status at last contact, days to death, vital status, days to last contact after initial diagnosisdiagnosis, year of last contact, tumour free survival, survival in years and age at death. Data items have been either directly extracted from individual XML-files holding clinical information publicly available at GDC or calculated based on the extracted information. Table S2. Clinical data of TCGA SKCM covering patient ID, gender, sample type (primary tumour and metastatic) and publication based data for RNA-seq cluster (immune / keratin / MITF-low). Table S3. Parameters of clinical samples and controls in the investigation dataset. Table S4. Ct values obtained for the new samples using qPCR arrays. During analysis, all absent (NA) values and Ct > 36 were replaced by 36, value selected as detection limit. Table S5. Summary of the ICA results for mRNA data. Stability of each component after 1000 runs, results of the survival analysis, number of genes significantly involved  and number of enriched GO biological processes  are reported. Lower and higher estimates of log hazard ratio (LHR) correspond to 95% C.I. Table S6. Summary of the ICA results for miRNA data. Stability of each component after 1000 runs, results of the survival analysis and number of significantly involved miRNAs  are reported. (XLSX 122 kb)


This compositional bias confounds inference of absolute abundances. Commonly used count data normalization approaches like library size scaling/rarefaction/subsampling cannot correct for compositional or any other relevant technical bias that is uncorrelated with library size.Count data derived from high-throughput deoxy-ribonucliec acid (DNA) sequencing is frequently used in quantitative molecular assays. Due to properties inherent to the sequencing process, unnormalized count data is compositional, measuring We demonstrate that existing techniques for estimating compositional bias fail with sparse metagenomic 16S count data and propose an empirical Bayes normalization approach to overcome this problem. In addition, we clarify the assumptions underlying frequently used scaling normalization methods in light of compositional bias, including scaling methods that were not designed directly to address it.Compositional bias, induced by the sequencing machine, confounds inferences of absolute abundances. We present a normalization technique for compositional bias correction in sparse sequencing count data, and demonstrate its improved performance in metagenomic 16s survey data. Based on the distribution of technical bias estimates arising from several publicly available large scale 16s count datasets, we argue that detailed experiments specifically addressing the influence of compositional bias in metagenomics are needed.The online version of this article (10.1186/s12864-018-5160-5) contains supplementary material, which is available to authorized users. Sequencing technology has played a fundamental role in 21st century biology: the output data, in the form of sequencing reads of molecular features in a sample, are relatively inexpensive to produce . This, aabsolute scale, are intimately tied to those of features that are perturbed in their absolute abundances, making the former appear differentially abundant. We refer to this artifact as compositional bias. Such effects are observable in the count data from the large-scale Tara oceans metagenomics project [This remarkable flexibility of sequencing comes with atleast one tradeoff. As noted previously in the literature –14 . The median approach simply returned zero values. CLR transforms behaved similarly. When one proceeds to avoid this problem by adding pseudo-counts, owing to heavy sparsity underlying these datasets, the transformations these techniques imposed mostly reflected the value of pseudocount and the number of features observed in a sample. A recently established scaling normalization technique, Scran , tried trelative abundances are performed. It is important to realize that compositional bias is infused in the count data, solely due to inherent characteristics of the sequencing process, even before it passes through any specific normalization process like scaling by library size. In practical conditions, because feature-wise abundance perturbations are also driven by technical sources of variation uncorrelated with total library size [Since we have presented the problem of compositional bias as one affecting inferences on absolute abundances, one might wonder if resolving compositional bias is needed when analyses on ary size –30, compary size , 32, PCRary size , all whiWrench) and evaluate its performance with simulations and experimental data showing that it can lead to reduced false positives and rich annotation discoveries. We close by discussing the insights obtained by applying Wrench and other scaling normalization techniques to experimental datasets, arguing both for addressing compositional bias in general practice and in benchmarking studies. Because all the aforementioned techniques, including our own proposal, assume that most features do not change across conditions on average, they would all suffer in analyses of features arising from arbitrary general conditions. In such cases, spike-in based techniques can be effective [The paper is organized as follows. We first set up the problem of compositional bias correction and with appropriate simulations, evaluate several scaling normalization techniques in solving it. We find that techniques based only on library size . The true absolute abundances of features in every sample organized as a vector Xgj·, the net total abundance of which is denoted by proportional to the absolute feature abundances represented in Xgj·. The output reads are processed and organized as counts in a vector Ygj·, which now retain only relative abundance information of features in Xgj·. The ultimate goal of a normalization strategy is to recover g and j.Figure X from Y, as it is in this step, that the sequencing process induces the bias we are interested in. We come back to the question of reconstructing X0 at the end of this subsection. Because we are ignoring all other technical biases inherent to the experiment/technology , our discussions apply to RNAseq/scRNAseq/metagenomics and other quantititative sequencing based assays. In this paper, our primary interest will be in the correction of compositional bias for metagenomic marker gene survey data, which are often under-sampled.Our goal is to evaluate existing normalization approaches based on how well they reconstruct i is given by qgi for all samples within a group g. It is also reasonable to assume an Xgj·|Tgj∼Multinomial, where qg· is the vector of feature-wise relative abundances  total absolute abundance of features in group g at the time of input. Similarly, i across samples in group g . If we set g=1 as the control group, and define, for every feature i, νgi is the log-fold change of true absolute abundances associated with group g relative to that of the control group. We can write: Although not strictly necessary, for simplicity, we shall assume that the relative abundances of each feature res Xgji –40). SimY) from the sequencing machine confounds our inference of the fold changes associated with absolute abundances of features at stage X, through a linear bias term Λg. Thus, to reconstruct the average absolute abundances of features in experimental group g, one needs to estimate the compositional correction factorThis indicates that the fold changes based on observed proportions  are also of technical origin, they can well be correlated with other sources of technical variation, and can be seen to estimate technical variation beyond what is accounted for by sample depth adjustments. Thus, it is interesting to ask under what conditions compositional factors arising from scaling techniques (including our proposed technique in this work) can reconstruct X0. In the supplementary, we show that in the presence of sequence-able experimentally introduced contaminants, utilizing existing compositional correction tools amounts to applying stricter assumptions than the often-cited assumption of “technical biases affecting all feature the same way”. The precise condition is given in the supplement  with 20M reads per sample, by and large, we found that all testing packages behaved the same way, and the key ingredient to overcome compositional bias always was an appropriate normalization technique  effK, 4.5K, 3.3K, 4.4K and 100K reads. In direct contrast, this value for the high coverage bulkRNAseq rat body map across 11 organs at a median sample depth of 9.7M reads, is.33. Large number of features, extreme diversity, and time-dependent dynamic fluctuations in microbial abundances can result in such high sparsity levels in metagenomic datasets. When working within the fundamental assumption that most features do not change across conditions, such extraordinary sparsity levels can then be attributed, by and large, to competition among features for being sequenced. As we illustrate in Fig. To overcome the issues faced by existing techniques, we devised an approach based on the following observations and assumptions. First, group/condition-wise feature count distributions are less noisy than sample-wise feature count distributions, and it may be useful to Bayes-shrink sample-wise estimators towards that of group-wise global estimates. Second, zero abundance values in metagenomic samples are predominantly caused by competition effects induced by sequencing technology  proposed in this work. More details are presented in the “K features whose proportions were chosen from the lung microbiome data, and let 35% of features change across conditions (see Methods for details on simulations). The net true compositional change resulting from each simulation, and their corresponding reconstructions by the various techniques when the count data are generated at different sequencing depths are shown. The following observations form the theme of these, and the more elaborate simulations summarized in Fig. Table independent Poissons/Negative Binomials – as is commonly done in benchmarking pipelines – does not inject compositional bias into simulated data. From the perspective of performance comparisons for compositional correction, doing so is therefore inappropriate. A renormalization procedure after assigning feature-wise fold-changes is necessary. Alternatively, if absolute abundances are generated, subsampling to a desired sample depth needs to be performed.We briefly note a key ingredient about our simulation procedure. Simulating sequencing count data as Below, we show five different results illustrating the improvements Wrench offers over existing techniques in experimental data. The first two show that Wrench leads to reduced false positive calls in differential abundance inference, while the other three demonstrate the improved quality of positive associations.Reduction of false positives We used two approaches to compare the performance of Wrench in reducing false positive calls in differential abundance inference. Each of these analyses was performed across all biological groups with atleast 15 samples in the mouse (2 diet types), Diarrheal (2 groups), Tara (5 oceans), HMP , and HMP  and averaged the results across these 41 experimental groups.We ignored the lung microbiome for these analyses as Scran had particular difficulty making direct comparisons hard. Owing to the heavy sparsity in these datasets, Scran failed to provide scales for 53 out of 72 samples of the lung microbiome, 10 out of 132 observations of the mouse microbiome, 6 out of 992 samples of the diarrheal dataset. Notice that Wrench not only recovers compositional scales for these samples, but also at magnitudes that were coherent with other samples from similar experimental groups (see next subsection) indicating some validity for the computed normalization factors.FOther/FWrench) ratio, where FOther is the total number of significant calls made by a competing method  and FWrench is the total number of significant calls made by Wrench. If Wrench is superior these logged ratios should be >0. The average of these ratios across all the experimental groups mentioned above is plotted in Fig. First, a standard resampling analysis was performed. For every given experimental group, two artificial groups are repeatedly constructed via resampling (without replacement), and the total number of significant calls made during differential abundance analysis is recorded in each repetition. For each iterate, we compute the log2 must be >0. The average of these values across all the experimental groups mentioned above is plotted in Fig. We next exploited the offset-covariate approach introduced in . For eveImproved association discoveries To compare the quality of associations achieved with the various normalization methods, we re-analyzed the Tara Oceans 16S microbiome dataset.Even though the contribution of true compositional changes and other technical biases are not identifiable from the compositional scales without extra information, we asked if the reconstructed scales correlate with orthogonal information on absolute abundances, and other measures of technical biases. The results are summarized in Table We next analyzed the quality of differential abundance inference arising from competing normalization techniques, by performing two sets of enrichment analyses.In the first procedure, we extracted broad genus-level functional annotations from the Faprotax database , and tesTo evaluate the methods in a more fine-grained setting, we devised the following validation approach. The design of the Tara oceans experiments - where 16S reconstructions are obtained from whole metagenome shotgun sequencing data - makes the following analysis feasible. Because the Tara project’s functional  and 16S data arise from the same input DNA samples, the same compositional factors should apply for both datatypes. We therefore estimated compositional factors from 16S data using the different normalization methods and applied the resulting estimates to the KM abundance data from the corresponding matched samples. Next, we computed Spearman rank correlation between OTU and KM normalized abundances and annotated OTUs with those KMs which showed correlation of at least 0.75. Finally, we identified OTUs that were positively associated with each layer using differential abundance analysis. With the KM annotations in place, we performed Fisher exact tests to compute the enrichment scores in the identified OTUs. Detailed tables are provided in Additional file Notice that the first analysis gives a broad sense of the genera identified by the competing methods in light of existing annotations, while the second gives a sense of the quality of annotations one might confer on the OTUs based on the normalized expression levels of OTUs and the measured functional content themselves. In both cases, Wrench is shown to retain relevant information, and the relatively more specific nature of the latter analysis reveals that Wrench demonstrably improves upon other methods.We further demonstrate the impact of compositional bias in downstream inference below. The experimental cell density measurements in the Tara Oceans project show a highly significant overall reduction in the mesopelagic samples when compared the surface layer . Thus, Summing the log-fold changes of significantly associated OTUs (both positive and negative) serves as a measure of a net change experienced by a community. If a given method produces fold change inferences that track the above mentioned empirical cell density measurements, we expect it to yield an overall negative net change value for the significantly differentially abundant OTUs in the mesopelagic community. As illustrated in Fig. not what we observe in samples from metagenomic datasets. All scale normalization techniques resulted in group-wise integrity in the scales they reconstructed within and across related phenotypic categories, potentially indicating the general importance of correcting for confounding induced by compositional bias in general practice. Total sum normalization is oblivious to these biases, making further experimental studies on compositional bias important. For instance, in the microbiome samples arising from the Human Microbiome Project [We next analyzed the phenotypic integrity of the compositional scales reconstructed by the various methods. In the absence of technical biases, following our discussion in the previous subsection, compositional factors should hover around 1 . This is  Project , as showFor completeness, we also attach similar results from all the 11 organs of the rat body map dataset in the Additional file For some researchers, statistical inference of differential abundance is a question of differences in relative abundances; for others, it is a matter of characterizing differences in absolute abundances of features expressed in samples across conditions , 57. In It is clear that the probability of sequencing a particular feature (ex: mRNA from a given gene or 16S RNA of an unknown microbe) in a sample of interest is not just a function of its own fold change relative to another sample, but inextricably linked to the fold changes of the other features present in the sample in a systematic, statistically non-identifiable manner. Irrevocably, this translates to severely confounding the fold change estimate and the inference thereof resulting from generalized linear models. Because the onus for correcting for compositional bias is transferred to the normalization and testing procedures, we reviewed existing spike-in protocols from the perspective of compositional correction, and analyzed several widely used normalization approaches and differential abundance analysis tools in the context of reasonable simulation settings. In doing so, we also identified problems associated with existing techniques in their applicability to sparse genomic count data like that arising from metagenomics and single cell RNAseq, which lead us to develop a reference based compositional correction tool (Wrench) to achieve the same. Wrench can be broadly viewed as a generalization of TMM  for zeroSome practically relevant notes on the application of proposed method to metagenomic datasets follow. First, our choice of methodology and simplifying assumptions were principally determined by the scale and sparsity of the 16s metagenomic datasets and estimation robustness. While fully joint parameter inference algorithms will certainly be more accurate, they are unwieldy and computationally intensive with large scale datasets boasting a large number of features with high sparsity. A case in point is the GAMLSS methodology , which iA few important insights on compositional bias emerge from our theory, simulation and experimental data analyses. In our simulations, we found reference based normalization approaches to be far superior in correcting for sequencing technology-induced compositional bias than library size based approaches. From a more practically relevant perspective, we found that in all the tissues from the rat body map bulk RNAseq dataset, the scale factors can be robustly identified. We expect that in other bulk RNAseq datasets, the assumptions underlying compositional correction techniques to hold well. These results reinforce trust in exploiting such scaling practices for other downstream analyses of sequencing count data apart from differential abundance analysis; for example, in estimating pairwise feature correlations. In the regimes where assumptions underlying these techniques are met, an analyst need not be restricted to scientific questions pertaining to relative abundances alone. The fundamental assumption behind all the aforementioned techniques is that most features do not change across conditions (or the closely related assumption that the log-fold change distribution is centered at 0). As we illustrated, these assumptions appear to hold rather well in bulk RNAseq. Do we expect these to hold in arbitrary microbiome datasets as well? This question is not easy to address without more experiments, but the relatively high correlations obtained with orthogonal measurements of technical biases, the similarity in the compositional scales obtained within samples arising from biological groups, and their sometimes highly significant shifts preserved across normalization techniques and across sequencing centers in large scale studies certainly reinforce the critical importance of characterizing compositional biases, if any, in metagenomic analyses by establishing carefully designed spike-in protocols. In particular, given the inverse dependence of compositional correction factors on the total feature content in the absence of technical biases, the large compositional scale estimates obtained for stool samples  is suspect. Compositional effects can amplify even when a few features experience adverse technical perturbations, and only carefully designed experiments can isolate these effects to inform further normalization approaches. Finally, our results also emphasize the tremendous care one needs to exercise before applying the most natural normalizations based on total sequencing depth or by applying pseudocounts when the data is excessively sparse .This brings us to the question of how effective spike-in strategies are in enabling us to overcome compositional bias. It is immediately clear that the widely used ERCC recommended spike-in procedure for RNAseq cannot help us in overcoming confounded inference due to compositional bias for the simple reason that it already starts with an extract, a compositional data source  that estimates the overall influence of linear technical biases with significantly improved accuracies by sharing information across samples arising from the same experimental group, and by exploiting statistics based on occurrence and variability of features. Such ideas can also be exploited in projects that integrate data from diverse sources. Results obtained with our and other techniques, suggest that substantial compositional differences can arise in (meta)genomic experiments. Detailed experimental studies that specifically address the influence of compositional bias and other technical sources of variation in metagenomics are needed, and must be encouraged.q0·, accounting for sample depth τgj, the mean model for the observed positive count of the ith feature can be written as: θgji encapsulate both the constant νgji, and can be viewed as the net fold change experienced by feature i in sample j from group g. For the purpose of metagenomic applications, and analytic convenience, we slighty relax the standard assumption that most features do not change across conditions by assuming that the feature-wise log-fold changes logνgji arise from a zero mean Gaussian distribution, a common assumption in differential abundance analysis [θgji follows a Gaussian distribution with a mean parameter θgji for every sample leads us to the desired compositional scale estimate θgji are estimated, and subsequently discuss the robust averaging procedure.Briefly, our normalization strategy can be described as follows. Based on Eq. , for a canalysis , 49, 50.Model We assume the following model for the counts Ygji: j from group g, the ith feature’s count value is sampled from a hurdle log-normal distribution, in which with probability πgji, a value of 0 is realized; and with probability 1−πgji a positive count is observed. The probabilities πgji are determined by sample covariates, including the total sequencing depth. The positive count value is realized as an exponential of a Gaussian random variable Zgji the mean of which is determined , two-way group-sample interaction (μgj), a three-way group-sample-feature interaction random effect agji and a noise term.The model assumes the following. For each sample τgj=Ygj+ is the total count of sample gj. The reference value for each feature i, qi0, is set to the average proportion value i in sample gj, i.e., ζg0 and θgji are determined based on the corresponding moments of the corresponding empirical distribution of the group-wise pooled raw ratios of proportions: i in the samples from the entire group. Specifically, we fix the group-wise compositional scale μgj and agji are estimated/predicted using standard random effects estimators: Estimation of regularized ratios Robust averaging of the mentclass2pt{minimAn advantage of these weights (and hence the model) is that the weighting strategies proceed smoothly for features with zero expression values as well, unlike the binomial weights employed in the TMM procedure. Furthermore, when constructing averages, the weights have a favorable property of downweighting zeroes at higher sample depths relative to those in samples at lower sample depths.In summary, we explored the performance of the following estimators for sample-wise compositional factors: W1,W2 and W3 to work comparably well in simulations and empirical comparisons, and W0 slightly less so at high sparsity levels at low sample depths. We prefer W2 as it systematically integrates both the hurdle and positive component variations. In our software implementation, users have the option for other weighted variants, and whether weighted averaging over zeroes is necessary as they see fit. Software documentation and supplementary material embark on further discussions on these ideas.We have found batch correction can be immediately made; this work is being planned for a forthcoming submission.Finally, with this framework setup, extensions for n=72) where the lung microbiome of smokers and non-smokers were surveyed . A diet study in which the gut microbiomes (n=139) of carefully controlled laboratory mice fed plant-based or western diets were sequenced [n=992) from diarrhea-afflicted and healthy children from various developing countries [n=139) was downloaded from The Tara Oceans project website under http://ocean-microbiome.embl.de/data/miTAG.taxonomic.profiles.release.tsv.gz. The flow cytometry counts for autotrophs, bacteria, heterotrophs, picoeukaryotes were obtained from TaraSampleInfo_OM.CompanionTables.txt from the same website and summed to serve as a rough measure of total cell count that correlates with sequence-able DNA material. The Human Microbiome Project count data were downloaded from http://downloads.hmpdacc.org/data/HMQCP/otu_table_psn_v35.txt.gz, and the associated metadata are from v35_map_uniquebyPSN.txt.bz2 under the same website.We principally demonstrate our results with five datasets from metagenomic surveys. A smoking study (equenced . A largeountries . 16S metountries . The TarThe processed bulk-RNAseq data corresponding to the rat body map from  was obtaThe Unique Molecular Identifier (UMI) single cell RNAseq data from Islam et al.  was downAll analysis and computations were implemented with the R 3.3.0 statistical platform. EdgeR’s compNormFactors for TMM, DESeq’s estimateSizeFactors, Scran’s computeSumFactors (with positive=TRUE in sparse datasets) and metagenomeSeq’s calcNormFactors for CSS were used to compute the respective scales. Implementation of CLR factors used a pseudo-count of 1 following , and werhttp://bioconductor.org/packages/Wrench.Wrench is implemented in R, and is available through the Wrench package at qi1 for features i=1…p, and the fraction of features that are perturbed across the two conditions f, we sample the set of true log fold changes (logνgi) from a fold change distribution (fold change distribution) for those randomly chosen features that do change. The fold change distribution is a two-parameter distribution chosen either as a two-parameter Uniform or a Gaussian. Based on the expressions from the first subsection of the “τ, the sequencing output Ygi· for all i were obtained as a multinomial with proportions vector f, and the two parameters of the fold change distribution, and ask, how various normalization and testing procedures compare in terms of their performance. For bulk RNAseq data, as illustrated in Additional file M reads per sample.Given a set of control proportions g. We used j∈1…ng for all g, where ng represents the number of samples in group g, for all i (including the truly null features), sample νgji from K), log(10K) and log(100K) reads. These parameters were chosen based on comparisons with MA plots, the sparsity levels and total sample depths observed in current experimental datasets. We repeated simulations for 20 iterations.For comparison of Wrench scales with other normalization approaches, we altered the above procedure slightly to allow for variations in internal abundances of features in observations arising from a group νgj· is the vector of fold changes for sample j in group g, and q1· is the average vector of feature-wise control proportions. As it can be seen from the expression for Λgj, notice that perturbing features with very low relative abundances do not demonstrably induce compositional bias at low sample depth settings (unless perturbed by very high fold changes). So for every simulation iteration, the fraction f of features that were perturbed in cases were chosen randomly according to their control proportions. We apply the term compositional correction factor for normalization factor for a sample as the product of its compositional correction factor with something that is proportional to that of its sample depth. Thus, all technical artifacts like total abundance changes, but sample depth, are incorporated into the definition of compositional factors.In both versions of simulations, the total induced abundance change relative to that of the control is For simulations, we used edgeR as the workhorse fitting toolkit. The compositional scale factors provided by all normalization methods were provided to edgeR as offset factors. We define detectable differential abundance in our simulated count data as follows. For each simulation, as we know the true compositional factors, we input them as normalization factors in edgeR, and the detectable differences in abundances are recorded. All the performance metrics are then defined based on this ground truth. Because we are interested in fold changes and their directions, the performance metrics we report are redefined as follows: Sensitivity as the ratio of the number of detectable true-positives with true sign over the total number of positives, False discovery as the ratio of the number of detectable true positives with false sign and false positives, over the total number of significant calls made.The offset-covariate analysis followed the procedure in . For reshttp://ocean-microbiome.embl.de/data/TARA243.KO-module.profile.release.gz) and the 16S reconstructions are obtained from the same input DNA through whole metagenome shotgun, the same compositional factors apply to both datatypes. Each normalization approach’s compositional factors for 16S data was used to rescale the KM relative abundance data. This normalized KM data was used to annotate each OTU by  KMs that Spearman correlate at a value of atleast.75.Fisher exact tests were used to perform functional enrichment analyses for positively associated OTUs. A Genus level functional enrichment analysis was first performed by aggregating annotations from the FAPROTAX1.1 database  at the Ghttp://bioconductor.org/packages/Wrench.Wrench is available from R/Bioconductor as an R package at the URL: Additional file 1Supplementary Note. Presents further discussions on compositional bias, and supplementary results in context. Additional file 2Enrichment Analysis Results. The results of enrichment analyses based on faprotax annotations and Kegg modules procedure described in the Methods section is presented. Names in the sheets and their descriptions are as follows: KM.POS.SIG.MES and KM.POS.SIG.DCM show the Kegg module based enrichment analyses for positively associated features in MES and DCM layers respectively. FAPRO.POS.SIG.MES and FAPRO.POS.SIG.DCM show the results of faprotax annotations based enrichment analyses for positively associated features in MES and DCM layers respectively. (XLSX 45 kb)


Recent advances in high-throughput sequencing have accelerated the accumulation of omics data on the same tumor tissue from multiple sources. Intensive study of multi-omics integration on tumor samples can stimulate progress in precision medicine and is promising in detecting potential biomarkers. However, current methods are restricted owing to highly unbalanced dimensions of omics data or difficulty in assigning weights between different data sources. Therefore, the appropriate approximation and constraints of integrated targets remain a major challenge. In this paper, we proposed an omics data integration method, named high-order path elucidated similarity (HOPES). HOPES fuses the similarities derived from various omics data sources to solve the dimensional discrepancy, and progressively elucidate the similarities from each type of omics data into an integrated similarity with various high-order connected paths. Through a series of incremental constraints for commonality, HOPES can take both specificity of single data and consistency between different data types into consideration. The fused similarity matrix gives global insight into patients' correlation and efficiently distinguishes subgroups. We tested the performance of HOPES on both a simulated dataset and several empirical tumor datasets. The test datasets contain three omics types including gene expression, DNA methylation, and microRNA data for five different TCGA cancer projects. Our method was shown to achieve superior accuracy and high robustness compared with several benchmark methods on simulated data. Further experiments on five cancer datasets demonstrated that HOPES achieved superior performances in cancer classification. The stratified subgroups were shown to have statistically significant differences in survival. We further located and identified the key genes, methylation sites, and microRNAs within each subgroup. They were shown to achieve high potential prognostic value and were enriched in many cancer-related biological processes or pathways. In current clinical practice, cancer is typically categorized based on its tissue source and pathological histology. However, cancer is also known as a well-characterized pathological system among the molecular level. Most cancers emerge along with complex molecular alterations at the germ and/or somatic level . As such, information on these regulatory patterns can improve our integrated analysis. Existing methods can be roughly divided into three categories based on their methodology: latent variable representation methods, probabilistic modeling methods, and network-based methods  integrates the similarities for each type of omics data into a unified and stable one, thus achieving a simplified link of the underlying mechanism of various types of expression. We modeled integrated similarity as the approximation to various high-order paths across each local dataset, the progressively increased high-order path can represent different consistency requirements. We especially emphasized interaction within each pair of local layers rather than updates using a single layer and average of the rest layers. HOPES models such similarity integration as a minimization problem consist of three subobjective functions, for which an efficient numerical algorithm was designed to obtain the solution. Through the optimization procedure, we strengthened the strong correlation between patients and removed the weak ties mainly caused by noise. Thereby, we successfully subtype cancers with significant clinical differences. Real experiments on five cancer projects of TCGA and a normal control set for cancer diagnosis and prognosis tasks demonstrated the excellent performance of HOPES in subtyping and identifying key oncogenesis pathway. The subsequent biological analysis of the resulted key pathway was shown to possess potential prognostic value and biological significance.We tested the proposed HOPES on five distinct tumor datasets, downloaded from TCGA. The tested samples consisted of five tumor types: glioblastoma multiforme (GBM), lung squamous cell carcinoma (LUSC), kidney renal clear cell carcinoma (KIRC), colon adenocarcinoma (COAD), and a cervical cancer dataset (CESC). Each tumor was measured by DNA methylation, gene expression, and miRNA expression. The overall survival information corresponding to each sample was also considered. The first four projects were the same as the experimental data obtained in a previous study . Preprocessing as mentioned above was also performed on the 35 normal controls. Although we simply integrate healthy samples from different tissues as a control set, the normalization step can remove differences between different tissues, and ensure the separability between cancer samples and healthy controls.Similarity network fusion(SNF) is a novel algorithm which integrates different omics data through computing and fusing patient similarity networks. SNF conduct the similarity fusing by iteratively updating every similarity network, making it more similar to the others with every iteration as follows:P represent the similarity matrix derived from each datasets, S represent the local affinity which only contains the nearest neighbors' information, and m is the number of different data types. Actually the iteration process means updating the similarity between node i and node j in Pv) This procedure treats each network as the same without weights constraints. (2) There is only one connection path between different datasets that across two intermediate nodes which is insufficient for depicting complex network interaction. (3) The information exchange only exists in one dataset and the average of the others. There are no direct mutual adjustments between different datasets which may cover some interconnection between specific data types. The incomplete network connection model makes it difficult to recover the most precise global similarity pattern or resist high-level noise in biological data.K nearest neighbor, (2) Path-1 similarity import one intermediate node to enhance the effect of each local affinity, (3) Path-2 similarity import two intermediate nodes to integrate interaction between different local affinity to enhance the commonality. The detailed numerical expression and constraint of the different order paths are as follows.To have a consistent and highly representative global similarity, HOPES simulate three different network connection models with different path length and try to find the fused pattern which retains the maximal commonality. As it was depicted in C different omics datasets, and their local affinities Si were evaluated by a scaled exponential similarity kernel  is to ensure proximity between the global affinity and the transformed affinity after it has been weighted by each local affinity. One can impose a stricter requirement that the fused global similarity is closed to the transformed similarity which has been filtered by each underlying local affinity through higher-order paths. For example, with path-2 proximity,It can be noted that m and those of node n, while neighbors' information of two vertexes is from two different datasets. This interactivity between different local affinity sharply strengthens the commonality requirement. The filtration process is supposed to weaken the original edges in W unless the correlation between node i and j is simultaneously supported by each pair of data types.Where Finally, combining the aforementioned constraints for modeling proximities of various path orders, we propose the determination of the global affinity by minimizing the following energy function:where α and β are hyperparameters that adjust the weight of different order constraints and can be empirically set. Details on parameter tuning was attached in the In conclusion, the three different order paths represent an incremental relationship from specificity to commonality and from weak constraint to strong constraint. They can simulate much more complex network connection models and set increasing consistency requirements on the global similarity. Therefore, we can take all the specialty of every single dataset, the interconnection between datasets, and global consistency into consideration and construct a more comprehensive and robust global similarity network. Moreover, the weights can be adjusted manually based on the real world condition which makes HOPES more flexible.Once we have the fused global similarity matrix, it can be the fundamental structure for much downstream analysis. The most directly is applying the spectral clustering to cluster the samples into different subgroups which can be used for cancer diagnosis or molecular subtyping. In this paper, to eliminate the variations due to clustering initialization, the consensus clustering .Except for clustering, we also tried to project the global structure into specific characteristics in every single dataset. Since these features are the most relevant to the fused results, they can not only be prognostic valuable but also may indicate some interconnection between different omics layers. We located these features using MCFS, an unsupervised feature selection algorithm for multi-cluster data  as a criterion for performance, and for each noise condition we ran repeated trials 20 times to eliminate accidental error. Collectively, all simulation results suggested that HOPES can always successfully recover the four pre-defined clusters from incomplete layers . As we dThe numerical results are shown in We then tested whether the proposed method HOPES can distinguish tumor samples from normal controls based on their omics measurements. We applied the HOPES and other comparative methods to combinations of COAD (92 samples), KIRC (122 samples), LUSC (106 samples) and 35 normal controls. The gene expression, methylation, and miRNA expression data for these case/control sets and the overlap among them are shown in We calculated the classification accuracy on the collected tumor vs. normal samples. Nevertheless, integration methods such as iCluster+ which splices all of the features, strongly rely on a priori gene selection; therefore, if the number of variables is imbalanced, it will be difficult to retain positive information. Thus, the classification accuracy falls in between the worst and best of single level analyse, so as for moCluster. The Clusternomics extract the global assignment based on the mixture of local partitions, so if clustering results were obscure in single data layer the global performance can not be satisfied. The sample size also influence the performance of Clusternomics a lot. We take an example of KIRC dataset for further analysis. One can see that the fused data clustered tightly and uniformly, as shown by the heatmap of the similarity matrix . One canP-value. To facilitate visual comparisons, the results on both the survival curves and the first three principal components are shown in P-value, highlighted in bold in To illustrate the prognostic ability of the elucidated similarity, we applied HOPES to five tumor omics datasets, namely CESC, GBM, COAD, KIRC, and LUSC. The similarities obtained by SNF and HOPES were used to cluster each tumor sample into three subtypes. Their corresponding survival curves were drawn and quantified by the log-rank test. The statistical significance of differences between them was denoted by the To clarify the beneficial characteristics of the similarity elucidated by HOPES, we took another example of CESC for further analysis. We compared the clustering results on each single type of omics data alone with those for the elucidated one. The results are plotted in a heatmap as shown in 2 test to determine whether the two clustering results are significantly associated, and our cluster results showed a strong correlation with each single genomic data cluster, with small P-values .We also found that the elucidated similarity highlights the molecular heterogeneity in cervical carcinomas. The subtyping by HOPES differed depending on the histological classification, showing a discrepancy between phenotype and gene-level types. For instance, the sub-clusters by HOPES largely corresponded to those by methylation level. The CESC project classified samples into six subgroups by histology. To determine the correspondence between the histological classification and HOPES, we merged four different types of adenocarcinoma into one type, as used in studying cervical cancer , six CpG sites , and six miRNAs . Second, we performed survival analysis on each single feature using the kmeans as a general clustering method, and found that more than 1/3 relevant features showed good partition ability with a Log-rank test p-value < 0.05. p-value < 10−6, notably, these significant terms strongly correlate with cancer. An example of this is the most significant term, namely respond to hypoxia. Numerous research has confirmed that pathological hypoxia plays a pivotal role in cancer progression and migration  were identified, p-value < 10−4. Among these pathways, cancer was the most common subclass such as pathways in cancer, microRNAs in cancer, Bladder cancer, colorectal cancer and pancreatic cancer. Besides direct cancer pathways, the PI3K-AKT-FoxO signaling cascade was identified, which has been previously identified to be involved in cancer and aging , which can contribute to cancer subtyping at the molecular level and further clinical treatment. The obtained subgroups are also shown to be promising for the identification of potential biomarkers by revealing the key components that drive the differences between subgroups. The enrichment analysis on the key components confirmed the power of HOPES in discriminating the biomarkers.https://doi.org/10.7908/C11G0KM9” (Broad Institute TCGA Genome Data Analysis Center, github.com/scutbioinformatics/HOPES.The CESC dataset generated during and analyzed during the current study are available in the Broad Institute TCGA Genome Data Analysis Center with identifier “AX and HC conceived, designed, and supervised all phases of the project. AX performed experiments and wrote the manuscript. AX and JC performed the bioinformatics analysis. JC, HP, and GH contributed to discussions, and editing of the paper. All authors read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Nowadays, analyzing circulating tumor DNA (ctDNA), a very small part of circulating free DNA (cfDNA) carried by blood, is considered to be an interesting alternative to conventional single-site tumor tissue biopsies, both to assess tumor burden and provide a more comprehensive snapshot of the time-related and spatial heterogeneity of cancer genetic/epigenetic scenery. The determination of ctDNA and/or mapping its characteristic features, including tumor-specific mutations, chromosomal aberrations, microsatellite alterations, and epigenetic changes, are minimally invasive, powerful and credible biomarkers for early diagnosis, follow-up, prediction of therapy response/resistance, relapse monitoring, and tracking the rise of new mutant subclones, leading to improved cancer outcomes This review provides an outline of advances published in the last five years in electrochemical biosensing of ctDNA and surrogate markers. It emphasizes those strategies that have been successfully applied to real clinical samples. It highlights the unique opportunities they offer to shift the focus of cancer patient management methods from actual decision making, based on clinic-pathological features, to biomarker-driven treatment strategies, based on genotypes and customized targeted therapies. Also highlighted are the unmet hurdles and future key points to guide these devices in the development of liquid biopsy cornerstone tools in routine clinical practice for the diagnosis, prognosis, and therapy response monitoring in cancer patients.  Cancer is one of the leading causes of death worldwide. According to the World Health Organization (WHO) statistics, cancer accounts for 1/6 of the global death toll, and more than 40% of cancers can be overcome if they are diagnosed early 3-/4- after hybridization with the target DNA resulted in a linear range from 50.0 fM to 1.0 nM, with a LOD of 1.72 fM and a clear discrimination against a single-base mismatched sequence. The label-free DNA sensor was used to analyze BRCA1 in spiked serum samples.Label-free and low-fouling biosensors for breast cancer susceptibility gene   a. HCR ison (HCR) b and to KRAS and BRAF in ctDNAs, from serum of cancer patients with no need for enzymatic amplification, has been proposed by O. Kelley group [2-coated silicon wafer to construct contact pads and electrical leads. Then, a Si3N4 layer was placed, in order to passivate the surface and 5 μm apertures. These were then opened in the top passivation layer by photolithography to supply a template for the growing of electrodeposited Au. The as-formed Au structures were then coated with a thin layer of Pd. The three-dimensional nanostructure of the NME allowed the probes to have an adequate alignment direction, thus increasing the hybridization efficiency. After target hybridization, the biosensors were interrogated, using an electrocatalytic reporter pair of Ru(NH3)63+ and Fe(CN)63−, by DPV. The voltammetric response increased in the presence of the target mutant. Ru(NH3)63+ was electrostatically attracted to the negatively-charged phosphate backbone of nucleic acids that binds to the probes immobilized on the surface of electrodes, and was reduced to Ru(NH3)62+ when the electrode was biased at the reduction potential [63−, present in solution, chemically oxidized Ru(NH3)62+ back to Ru(NH3)63+, which allowed for multiple turnovers of Ru(NH3)63+ and generated a high electrocatalytic current  by DNA methyltransferases is the most studied epigenetic alteration, due to its important role in carcinogenesis. Apart from 5-mC, the Ten-Eleven Translocation (TET) enzymes mediate sequential oxidation of 5-mC to 5-hydroxymethylcytosine (5-hmC), then to 5-formylcytosine (5-fC), and finally to 5-carboxylcytosine (5-caC) . These i2O2. The method allowed the detection of as little as 40 pg of methylated genomic DNA, 1% methylation level, and tumor-specific methylated DNA in plasma of NSCLC patients, attaining a very high clinical sensitivity of 91%. The electrochemical analysis of circulating methylated DNA in plasma was proposed by Chen et al. , impleme2O2/TMB system, the method allowed the successful examination of just a single methylated DNA molecule in the presence of a 1,000-fold excess of unmethylated alleles and was applied to plasma samples from lung cancer patients.Wang et al.  proposedRASSF1A promoter methylation, using Fe3O4/N-trimethyl chitosan/gold nanocomposite, as a tracing tag to label a DNA detector probe, and a SPCE modified with anti-5-mC antibody entrapped in thin polythiophene film for the selective capture of methylated DNA. The electrochemical detection implies oxidation of the Au nanoparticles and monitoring their subsequent reduction by DPV. The method exhibited a linear range from 1 × 10−14 M to 5 × 10−9 M and a LOD of 2 × 10−15 M for the synthetic methylated target DNA. Moreover, successful recoveries were reported in the analysis of plasma samples, spiked with increasing concentrations of synthetic methylated target DNA.Daneshpour et al.  reportedPIK3CA gene in ctDNA , antibodies specific for the target methylated cytosines, and were used either to capture or detect the methylated DNA, specific biotinylated DNA probes, and amperometric detection at screen-printed carbon electrodes ,30. The Common infections with particular viruses, such as human papillomaviruses (HPVs), are often cleared by the immune system without serious consequences. However, a small fraction of these infections become persistent over longer periods of time and are associated with an increased risk of developing pre-cancerous lesions, and ultimately cancer. On the other hand, there is evidence that people infected with Hepatitis B virus (HBV) are at high risks of developing liver cancer . Accordi−5 to 1 × 10−3 M, a LOD of 0.8 µM of target DNA, and was successfully employed for the determination of amplicons obtained from patients´ blood samples using limited PCR cycles.Ahangar and Mehrgardi  prepared2O2/HQ system, at a screen-printed electrochemical array comprising eight carbon electrodes. These methods yielded linear ranges from 1 pM to 1 nM, with a LOD of 1 pM, and from 0.1 to 50.0 ng and LODs of 0.1 and 0.7 ng, for the synthetic target DNA, and the DNA extracted from CaSki cells for the PCR, and LAMP-based methods, respectively. These MBs-involving biosensing strategies allowed the discrimination between these two hrHPVs and were used for the analysis of both, cancer cell lines and real patients’ cervical brush smears. Bartosik et al.  developeCompared with other varieties of cancer-related biomarkers, ctDNA has an exclusive clinical value. Apart from the intrinsic advantages of employing liquid biopsies, such as handy sampling, low invasiveness, and real-time monitoring, its specificity is higher and can solve the problem of tumor heterogeneity . AlthougApart from these unique features, the smart selection of bioreceptors, bioassay format, and amplification strategies, involving mainly the use of nanomaterials, nucleic acid amplification strategies, and multi-tags reagents, are key aspects to placing electrochemical biosensors in a privileged position for the analysis of ctDNA and their specific features. 3O4/TMC/Au [The methods discussed above show the involvement of unconventional probes such as THMS , DCPs 2, PNA 2525,31 and4/TMC/Au ), or car4/TMC/Au  or enzym4/TMC/Au , allowinThe selected methods, involving the use of different electrodes substrates , formats (MBs-based or integrated), affinity bioassays  and electrochemical techniques  are just a small sample of the versatility and attractiveness of electrochemical biosensors in the clinic to perform single or simultaneous determination of circulating tumor DNA features by targeted or untargeted analysis. Electrochemical biosensors have been applied mostly to the determinations of tumor-specific mutations and methylation events, and less to ctDNA quantification and cancer-related viral DNA sequences. As shown in It is worth remarking here that electrochemical biosensors offer interesting advantageous features compared with the other most common type of biosensors proposed for ctDNA detection based on optical detection. Although optical reporters can be directly conjugated to the synthetic probe and are less prone to inhibitory effects than the enzyme labels often used in electrochemical strategies, they use bulky, expensive, high-power requirement detectors. On the contrary, electrochemical biosensors overcome the limitations of the optical ones in terms of cost, portability, and compatibility with POC devices, which make them very promising tools, particularly in clinical diagnosis. Moreover, due to the inherent miniaturization of electrochemical biosensors, and their compatibility with standard microfabrication and semiconductor technologies, simple, accurate, portable, and inexpensive platforms can be constructed for ctDNA analysis. It is important also to mention that the strong optical background, that arises from the scattering and absorbance of complex samples, significantly limits the usefulness of optical biosensors when challenged directly in complex environments. These factors explain, as well, why electrochemical biosensors have been increasingly gaining ground compared with their optical counterparts in ctDNA analysis during the past few years ,40.Despite the skyrocketing development of electrochemical biosensors and the great promise of ctDNA-based liquid biopsy for cancer diagnosis, prognosis, and personalized treatment , hard woSome of the most crucial challenges in ctDNA assessment include its isolation and amplification or sequencing analysis, due to its highly fragmented nature and wide variability in the fragment sizes, which affect the accuracy of the results. Another important biological challenge is the low abundance of ctDNA (≥ 1 genome in 5 mL of plasma). Thus, increased volumes of blood samples are needed to perform the determination . MoreoveIt is important to point out the strong dependence of ctDNA concentration with various pre-analytical factors, including sample source, collection, and processing . All these factors should be standardized and considered to develop reliable ctDNA clinical tests ,5. The low yield of ctDNA extracted , and theOther important challenges are related to the insufficient knowledge of the tumor microenvironment and the immunologic response to ctDNA released in liquid biopsies, and with the adoption of ctDNA analysis in the clinical environment, where not only the laboratory personnel must get familiar with the newly methodologies, but also the medical personnel must increase their knowledge on the potential of this biomarker, and how to implement it in their diagnostic routine. The widespread use of ctDNA analysis in the clinic requires greater standardization and validation of the methodologies, which would provide an efficient framework for their implementation into clinical practice . Nowadays, there are scarce studies on the direct comparison among various ctDNA analytical methodologies. Therefore, appropriate methods for reliable ctDNA quantification and efficient recovery for molecular analysis are unsatisfactorily defined. There is a glaring requirement to develop well-established standard operating procedures for ctDNA analysis, bearing in mind all feasible analytical and pre-analytical factors that may affect the test results . FurtherRegarding clinical validation, the development of a ctDNA biomarker cancer detection and monitoring methodology needs vast clinical studies and sample evidence both, for the efficiency of the method and reliability of the marker. The clinical utility of the developed test by performing independent tests, at multiple centers, using large cohorts of patients for each targeted tumor type ,6. MoreoAdditional progress of novel methodologies is needed to exploit to the fullest ctDNA’s possibilities for early stage cancer patients and those undergoing post-treatment monitoring. Techniques allowing single molecule resolution may prevail in the foreseeable future, given the quality of statistical information they can supply, compared to bulk measurements . NeverthIn conclusion, measuring tumor DNA dynamics in blood, through ctDNA, is a nascent field garnering indisputable attention because of the benefits it brings to cancer management. Moreover, it is poised to advance rapidly both, by overcoming the caveats and technical issues associated with ctDNA as a biomarker, and in the development of novel technologies surpassing the limitations of the conventional ones for its determination. Within this context, electrochemical biosensors constantly pursued over the last five years for this purpose, are envisioned to be indispensable to propel this field forward, by facilitating the ctDNA adoption in a clinical environment.


Cancer subtypes were usually defined based on molecular characterization of single omic data. Increasingly, measurements of multiple omic profiles for the same cohort are available. Defining cancer subtypes using multi-omic data may improve our understanding of cancer, and suggest more precise treatment for patients.We present NEMO (NEighborhood based Multi-Omics clustering), a novel algorithm for multi-omics clustering. Importantly, NEMO can be applied to partial datasets in which some patients have data for only a subset of the omics, without performing data imputation. In extensive testing on ten cancer datasets spanning 3168 patients, NEMO achieved results comparable to the best of nine state-of-the-art multi-omics clustering algorithms on full data and showed an improvement on partial data. On some of the partial data tests, PVC, a multi-view algorithm, performed better, but it is limited to two omics and to positive partial data. Finally, we demonstrate the advantage of NEMO in detailed analysis of partial data of AML patients. NEMO is fast and much simpler than existing multi-omics clustering algorithms, and avoids iterative optimization.https://github.com/Shamir-Lab/NEMO.Code for NEMO and for reproducing all NEMO results in this paper is in github: Bioinformatics online. Recent technological advances have facilitated the production of multiple genome-wide high throughput biological data types, collectively termed ‘omics’. These include genomics, transcriptomics, proteomics and many more. Analysis of omics datasets was proven invaluable for basic biological research and for medicine. Until recently, research in computational biology has focused on analyzing a single omic type. While such inquiry provides insights on its own, methods for integrative analysis of multiple omic types may reveal more holistic, systems-level insights.Omic profiles of large cohorts collected in recent years can help to better characterize human disease, facilitating more personalized treatment of patients. In oncology, analysis of large datasets has led to the discovery of novel cancer subtypes. The classification of tumors into these subtypes is now used in treatment decisions  based analyses. Dimension reduction approaches include jNMF, MultiNMF , a simple algorithm for multi-omics clustering. NEMO does not require iterative optimization and is faster than prior art. NEMO is inspired and bulids on prior similarity-based multi-omics clustering methods such as SNF and rMKL-LPP. NEMO’s novelty lies in its simplicity, and in its support of partial data. Its implementation, as well as code to reproduce the results in this paper, are available in github: We evaluated the performance of NEMO by comparing it to a wide range of multi-omics clustering methods on several cancer data types. On full datasets, despite its simplicity, NEMO performed comparably to leading multi-omics clustering algorithms. In order to evaluate performance on partial multi-omic data, we compared NEMO to PVC and to data imputation followed by clustering using several methods. In most tests on synthetic data and on real cancer data, NEMO had clear advantage. Finally, we analyzed NEMO’s clustering solution for Acute Myeloid Leukemia, and showed the merit of using multiple omics with partial data.NEMO works in three phases. First, an inter-patient similarity matrix is built for each omic. Next, the matrices of different omics are integrated into one matrix. Finally, that network is clustered.n subjects (samples or patients). Given L omics, let lX denote the data matrix for omic l. lX has dimensions lp × n, where lp is the number of features for omic l. The input to NEMO is a set of data matrices of lix the profile of sample i in omic l (column i in lX). Let liη denote its k nearest neighbors within omic l, where Euclidean distance is used to measure profile closeness. For omic l, an n × n similarity matrix lS is defined as follows:Denote by ith and jth samples to their nearest neighbors and the squared distance between these two samples  the omic types available for both samples. Then:NEMO can handle samples that were measured on only a subset of omics. Specifically, we require that each pair of samples has at least one omic on which they were both measured. Note that this holds in particular if there is an omic for which all samples have measurements, which is often the case for gene expression data. Under these conditions, lX is a full matrix, albeit with fewer rows. For example, the expression of the same set of genes is measured for all patients with RNA-seq data. When patients have different sets of measured features in the same omic, either intersection of the features or imputation of missing values is required.Note that we require that all samples that have measurements for some omic, have measurements for the same set of features in that omic, such that even in the partial data settings each l may have a different number of samples k of nearest neighbors is chosen per omic. Generalizing the full data setting, for omic l we set On partial datasets, each omic l takes k nearest neighbors of each patient and its average distance to them in a specific omic can be computed in time O(n) per patient (O(k) time. Each entry in lRS is also calculated in O(k). ARS calculation therefore requires Computing the distance between a pair of patients in omic Other similarity-based methods such as SNF and rMKL-LPP need the same In datasets where the true clustering is known, to gauge the agreement between a clustering solution and the correct cluster structure, we used the adjusted Rand index (ARI) .P-values that overestimate the significance , Breast Invasive Carcinoma (BIC), Colon Adenocarcinoma (COAD), Glioblastoma Multiforme (GBM), Kidney Renal Clear Cell Carcinoma (KIRC), Liver Hepatocellular Carcinoma (LIHC), Lung Squamous Cell Carcinoma (LUSC), Skim Cutaneous Melanoma (SKCM), Ovarian serous cystadenocarcinoma (OV) and Sarcoma (SARC). For each dataset, we analyzed three omics: gene expression, methylation and miRNA expression. When some of the patients lacked measurements for some of the omics, we included only those patients that had data from all omics. We have previously used these datasets to benchmark multi-omics clustering methods . Datasetk, the number of neighbors in NEMO to We compared NEMO on each dataset to nine different multi-omics clustering methods. As early integration methods we used LRAcluster, and k-means and spectral clustering on the concatenation of all omic matrices. For late integration we used PINS. We used MCCA, MultiNMF and iClusterBayes as joint dimension reduction methods. Finally, SNF and rMKL-LPP represented similarity-based integration. We set rk study , where fTo assess the clustering solutions we compared the survival curves of different clusters, and performed enrichment analysis on clinical labels (see Section 2). To avoid biases, we chose the same set of clinical parameters for all cancers: age at initial diagnosis, gender and four discrete clinical pathological parameters. These parameters quantify the progression of the tumor (pathologic T), cancer in lymph nodes (pathologic N), metastases (pathologic M) and total progression (pathologic stage). In each cancer type we tested the enrichment of each parameter that was available for it.P-value for KIRC, the only other dataset for which NEMO did not reach significance, was 0.063. NEMO had an average logrank P-value of 1.64, second after MCCA (1.75). NEMO found at least one enriched clinical parameter in eight of the ten datasets, the highest number found and tied with spectral clustering, LRACluster, rMKL-LPP, PINS and MCCA. The average number of enriched clinical parameters for NEMO was 1.5, second only to rMKL-LPP with 1.6. Standard deviations across the different datasets for Compared to the other methods, NEMO tended to choose an intermediate number of clusters per dataset  data were kept full. The θ values tested were between 0 and 0.7. In all datasets, the first omic was DNA methylation, and the second (from which samples were removed) was gene expression. In the three-omic scenario, the last omic was miRNA expression. We repeated each test five times, and the P-values reported here are the geometric averages of the observed P-values.We next compared NEMO to other methods on partial cancer datasets, by simulating data loss on the ten full TCGA datasets analyzed above. We tested two scenarios, (i) using three omics for all subtypes, and (ii) using only two omics, to allow comparison with PVC. We randomly sampled a fraction Full details on how each method was executed are in θ = 0) and its previous results  is believed to be the most informative omic. While on average performance across the cancer types was not consistent, we did see a decrease in performance on some of the datasets. The difference between the performance of MCCA for full data here  to perform imputation for the BIC dataset with methylation and mRNA expression omics, when k, the number of neighbors, and with respect to the number of clusters. We first tested robustness on the simulated data. We executed NEMO on the three-omic simulated data described previously. We used k, except for low values.We sought to assess NEMO’s robustness with respect to the parameter k values we used in the full and partial data analyses. P-values for logrank test for each value of k. Generally, the performance of NEMO was robust with respect to k. In a few cases, such as the GBM, SKCM and SARC datasets, the results varied more depending on k. This is partially explained by the different number of clusters NEMO chose for different values of k . The significance was higher than obtained by all other nine clustering methods on the full data subcohort . This shows the higher significance gained from analyzing more samples, including partial data.We applied NEMO to an AML cohort of 197 patients from TCGA. This is a partial dataset, containing 173 patients with gene expression profiles, 194 with methylation and 188 with miRNA profiles. As it is partial, the dataset cannot be directly clustered using other algorithms for multi-omics clustering. To apply these methods, one must limit analysis to a sub-cohort of 170 patients that have full data, or perform imputation. NEMO suggested five clusters for this dataset; their sizes appear in P-value 5.4e−2, which shows NEMO’s favorable prognostic value. Executing NEMO using only a single omic, results for gene expression, methylation and miRNA expression data had logrank P-values 3.4e−2, 3.4e−3 and 3.7e−3 respectively. These results demonstrate the improved clustering obtained by NEMO using multi-omic data.We compared the prognostic value of NEMO’s clusters to that of the FAB (French-American-British) classification. FAB is a well-accepted clinical classification for AML tumors  outperformed all other methods on the partial cancer datasets with two omics, while NEMO was better on the simulated partial datasets. As PVC is limited to two omics, extension of that NMF-based algorithm to more omics and to include a mechanism for determining the number of clusters is desirable.In some of the cancer datasets the results obtained using only mRNA expression and DNA methylation were superior to those achieved when also considering miRNA expression. In addition, in some of the datasets we did not observe a significant decrease in performance when removing a fraction of the gene expression data for cancer patients. This phenomenon suggests that multi-omics clustering does not necessarily improve with more omics see also . A possiClustering cancer patients into subgroups has the potential to define new disease subtypes that can be used for personalized diagnosis and therapy. The increasing diversity of omics data as well as their reduced cost creates an opportunity to use multi-omic data to discover such subgroups. NEMO’s simplicity, efficiency and efficacy on both full and partial datasets make it a valuable method for this challenge.btz058_Supplementary_DataClick here for additional data file.