To date, most studies involving high-throughput analyses of sputum in asthma and COPD have focused on identifying transcriptomic signatures of disease. No whole-genome methylation analysis of sputum cells has been performed yet. In this context, the highly variable cellular composition of sputum has potential to confound the molecular analyses.Whole-genome transcription (Agilent Human 4 × 44 k array) and methylation (Illumina 450 k BeadChip) analyses were performed on sputum samples of 9 asthmatics, 10 healthy and 10 COPD subjects. RNA integrity was checked by capillary electrophoresis and used to correct in silico for bias conferred by RNA degradation during biobank sample storage. Estimates of cell type-specific molecular profiles were derived via regression by quadratic programming based on sputum differential cell counts. All analyses were conducted using the open-source R/Bioconductor software framework.A linear regression step was found to perform well in removing RNA degradation-related bias among the main principal components of the gene expression data, increasing the number of genes detectable as differentially expressed in asthma and COPD sputa (compared to controls). We observed a strong influence of the cellular composition on the results of mixed-cell sputum analyses. Exemplarily, upregulated genes derived from mixed-cell data in asthma were dominated by genes predominantly expressed in eosinophils after deconvolution. The deconvolution, however, allowed to perform differential expression and methylation analyses on the level of individual cell types and, though we only analyzed a limited number of biological replicates, was found to provide good estimates compared to previously published data about gene expression in lung eosinophils in asthma. Analysis of the sputum methylome indicated presence of differential methylation in genomic regions of interest, e.g. mapping to a number of human leukocyte antigen (HLA) genes related to both major histocompatibility complex (MHC) class I and II molecules in asthma and COPD macrophages. Furthermore, we found the SMAD3 (SMAD family member 3) gene, among others, to lie within differentially methylated regions which has been previously reported in the context of asthma.In this methodology-oriented study, we show that methylation profiling can be easily integrated into sputum analysis workflows and exhibits a strong potential to contribute to the profiling and understanding of pulmonary inflammation. Wherever RNA degradation is of concern, in silico correction can be effective in improving both sensitivity and specificity of downstream analyses. We suggest that deconvolution methods should be integrated in sputum omics analysis workflows whenever possible in order to facilitate the unbiased discovery and interpretation of molecular patterns of inflammation. Respiratory research has greatly benefited from the application of molecular high-throughput (“omics”) technologies , 2. SignSputum samples contain a mixture of immune cells , but also contaminating cells . The relative abundancy of cell types varies substantially and can be used to distinguish disease subgroups such as “T2 high” from “T2 low” types in asthma by eosinophil counts , 26. ThiHowever, the aforementioned approaches do not allow to infer cell-type specific molecular profiles from mixed-cell data and, so far, the high-throughput molecular analysis of mixed-cell sputum samples has generally been limited to be used as a molecular “fingerprint” to describe inflammatory processes.Over the last years, tailored in silico methods, so-called deconvolution algorithms, have been designed to solve the problem of inferring cell type-specific omics profiles from mixed-cell data –41. ThesIn this exploratory and methodology-oriented study, we examine the applicability of sputum whole-genome methylation analysis in molecular profiling of asthma and COPD. Furthermore, we provide insight into how in silico RNA quality correction can benefit the transcriptome analysis of sputum samples from long-term storage and, for the first time, apply a deconvolution method based on linear regression by quadratic programming to infer cell type-specific omics profiles from mixed-cell sputum data.Sputum samples were obtained from biomaterial depositories of the German prospective cohort studies ALLIANCE  (asthma Asthma samples were selected from 9 subjects representing a phenotype with eosinophilic (type 2) inflammation and overall good disease control at the time of sample collection based on sputum and blood eosinophil count  as well as total asthma control test (ACT) score (≥ 20 points). In addition, subjects had to be non-smokers (smoking cessation > 12 months before sample collection) with a neglectable smoking history . No subject was treated with biologics, antihistamines or oral corticoids at the time of sputum collection. Out of the 9 subjects, 7 had a proven allergy . A total of 5 subjects presented with severe asthma  and 4 presented with a mild-to-moderate type (≤ 500 µg per day).A total of 10 COPD samples was selected from subjects that had not experienced any moderate or severe exacerbation  for ≥ 12 months as well as had successfully accomplished smoking cessation for ≥ 12 months. Of the 10 selected subjects, 7 had moderate (GOLD 2) and 3 had severe COPD (GOLD 3).Healthy controls 10 samples) were defined as subjects without any history of pulmonary or systemic-inflammatory disease, allergies or respiratory tract infection within the last 12 months. None of the selected control subjects had any smoking history. Descriptive statistics can be found in Table 0 samplesFor a graphical representation of the overall workflow, see Fig. Details about sputum induction and processing are provided in Additional file Samples were either stored in RLT Plus extraction buffer  at − 80 °C , or presFrom HOPE-preserved, paraffin embedded samples, sputum cells were extracted by cutting slices on a microtome  which were deparaffinized subsequently by incubation with xylene (2 × 10 min) and ethanol (2 × 10 min), followed by a drying step using a vacuum centrifuge before addition of RLT Plus lysis buffer , 47. SpuExtracted total RNA was processed with Agilent’s Low Input Quick Amp Labeling Kit. Labeled complementary RNA (cRNA) was purified using the RNeasy Mini Kit (Qiagen) and 1650 ng of labeled cRNA per sample was hybridized to Agilent Human GE 4 × 44 K v2 arrays. All steps were performed according to the manufacturers’ standard instructions. Hybridized arrays were scanned with an Agilent SureScan microarray scanner  and scan images were analyzed with Agilent’s Feature Extraction Software . All hybridized arrays passed the manufacturer’s standard quality controls.Genomic DNA was bisulfite converted utilizing the EZ DNA Methylation kit  following the manufacturer’s instructions. Converted DNA was further processed and hybridized to Infinium HumanMethylation 450 k BeadChips  following the standard Illumina workflow. Hybridized chips were scanned with an Illumina iScan system on default settings. All chips passed the manufacturer’s standard quality controls as well as further quality controls applied within the downstream in silico analysis. Due to a technical error, three samples were lost during processing, limiting the total number of samples from which methylation data was available to 26 .https://www.r-project.org, https://www.bioconductor.org). Supplementary methodological information as well as a comprehensive list of utilized software packages is provided in Additional file Downstream data analysis was entirely performed using the open-source R/Bioconductor software framework   via the  package . Quantillimma comparing disease entities to healthy controls (asthma vs. controls and COPD vs. controls).Differentially expressed genes (DEGs) as well as differentially methylated CpGs  were determined via 2-transformed expression values with Benjamini–Hochberg (BH)-adjusted p value < 0.05 and absolute log2-fold change (log2FC) ≥ 1.5 as statistical significance cutoffs. To remove redundancy from the data set and to simplify the biological interpretation of results, DEGs were filtered for well-annotated transcripts (based on available ENSEMBL and RefSeq annotation) and the most significantly differentially expressed transcript per gene was reported.For DEGs, statistics were calculated on logDMPs were determined on the beta value scale and considered statistically significant at a BH-adjusted p value < 0.05 and delta beta ≥ 0.1.2-transformed) and methylation values on the beta value scale for the purpose of deconvolution. The general performance of a multiple linear regression approach was evaluated by fitting models with built-in functions of R (stats R core package). The estimation was carried out by quadratic programming (QP), allowing us to specify biological constraints under which the regression parameters were estimated. This approach had previously been successfully applied to methylation and gene expression data [quadprog R package (https://cran.r-project.org/web/packages/quadprog/index.html) which implements the dual method of Goldfarb and Idnani to solve quadratic programs [2FC ≥ 1.5.Generally speaking, the deconvolution we applied is based on the idea that estimates for cell type-specific expression/methylation can be derived by finding (optimizing) estimates that, given the relative cell counts for each sample, best match the observed (measured) mixed-cell expression/methylation. This poses a classical regression problem which gets complicated by the circumstance that both expression and methylation have biological limits  that must not be violated by the mathematical optimization process in order to get biologically possible and meaningful results. In technical detail, we performed regression-based deconvolution (by quadratic programming) using the differential sputum cell counts as predictor variables and the measured mixed-cell omics profiles (expression/methylation) as response variables in the underlying linear models. To allow for linear combinability of the input data, expression values had to be analyzed on the linear  were identified via DMRcate . For theclusterProfiler package [Analyses for enrichment in Gene Ontology (GO) terms  and Kyot package . HypergeAsthma samples were largely composed of eosinophils, alveolar macrophages and neutrophils. Whilst eosinophils were nearly absent in COPD and control samples, COPD sputum was greatly composed of neutrophils and that of healthy controls mainly of alveolar macrophages  whilst not necessarily leading to a higher proportion of false positives. Should the extent of degradation be distributed unequally among samples (the COPD samples exhibited a higher extent of degradation than the asthma or control samples), however, RNA degradation-biased expression data can in fact be expected to lead to falsely identified DEGs . Concordantly, only a minor number of DEGs in asthma identified in the uncorrected data was discarded by correlation filtering whilst RNA integrity correction by linear regression led to identification of additional DEGs Fig. a. In COPThe methylation data, in contrast, exhibited no major influence by the respective sample preservation method Fig. . WhereasSince monocytes were only present in an overall very low quantity  clearly showed a pattern of estimated predominant expression in eosinophils (and partly neutrophils) whilst being lowly expressed in macrophages. In the background of higher sputum eosinophil counts in asthma this exemplifies how mixed-cell sputum analyses can be biased by disease-specific variation of cellular composition. For downregulated DEGs, the picture was the opposite around  terms highly related to immune response and regulation  in the mixed-cell data and in 39  and 2161  DEGs in macrophages and neutrophils after deconvolution, respectively. Whereas enriched GO terms were highly related to inflammatory processes (foremost neutrophil immunity) before deconvolution , no enriched GO terms could be identified in macrophages after deconvolution. CXCL9, chemokine (CXC motif) ligand 9, however, was found to be among the DEGs along with MMP13 . GO enrichment in the neutrophils’ DEGs resulted in a predominant picture of metabolic processes and regulation. Whilst enriched KEGG pathways were immunity-related in the mixed-cell analysis , enrichment in macrophages, similar to the GO analysis, did not produce statistically significant results. Pathway terms significantly enriched in neutrophils were again related to metabolism, including the peroxisome and lysosome.Genes that could be associated with differentially methylated regions in asthma  included a small quantity of immunity-related members such as IL27RA , IL20 (interleukin 20) and TNF but were overall dominated by small nucleolar RNA (snoRNA) as well as small Cajal body RNA (scaRNA) genes and thereby enriched in the GO term “Cajal body”  and IL20RA  were found to be DMR-associated. Enriched KEGG pathways were related to inflammation and immunological regulation in the mixed-cell analysis and continued to be in macrophages after deconvolution. Again, HLA loci associated both with MHC class I and II  contributed to this finding. No pathways were significantly enriched in COPD neutrophils  macrophages before –75. A moDeconvolution of transcriptomic signatures further allowed to identify interesting candidates regarding cellular regulation: Our data indicated an upregulation of IL4R (interleukin 4 receptor) in asthma neutrophils which had been shown to play an important role in the regulation of neutrophil apoptosis . FurtherFor now, the experimental gold standard to retrieve cell type-specific molecular data remains to be cellular separation by techniques such as gradient centrifugation , 30. HowFrom a phenotypical perspective, a large variability of cellular composition within a given set of samples, whilst benefiting the fit of a regression model, potentially indicates that several disease entities are comprised . The validity of estimates derived from deconvolution steps thereby directly depends on the accuracy of the preceding definition of sample groups. Therefore, the application of a regression-based deconvolution approach has to be critically evaluated in any experiment and might find complimentary use to deepen the molecular understanding after distinct pheno-/endotypes were separated (e.g. via the method established by Peters and colleagues ).We further demonstrated that, should RNA degradation be of concern, e.g. due to suboptimal or long-term biobank storage, in silico correction can remove RNA integrity-associated bias from transcriptome data, thereby not only reducing the potential for the occurrence of false positives, but also increasing the overall sensitivity. In our data, a separate regression step performed well to remove degradation-related bias which is congruent with previous findings . The cutThanks to optimized and streamlined purification workflows, parallel preparation of DNA and RNA from sputum samples is cost effective and efficient. With continuing innovation in the field of omics technologies and constantly growing affordability thereof, large-scale multi-omics analysis of sputum samples is close at hand. The application of the methods described here is by far not limited to sputum but can be expected to be successfully transferred to bronchoalveolar lavage and other respiratory samples to enhance biomarker discovery and pathophysiological understanding. Beyond microarray analysis, omics deconvolution and RNA integrity correction can further be expected to be of avail for sequencing-based methods as these can be similarly affected by RNA degradation and cell composition bias.Analysis of the sputum methylome can broaden the profiling and understanding of chronic pulmonary inflammation and adds important additional information to commonly performed transcription analyses. The necessity of in silico correction for RNA degradation should be evaluated in every sputum transcriptome dataset. Finally, with suitable deconvolution approaches such as the algorithm described here, pathophysiological and regulative changes in chronic inflammatory lung diseases can be substantially better explored wherever single-cell analysis or cell separation may not be feasible. We therefore strongly recommend the application of unbiased deconvolution methods as such to all future whole-sputum omics analyses in order to complement methods that have already been established.Additional file 1. Supplementary Information, Figures and Tables.Additional file 2.  Results of the differential expression analyses.Additional file 3. Results of the differential methylation analyses on the CpG level.Additional file 4. Results of the differential methylation analyses on the gene region level.Additional file 5. Results of gene ontology enrichment analyses of the gene expression data.Additional file 6. Results of KEGG pathway enrichment analyses of the gene expression data.Additional file 7. Results of gene ontology enrichment analyses of the methylation data.Additional file 8. Results of KEGG pathway enrichment analyses of the methylation data.Additional file 9. Differentially expressed genes that were found to correspond to differentially methylated genomic regions.Additional file 10. Genes whose expression was found to discriminate eosinophils, neutrophils and macrophages in asthma sputum.


Most methods for inferring gene-gene interactions from expression data focus on intracellular interactions. The availability of high-throughput spatial expression data opens the door to methods that can infer such interactions both within and between cells. To achieve this, we developed Graph Convolutional Neural networks for Genes (GCNG). GCNG encodes the spatial information as a graph and combines it with expression data using supervised training. GCNG improves upon prior methods used to analyze spatial transcriptomics data and can propose novel pairs of extracellular interacting genes. The output of GCNG can also be used for downstream analysis including functional gene assignment.https://github.com/xiaoyeye/GCNG.Supporting website with software and data:  Several computational methods have been developed over the last two decades to infer interaction between genes based on their expression . Early wCurrent methods for inferring extracellular interactions from spatial transcriptomics have mostly focused on unsupervised correlation-based analysis. For example, the Giotto method calculated the effect upon gene expression from neighbor cell types . While tTo overcome these issues, we present a new method that is based on graph convolutional neural networks (GCNs). GCNs have been introduced in the machine learning literature a few years ago . Their mTo apply GCN to the task of predicting extracellular interactions from gene expression (GCNG), we first convert the spatial transcriptomics data to a graph representing the relationship between cells. Next, for each pair of genes, we encode their expression and use GCNG to convolve the graph data with the expression data. By this way, the NN can utilize not just first-order relationships, but also higher-order relationships in the graph structure. We discuss the specific transformation required to encode the graph and gene expression, how to learn parameters for the GCNG, and how to use it to predict new interactions.We test our approach on three datasets from the two spatial transcriptomics methods that profile the most number of genes right now, SeqFISH+  and MERFWe extended ideas from GCN , 19 and While a number of recent methods have been suggested for spatial profiling of single cell RNA-Seq data –11, we dGCN requires labeled data for supervised training. While the exact set of signaling interactions between cells in the spatial data we studied is unknown, we used as true interactions a curated list of interacting ligands and receptors . LigandsFor evaluation, GCNG adopted a tenfold cross-validation. Train and test sets were completely separated to avoid any information leakage Fig. b. See thWe first evaluated GCNG’s ability to predict ligand-receptor interactions. For this, we used two datasets. The first is seqFISH+ mouse cortex tissue which contains the expression of 10,000 genes in 913 cells. Our labeled set consisted of 1056 known interactions between 309 ligands and 481 receptors. The second is a MERFISH dataset with 10,050 genes from 1368 cells, and 841 known interactions between 270 ligands and 376 receptors.We enforced a strict separation between the training and test sets in the 10-fold cross-validation (CV) Fig. . We compWe also compared GCNG to two alternative methods that do not use spatial information at all to determine the contribution of neighborhood data. These included Pearson’s correlation between the expression of ligand and receptors within each cell  and our Results are presented in Fig. To test if the interactions identified are likely active in the tissue tested, we further compared the performance when using the real interaction data to running GCNG on a permuted training and test dataset (in which we permute the set of interacting ligand-receptor pairs). We observed a large drop in performance when using the randomized data (autocrine plus GCNG in terms of mean AUROC for MERFISH (seqFISH+), real vs. random: 0.69 vs. 0.55 (0.65 vs. 0.52); exocrine GCNG vs. random: 0.58 vs. 0.50 (0.60 vs. 0.43). See Additional file To further explore the predictions of our GCNG and to map them back to the original spatial representation, we looked at some of the top correctly predicted pairs. For each such pair (a ligand and receptor predicted to interact), we projected their expression on the cell distribution figures. Figure La, Rb) gene pair, we introduce a negative sample  with label 0. The same tenfold cross-validation strategy is used to evaluate GCNG’s performance here. Results are presented in Fig. While correlation-based methods can be used to identify gene co-expression interactions and networks , 26, theWe next tested whether GCNG can be used for applications that utilize predicted interactions as features for downstream analysis. Specifically, we tested whether the outcomes of GCNG can be used as features for assigning function to genes. A popular method for such assignment is Guilt By Association (GBA) . In GBA Given its performance on accurately identifying known genes from the GSEA functional sets, we next used GCNG to predict novel functional genes for these three GSEA cell interaction sets using the MERFISH dataset. Additional file Gene expression data has been extensively and successfully used to infer interaction between genes, gene regulation and temporal and causal effects , 42, 43.We presented a supervised GCN approach which can be used to identify new interactions from spatial scRNA-Seq data. GCNs have recently been used in computational biology, though prior applications did not focus on cells but rather on intracellular pathways and utilizing known gene-gene and gene-drug interactions to define the graph structure , 46. ForApplication of our GCNG method to datasets that provide the highest coverage of genes shows that it can successfully identify known ligand-receptor pairs and that it is much more accurate when compared to prior methods proposed for this or to methods that do not utilize the spatial information. Visualization of some resulting predictions highlights the ability of GCNG to focus on a relevant subset of locations rather than on global correlation. The output of GCNG can also be used as features for downstream analysis including methods for gene function assignment and methods for learning interaction networks.entire set of known ligand-receptor pairs. While some are likely active in the tissues we analyzed, many pairs that are listed as “positives” in the test data are not, and so labeling them as “negative” is the actually the correct answer . More generally, if we had a better ground truth data, we would expect that the results would be much better.There are several ways in which GCNG can be improved. First, the choice of the number of convolutional layers to use (which relates to the assumption about the propagation distance of secreted proteins) needs to be better handled to fit the needs of individual datasets. Second, GCNG can focus more on specific cell types rather than on the overall interactions. We expect to address these and other issues in future work. Another important direction is that compared to the intra-cellular case, the extra-cellular interactions between genes might be more complex, including different kinds of functional mechanisms, so we hope future GCNG can model them with more details rather than treating them as an identical case. Furthermore, it is noticed that the mean and median performance for the same method are some different and sometimes the compared prior method is even worse than random guess, which is due to the small sample size of train and test dataset. Finally, the results reported are likely an under-estimate of the performance of the method. Note that we use as the test data the https://github.com/xiaoyeye/GCNG, and Zenodo [GCNG is implemented in Python and both data and an open source version of the software are available from the supporting website, d Zenodo .The two seqFISH+ datasets were downloaded from . These di represents cell i and j represents gene j. We also downloaded the cell location files for all the three datasets to generate graph matrices.where A. In other words, for the symmetric network, A, Aij = Aji = 1 if i and j are neighbors and 0 otherwise. Using the adjacency matrix A, the normalized (symmetric) Laplacian matrix LN is defined as [To determine the neighbors of each cell, we calculated the Euclidean distance in the image coordinates for all cells and used a distance threshold to select neighbors. The threshold value was selected using 10-fold cross-validation  with a size of 2 × 32, where 2 corresponds to the two-dimension gene expression of each node, and 32 represents 32 filters or feature maps. b is the bias vector term with a size of 1 × 32. The “elu”  function is defined as:α = 1 by default. Here, Z represents the embedding vectors of all cell nodes with a size of 913 × 32. Note that we are using two convolutional layers here allowing the method to learn indirect graph relationships as well. Since the impact of secreted proteins can be larger than just direct neighbors, such an approach allows the method to infer interactions that may be missed by only considering direct neighbors.where ReLU activation function. Finally, a dense layer with one-dimensional output is used to predict the interaction probability based on the sigmoid activation function. The activation functions used by the different layers are defined below.The first graph convolutional layer combines the two inputs and converts them to embedding vectors for cell nodes of dimension of 913 × 32. The second graph convolutional layer combines the embedding vector of each cell with the one learned for its direct neighbors. The flatten layer then converts the matrices generated by the second layer to a vector using And the objective function for the entire GCNG model is as follows:i represents the ith sample, yi represents the label for the ith sample, and Θ represents all parameters that need to be optimized in GCNG.where We tested one, two, and three graph convolutional layer networks and determined that two layers network led to the best performance. In addition, we also tried GCNG with cell type information as node attribute using one-hot encoding, distance value as edge attributes, and other GNN architectures including “EdgeconditionConv” model  and grapWe evaluated GCNG’s performance using tenfold cross-validation. Train and test sets were completely separated to avoid information leakage: for each fold, 90% of ligands and 90% of receptors were selected at random for training. Known interactions between the 90% training 10% test) proteins were used as the positive train (test) set and the negative train (test) set was composed of randomly selected ligand-receptor pairs that are not known to interact among the training (test) proteins (on average each ligand only interacts with very few receptors so ∼ 99% of random pairs are expected to be negative). Note that pairs for which one of the proteins was part of the training set while another was in the test set were removed and so all proteins in the test set are never seen in training (Fig. 0% test pAdditional file 1: Supplemental data. Supplementary data contains supplementary Methods description, a list of supplementary Figures and Tables mentioned in the paper.Additional file 2. Review history.


Power analysis becomes an inevitable step in experimental design of current biomedical research. Complex designs allowing diverse correlation structures are commonly used in RNA-Seq experiments. However, the field currently lacks statistical methods to calculate sample size and estimate power for RNA-Seq differential expression studies using such designs. To fill the gap, simulation based methods have a great advantage by providing numerical solutions, since theoretical distributions of test statistics are typically unavailable for such designs.In this paper, we propose a novel simulation based procedure for power estimation of differential expression with the employment of generalized linear mixed effects models for correlated expression data. We also propose a new procedure for power estimation of differential expression with the use of a bivariate negative binomial distribution for paired designs. We compare the performance of both the likelihood ratio test and Wald test under a variety of simulation scenarios with the proposed procedures. The simulated distribution was used to estimate the null distribution of test statistics in order to achieve the desired false positive control and was compared to the asymptotic Chi-square distribution. In addition, we applied the procedure for paired designs to the TCGA breast cancer data set.In summary, we provide a framework for power estimation of RNA-Seq differential expression under complex experimental designs. Simulation results demonstrate that both the proposed procedures properly control the false positive rate at the nominal level. RNA-Seq has become a popular tool for studying dynamics of gene function through transcriptomic data of individuals with multiple samples of different origins , 2, diveSince the emergence of RNA-Seq data, several papers have used Poisson or negative binomial (NB) distribution to model count-based expression data –9. But tSeveral studies provide methods for sample size calculation and power estimation at the marginal level –17 or daX|G=g∼Poisson(μg) and Y|G=g∼Poisson(γμg) with a Gamma random variable G∼Gamma. The probability mass function for the joint distribution of  isThe BNB distribution can be obtained by compounding two conditionally independent Poisson random variables γ to denote the fold ratio of a gene between two conditions. We are interested in testing hypothesis H0:γ=γ0 vs. hypothesis H1:γ≠γ0. A Wald test for testing log transformed γ is H0:log(γ)=log(γ0) vs. H1:log(γ)≠log(γ0). The likelihood ratio test (LRT) statistic and the Wald test statistic for the above hypothesis with BNB distribution are defined in Rettiganti and Nagaraja [Without loss of generality, we use Nagaraja .Poisson or NB distribution is modeled through the log link function of a linear predictor of mixed effects asβ are fixed effects and b are random effects following normal distributions. For inference on fixed-effects β, hypotheses H0:Lβ=0 vs.H1:Lβ≠0 is tested by LRT or Wald test. Random effects b can be tested by z-statistic for difference from 0.where In this study, we used our previously published simulation-based empirical parametric test for inferences  and the n; mean expression μ; dispersion ϕ; fold ratio γ between conditions, nominal false positive rate α, number of simulations T.Specify all input parameters: sample size per condition T times from BNB under both the null and alternative hypotheses using the input parameters listed in Step 1.Simulate count data Fit BNB model or GLMM and obtain test statistics  under the null hypothesis for each simulation run.α)th percentile of the empirical null distribution of test statistics  as the critical value.Calculate the 100 under the alternative hypothesis for each simulation run.Calculate power  for the input parameters listed in Step 1.n subjects. The input parameters for power calculation at the marginal level are sample size n, mean expression μ at baseline, fold ratio γ between the two conditions, dispersion ϕ, and nominal false positive rate α. Parameter values for each are Count data were simulated from a Poisson-Gamma (BNB) distribution under two experimental conditions (e.g. baseline vs. treatment) for n=5,10,15,20,25; μ=10; ϕ=1. The null distribution of LRT statistics under the BNB model can be approximated to a Chi-square distribution with 1 degree of freedom, but Wald test statistics under the BNB model are slightly above the Chi-square distribution. The null distribution of LRT statistics under the Poisson-LMM model can be approximated to a Chi-square distribution with 1 degree of freedom, but LRT statistics under the NB-LMM model are moderately below the Chi-square distribution. Wald test statistics under both the Poisson-LMM and NB-LMM models have unusually large values due to computational instability and dramatically deviate from the Chi-square distribution, therefore these two tests are not pursued further for power analysis.Figure α=0.001 by using the empirical parametric test or the Chi-square distribution. Both the LRT under the BNB model and the LRT under the Poisson-LMM model with the use of the empirical parametric test have similar critical values as the Chi-square distribution. However the Wald test under the BNB model with the use of the empirical parametric test has larger critical values than the Chi-square distribution especially at smaller mean expression levels. The LRT under the NB-LMM model with the use of the empirical parametric test has lower critical values than the Chi-square distribution. When the approximated Chi-square distribution is used instead of the empirical parametric test  for the four tests at α level are shown in Fig. n=5 samples per group to detect a 2-fold up-regulation or n=9 samples per group to detect a 2-fold down-regulation for genes at the mean expression level of 14 and the dispersion of 1. Results for all combinations of the mean expression level and the dispersion values are included in the additional file To study and demonstrate the proposed power estimation procedure in a real data application, we used the TCGA breast cancer data set as a pilot data set for designing a new study to detect differential expression using a paired design. The TCGA breast cancer data set BRCA (acquired in Feb. 2019 from FireBrowse) contains 1,212 tumor samples and 20,531 genes with non-zero counts. TMM method was used for normalization of all samples . We chosSeveral studies discovered excessively inflated false positive rates for differential expression detection by using popular NB methods  in RNA-Seq data analysis –26. A reγ>1 for paired designs, the Wald test of BNB is recommended since it has the highest power among all four tests. But when testing γ<1 for paired designs, either the LRT under the BNB model or the LRT under the Poisson-LMM model is recommended. This unbalanced effect on power for the Wald test is related to selected transformation functions g(.), which was also reported in the article by Rettiganti and Nagaraja [We observed that the LRT under the BNB model and the LRT under the Poisson-LMM model have similar performance under both the null and alternative hypotheses. The main reason of the equivalent performance of these two tests is that the employed BNB model is based on the Poisson-Gamma compound distribution, which is similar to fit the Poisson-LMM model. When testing Nagaraja . We alsoIn almost all current studies that use a NB model for differential expression detection or power analysis, the dispersion parameter is assumed equal across conditions. We have proposed unequal dispersion parameters across conditions for power analysis . SimilarMany methods on sample size calculation and power estimation have already been proposed for RNA-Seq data over last decade. However nearly all of them were developed for experiments with independent measurements. To overcome this limitation in current methods, we provide a framework for power analysis of RNA-Seq experiments with correlated measurements . Our simulation based procedures provide proper control of false positive rate, and our novel GLMM procedure can be used for complex designs by allowing diverse correlation structures with both random effects and random residual errors.Additional file 1 This pdf file contains all supplementary figures referenced in results section.Additional file 2 This text file contains all R functions used in simulations and the TCGA breast cancer data analysis.Additional file 3 This R markdown file contains R code and results for the TCGA breast cancer data analysis.


With the advance of high throughput sequencing, high-dimensional data are generated. Detecting dependence/correlation between these datasets is becoming one of most important issues in multi-dimensional data integration and co-expression network construction. RNA-sequencing data is widely used to construct gene regulatory networks. Such networks could be more accurate when methylation data, copy number aberration data and other types of data are introduced. Consequently, a general index for detecting relationships between high-dimensional data is indispensable.2 (the modified RV-coefficient). Permutation test and other validation methods were used on simulated data to test the significance and rationality of KBRV. In order to demonstrate the advantages of KBRV in constructing gene regulatory networks, we applied this index on real datasets (ovarian cancer datasets and exon-level RNA-Seq data in human myeloid differentiation) to illustrate its superiority over vector correlation.We proposed a Kernel-Based RV-coefficient, named KBRV, for testing both linear and nonlinear correlation between two matrices by introducing kernel functions into RVWe concluded that KBRV is an efficient index for detecting both linear and nonlinear relationships in high dimensional data. The correlation method for high dimensional data has possible applications in the construction of gene regulatory network. With the rapid advance in high throughput sequencing technologies, multiple, high-dimensional data types are widely available. In recent years, the advance in next-generation sequencing and single-cell sequencing offers a significantly increased level of biological details than just total gene expressions –5. MoreoA and B, we might see the data from different aspects and acquire different information. For example, when we look at the expression of gene pairs, if we consider level I, level II and level III in Fig. 2) to improve this measure and extended it to partial matrix correlations . We could estimate the type of correlation based on α. For simplicity, when α≥0.5, we think the correlation between matrix A and B is linearly dominant, and we consider it as nonlinearly dominant when α<0.5.where KBRV was compared to A in the ith permutation. Subsequently, the P-value could be obtained from the following equationTo evaluate the effectiveness of KBRV, we applied a permutation test to assess significance of this index. n is the number of permutations. Because RV2 is a special case of KBRV (α=1), we could compare RV2 with KBRV, by the way, when we calculate the significance with different α.where p<αsig, where αsig equals 0.05 in our research.Combining Eqs.  and 9),,9), the A(aij) and B(bij) in several different cases. In the fisrt case, A(aij) and B(bij) were both random matrices drawn from random numbers between 0 and 1, respectively, which means A and B were independent matrices. In the following cases, A(aij) was drawn in the same way while bij in matrix B were set as different functions of aij. Here, noise was derived from standard normal distribution, gamma distribution and bimodal distribution and their levels was discussed [bij with different noise types were explored in Tables α of KBRV . The computational cost of the permutation test and statistical power are shown in Tables We generated two matrices iscussed . We tookA(aij) of size M×500 and B(bij) of size M×800 are generated randomly. Under this circumstance, A and B are repeated 100 times for each M, where M was the number of matrix’s rows and increased from 50 to 1000 with step size 50. In the second case, A(aij) and B(bij) are drawn from standard normal distribution while a random proportion of elements in B(bij) is replaced by aij and α of KBRV .To further validate the rationality of KBRV, we did some simulations concerning matrix size and sparsity. In the first case, we would like to show that as long as two matrices are independent, KBRV is equal to 0 regardless of the size of the matrices. Here, matrix S×J, where S is the number of samples and J is the number of exons. Here, we evaluate the performance of KBRV by ROC curves and AUC values based on simulated exon-level gene co-expression networks [S×J1/2 matrices N with i∈{1,2} and j∈{1,⋯,J1} or {1,⋯,J2}. In contrast with independent gene pairs A=, dependent (co-expressed) gene pairs B= are drawn such thatTo verify the validity of KBRV not only for general matrices, but also for biological data, in this section, we applied KBRV method to exon-level simulation data. Compared to gene expression in vector form, exon-specific expression could be represented as a matrix of order networks . For nonc0 is a constant that indicates the association strength of gene isoforms B1,B2.wherec0=0, which means the correlation between A1 and A2 should be zero. Meanwhile, B1 and B2 are correlated because c0≠0 bigger c0 implying stronger correlation. Furthermore, B1 and B2 while other nonlinear F indicate nonlinear relationships between B1 and B2. In our simulations, the number of exons (k and l) are set to 50-50, 100-100, 50-200. The sample size S and the association strength are set to be 50, 100, 200 and 0.1, 0.2, 0.3, respectively. Firstly, as for these 27 combinations, we generate 1000 pairs of matrices  under each combination and another 1000 pairs of matrices  with the same number of exons and sample size while setting association strength equal to zero. Once having the label of gene pairs, we could use ROC curves and AUC values to evaluate the capabilities of KBRV under different parameters. The effects of the number of exons, sample size and association strength on the KBRV in linear and nonlinear scenarios were discussed respectively. Furthermore, we test KBRV’s ability to distinguish between linear gene pairs and nonlinear gene pairs. We generate 1000 pairs of matrices  which are linearly dependent under these 27 combinations and another 1000 pairs of matrices  having nonlinear relationships with the same number of exons, sample size and association strength. Bl1 and Bl2 are set to be Bn1 and Bn2 are set to be Here, gene pairs are independent when https://portal.gdc.cancer.gov/repository). This cancer data taken from 385 patients consist of two parts: the gene expression data and the DNA methylation data . According to previous research, FOXM1 transcription factor network is altered in most ovarian cancer patients [α=0.6), to calculate the correlation between different genes through gene expression data and construct a gene regulatory network. After that, the matrix method, KBRV, was used to calculate the correlation between the nine 385×2 matrices by integrating gene expression data and DNA methylation data. It is worth mentioning that for each calculation, we chose different α and combined KBRV value with permutation test, which means the p<0.05. After getting the correlation matrix, regulatory edges were selected by introducing a hard threshold. The top 20% are kept in the network.We applied KBRV to ovarian cancer data which are taken from the TCGA database (patients . In thisJ×21 samples) were calculated in three different cell lines using MIC(α=0.6) and KBRV(p<0.05), respectively. Similar to the previous part, top 10% regulatory edges were kept in the network after getting the correlation matrix.We further applied KBRV to construct gene regulatory network with the exon-level RNA-Seq data from macrophage, neutrophil and monocyte cell lines in human myeloid differentiation, respectively. Compared with gene-level RNA-Seq data, exon-level RNA-Seq reveals more biological details about gene expression, which in turn requires us to use more advanced methods to calculate because gene samples at the exon-level could be represent as matrices rather than vectors. Here, we focus on 18 transcription factors that are important in human myeloid differentiation . The exoA and B are both random matrices. When A and B are linearly correlated, Tables α could both make good judgements with different types of noise. The remaining rows in Tables The first case in Tables A and B is, indicating they are independent. Besides, it is worth mentioning that the KBRV value fluctuates slightly when sample size is very small, possibly due to the huge difference in the number of rows and columns. The calculated results reflecting sparsity with different parameter α are shown in Fig. α=1) has the whole RV2 while containing no RVA or RVB, so it predicts the linear relationship best, which appears larger value in Fig. 2 component decreasing and the RVA plus RVB part growing, KBRV is losing its power to detect the linear relationship. KBRV (α=0) has the whole RVA and RVB while containing no RV2, so it performs better in assessing the nonlinear relationship between the matrices A and B, which appears larger value in Fig. From Fig. α were significantly increasing as the association strength c0 growing except KBRV with α=0. However, RV2 is a special case of KBRV with α=1, which performs better than others. The results for the nonlinear case (cosine) are shown in Fig. c0=0.2 and the sample size from 50 to 100. Figure α=1, which is just the opposite of Fig. α=1) outperforms others when α=0) performs the best when Figure c0 is growing. Most importantly, KBRV is better than RV2 (α=1) especially when c0=0.2 where KBRV’s AUC attains 1. Figure c0=0.1 while the number of exons change from 50-50 to 50-200. From (c) and (d), RV2 (α=1) becomes smaller as the difference between the number of exons increases. However, KBRV(α≠1) continues to maintain high accuracy.Figure For a heat map of the correlation matrix calculated through MIC shown in Fig. RUNX1, REL and STAT family are the most important genes in human myeloid differentiation. For example, RUNX1 plays a central role in hematopoiesis of all lineages . REL pla2. It is worth noting that KBRV is an extension of RV2 and inherited some good properties of RV2. We suggest calling them the family of KBRV coefficient. This family of correlation coefficients has a parameter α, which regulates its weights for a linear and nonlinear relationship. For simulation data, α=1 has the strongest ability to recognize the linear relationship. Meanwhile, α=0 has the highest AUC value when the relationship is nonlinear. When it comes to real data, we recommend choosing a step size and exhausting all the results based on both KBRV and permutation test. After that we can figure out the best In this study, we proposed a novel index to detect linear and nonlinear correlations for high dimensional data. The proposed KBRV is a universal index, which overcomes the shortcoming that some measures are not able to identify a nonlinear relationship when compared to its special form RVβ value, which represents the ratio of the methylated bead type intensity to the intensity of combined locus. Considering that multiomics data are different in measurement and are difficult to integrate into a single matrix, we think it is possible to consider integrative analysis of multiomics data as a data pre-processing method to obtain standardized multiomics data matrix. For example, robust network-based analysis provides a novel perspective in modeling regulations between gene expressions, copy number variations, DNA methylation and other omics data [However, although the numerical results of KBRV are good, there are still some challenges. First of all, we only get the rationality of the numerical simulation but lack theoretical proof of this index. Besides, when this approach is used to integrate multiomics data, it is inevitable to face associations and differences between different types of data. For example, RNA-seq gene expression data have various expression units such as TPM, RPKM, FPKM and even raw reads counts. However, the level of DNA methylation is usually expressed by ics data . Taking Appropriate inference about clinical or environmental covariates might help elucidate the genetic basis of complex diseases and improve the accuracy of our method. As far as we know, Wu et al. have proposed many effective methods such as semiparametric bayesian variable selection, additive varying-coefficient model, penalized robust semiparametric approach, etc. in dealing with gene-environment interactions –29. Here2. The KBRV was used to construct regulatory networks after its rationality was verified by simulated matrices and simulated exon-level data. As the dimensions of the data increases, some novel methods have been brought up in order to work out some problems that can not be solved by conventional approaches. As for correlation studies, the expansion from low dimensions to higher dimensions is also indispensable. Today, most existing methods focus on vector data, but there is a lack of research on matrix or even tensor data. Improper use of vector methods could lead to partial or even opposite conclusions. Therefore, correlation methods like KBRV for detecting high dimensional data rather than vector data have potential value in practical application such as the construction of gene regulatory networks, co-expression networks, etc.In this study, we brought up an efficient index for detecting both linear and nonlinear relationships for high dimensional data, named KBRV, which has a broader application scenario than the original index, RV


Advanced tumours are often heterogeneous, consisting of subclones with various genetic alterations and functional roles. The precise molecular features that characterize the contributions of multiscale intratumour heterogeneity to malignant progression, metastasis, and poor survival are largely unknown. Here, we address these challenges in breast cancer by defining the landscape of heterogeneous tumour subclones and their biological functions using radiogenomic signatures. Molecular heterogeneity is identified by a fully unsupervised deconvolution of gene expression data. Relative prevalence of two subclones associated with cell cycle and primary immunodeficiency pathways identifies patients with significantly different survival outcomes. Radiogenomic signatures of imaging scale heterogeneity are extracted and used to classify patients into groups with distinct subclone compositions. Prognostic value is confirmed by survival analysis accounting for clinical variables. These findings provide insight into how a radiogenomic analysis can identify the biological activities of specific subclones that predict prognosis in a noninvasive and clinically relevant manner. Tumours are made up of heterogeneous subclones. Here, the authors show using breast cancer imaging and gene expression datasets that these subclones can be inferred by the deconvolution of gene expression data, mapped to MRI derived radiogenomic signatures and used to estimate prognosis. Genomic heterogeneity contributes to adverse clinical outcomes including resistance to therapy3 and decreased overall survival (OS)5. Characterizing the heterogeneity of tumours and complex tissues is a major challenge6. Deconvolution methods applied to gene expression profiles can estimate the underlying genomic subclones8. For example, data deconvolution applied to tumour/stroma gene expression profiles identified an immune subclone that is associated with decreased survival of cancer patients10. Decomposed genomic subclones are often relevant to cancer treatment, as has been shown for some immune checkpoint blockade therapies11. Nonetheless, significant improvements in tools and workflows are urgently needed to identify clinically and biologically meaningful genomic subclones from heterogeneous tumours that can better inform prognosis and guide treatment decisions.Cellular and molecular heterogeneity is common in solid tumours. Human cancers contain divergent genomic subclones in varying proportions, each with different gene expression patterns and biological functions12. However, these methods cannot identify unknown biomarkers that better characterize tumour heterogeneity. Variability in the reference matrix can introduce bias into the results obtained from specific cancer types. Many known molecular signatures available to support supervised deconvolution can also be limiting and incomplete or even unreliable when the tumour microenvironment changes. In marked contrast, unsupervised approaches can extract known subclones in an unbiased manner and discover additional yet unknown subclones without the need for prior information. Transcriptional heterogeneity is modelled to identify molecularly unique genomic subclones from within the gene expression profiles of heterogeneous tumour samples13. Whether the molecular signatures and/or compositions of genomic subclones (including unknown subclones) identified by an unsupervised deconvolution of tumour gene expression profiles can be used either to understand cancer biology and/or to support noninvasive imaging-based prognosis is underexplored.Current gene expression deconvolution approaches use reference profiles in a mixture of tissue, where gene expression patterns associated with different disease states are explored in a basis matrix14. Intratumour heterogeneity can be captured by 3D imaging of the entire tumour and surrounding parenchyma16. Radiogenomics explores the relationships between radiomic features and genomic characteristics, with the goal of noninvasively uncovering relevant features that reflect the underlying biological functions most strongly associated with clinical outcomes. For example, prior studies have reported the quantitative analysis of computed tomography (CT) images in the setting of non-small cell lung cancer (NSCLC)18 and magnetic resonance imaging (MRI) of tumour-adjacent parenchyma19. In these examples, imaging features were associated with both gene expression profiles and patient survival. A recent study identified an imaging biomarker of the genomically determined abundance of CD8 T cells that could be used to predict clinical outcomes in patients treated with immunotherapy20. Despite these initial efforts, the clinical value of using imaging features to determine robust prognostic genomic subclones is uncertain.While most recent studies of tumour heterogeneity have focused on the molecular characterization of tissue samples, these techniques require the collection of invasive biopsies. Radiomics can be used to mine high-throughput quantitative and noninvasive image features to improve cancer diagnosis and treatment21. We have used data from two scales, specifically transcriptome data and imaging data. Tumour subclone heterogeneity is identified at the genomic (transcriptome) scale using a fully unsupervised deconvolution method applied to gene expression profiles. Imaging scale intratumour heterogeneity is characterized using a set of radiomic feature analyses. The noninvasive radiogenomic signatures associating these two scales are further identified to classify patients into groups with distinct subclone compositions. Here, we investigate the biological and clinical relevance of modelling multiscale intratumour heterogeneity by conducting a radiogenomic analysis of 1310 samples of breast cancer patients on five datasets of three data cohorts . A fully unsupervised convex analysis of mixture (CAM) method23 was applied to deconvolute the gene expression profiles in the genomic development dataset (n = 660) from The Cancer Genome Atlas (TCGA). Grouped samples were used independently (exclusively) in different stages/steps of this study . A detailed description of the pathways is presented in Supplementary Table 24, ECM-receptor interaction25 and primary immunodeficiency26. The cell cycle subclone had the highest fraction value, accounting for ~22% of all subclones . The cell cycle and primary immunodeficiency subclones stratified patients into poor and good OS groups with significantly different survival rates . Tumours containing the cell cycle subclone at >18.4% were more likely to exhibit poor OS, whereas tumours containing the primary immunodeficiency subclone with a prevalence of >3.55% were more likely to exhibit good OS.The prognostic power of each tumour subclone was evaluated using its fraction of the total subclones to determine its correlation Table  with OS 30. The number of clusters that produced the most stable consensus matrix runs was selected as optimal30. Subsequently, patients were clustered into two groups, good-survival (n = 316) and poor-survival (n = 344), based on the cell cycle and primary immunodeficiency prognostic subclone compositions. OS rates differed between the clustered patients; a smaller p value (p = 0.0012) was obtained compared with the p value for either the immunodeficiency or cell cycle subclone alone. In the poor-survival group, a significantly higher proportion of the cell cycle subclone was present when compared with the good-survival group . In contrast, tumours associated with the primary immunodeficiency subclone were present at a higher fraction in the good-survival group than in the poor-survival group .Patient samples were further clustered by their subclone composition using consensus clusteringp < 0.05 for the cell cycle and primary immunodeficiency subclones  > 1.5 and nes Fig. . In the ons Fig.  and is en = 153) and poor survival (n = 176) groups  using the proportional compositions of key predictive subclones. Tumours with a high fraction of cell cycle and a low fraction of primary immunodeficiency subclones correlated with poor survival. Thus, intratumour genomic subclone heterogeneity is strongly associated with breast cancer survival.The prognostic value of the tumour subclones was evaluated using the genomic testing dataset (n = 329). The gene expression profile was deconvoluted using the reference matrix obtained from the genomic development dataset, which generated the subclone fraction values. Patients were clustered into significantly different good survival (n = 87) were obtained from TCGA-BRCA of The Cancer Imaging Archive (TCIA) cohort (see “Methods”). The gene expression profile was deconvoluted under supervision, where the subclone proportion in each tumour was estimated using the reference gene expression matrix in the genomic development dataset. Patients were grouped by consensus clustering using the fractions of the cell cycle and primary immunodeficiency subclones by the same procedure applied to the genomic development dataset.Radiogenomic signatures were identified as a surrogate for the prognostic genomic signatures by associating radiomic features with these genomic signatures of intratumor heterogeneity. The images and their corresponding gene expression profiles in the radiogenomic dataset (n = 40) or good-survival (n = 47) groups (see Methods). The predictive model used the optimal feature subset (n = 15) and produced an area under the receiver operating characteristic (ROC) curve (AUC) value of 0.833, with a sensitivity of 0.723 and a specificity of 0.950. The detailed optimal feature subsets are provided in Supplementary Table p = 0.016) in the poor-survival group  data and used to train a predictive model for classifying patients into the poor-survival  with matched DCE-MRI and survival data were obtained from the NACT-pilot and ISPY-1 cohorts, respectively, in TCIA. The trained predictive model and the radiogenomic signatures from the second phase were used to classify patients into the poor or good survival groups. Differences in either OS or recurrence-free survival (RFS) between the two groups were compared to evaluate the prognostic significance of the radiogenomic signatures.n = 57) or good (n = 116) OS . These signatures were further tested for RFS in the prognostic testing dataset by separating patients into the poor- (n = 26) and good-survival (n = 35) groups . Each of these studies independently validated the effectiveness of the radiogenomic signatures as predictors of breast cancer prognosis.Radiogenomic signatures clearly discriminate between patients with poor  status, progesterone receptor (PR) status, human epidermal growth factor receptor (HER2) status, we conducted multivariate survival analyses on both the prognostic assessment and prognostic testing datasets Table .Table 3Mp = 0.0067; prognostic assessment dataset) and RFS . Second, including the proposed radiogenomic signatures in the model as an explanatory variable, the experimental results on the prognostic assessment dataset showed a significantly increased (p < 1e-6) model fit for OS (p = 0.00014) compared with using only the clinical variables (p = 0.0010). The consistent increase in prognostic power was replicated in the prognostic testing dataset. The multivariate survival model showed a significantly increased (p = 0.0012) correlation with RFS after inclusion of the radiogenomic signatures (p = 0.0029) compared with using only the clinical variables (p = 0.02). These results showed that our prediction model using the proposed radiogenomic signatures has additional and independent prognostic power after accounting for these clinical variables.First, after adjusting the model for the clinical variables, the proposed radiogenomic signatures maintained independent significance for both OS  are increasingly used in clinical breast cancer prognostication, their overall prognostic accuracy is somewhat limited. These assays rely on biomarker expression patterns derived from a population of tumour biopsies and applied to a single biopsy  from each individual patient. Since core biopsy sampling rarely adequately captures information about the entire tumour ecosystem, these invasive methods can be imprecise and are often difficult to repeat in individual patients. In contrast, we have developed predictive and noninvasive radiogenomic signatures by enriching the radiomic features  with a priori predictive genomic signatures (derived from key predictive subclone compositions). Moreover, the imaging-based tests can be performed repeatedly over time, allowing for longitudinal studies that are often challenging when multiple repeated biopsies would otherwise be required of patients.While multigene assays . This reference matrix was further used as a guide for supervised gene expression profile deconvolution to validate genomic subclones that accurately predict prognosis. The genomic subclone was re-analysed using the reference matrix associated with aberrant biological functions and poor survival (second phase). This approach decreases bias in the gene expression deconvolution method that may arise from variability in cancer types or gene expression platforms. To design more stable and flexible models targeting patient outcomes, additional gene expression profile data that represent comprehensive cancer-related functions should be included.The gene expression deconvolution method builds upon fundamental mathematical theorems27. A related radiogenomic study revealed an association between tumour radiomics and gene expression patterns and showed enriched pathways of the cell cycle in head and neck cancer patients15. Overexpression of cell cycle genes and prevalence of the cell cycle subclone further support a central role for increased cell growth as a driver of poor survival.Tumours with a high proportion of the cell cycle subclone and a low proportion of the primary immunodeficiency subclone were associated with poor survival. Notably, subclones with the most significantly enriched pathways also had the strongest correlation with survival. The cell cycle subclone had the highest proportion among all the genomic subclones and was correlated with poor survival. Among the signalling pathways within this subclone, the cell cycle and DNA replication pathways likely reflect cell proliferation and may be used for prognostication42, which is broadly reflective of the results reported here. Others reported that the inactivated Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways we detected, namely, cytokine-cytokine receptor interaction, haematopoietic cell lineage, and Jak-STAT signalling pathway, were also altered in lung cancer subtypes43. Genes defining the primary immunodeficiency pathway were significantly enriched in hepatocellular carcinomas (HCCs) and correlated with the density of Epstein-Barr virus (EBV)-positive tumour-infiltrating lymphocytes (TILs)44, suggesting that the immunodeficiency pathway may reflect the degree of immune cell infiltration in tumours. Breast tumours lacking immune infiltration are associated with a poor prognosis5, consistent with our data showing that tumours with a high fraction of immune-related subclones were associated with improved OS.Among the pathways definitive of the primary immunodeficiency subclone profile, the primary immunodeficiency pathway was most enriched. A previous study reported that genes upregulated in this pathway were associated with prolonged relapse-free survivalNDUFA13 gene in the pathways has been shown to correlate with lymph node metastasis and advanced tumour-node-metastasis (TNM) stage in breast cancer45. The peroxisome subclone includes peroxisome, prostate cancer, pathways in cancer, metabolic pathways. Among these, the peroxisome pathway is reported as enriched among all breast tumour subtypes46 and is correlated with cell proliferation and tumorigenesis48. The extracellular matrix (ECM)-receptor interaction subclone includes ECM-receptor pathway, which is associated with progression and resistance to cytotoxic and hormonal treatments in breast cancer49. Moreover, the dysregulated PI3K-AKT signalling pathways in this subclone are often activated by mutations in breast cancers and so can be targeted by drugs50. The ECM-receptor interaction and the protein digestion and absorption pathways are reported as significantly enriched in analysis of differentially expressed genes between tumour tissues and paracancerous tissues51. The cholinergic synapse subclone includes key gene of BCL2, which is an established prognostic biomarker in early breast cancer52.The Alzheimer’s diseases subclone includes pathways with mitochondrial genes as annotated by the pathway analysis tools. Down-regulation of the 53. Thus, imaging technology can aid in our understanding of biological functions in tumours that drive breast cancer patient outcomes. For example, we show that a high feature value of maximum probability for the parenchymal region surrounding the tumour, which reflects high intratumour heterogeneity, correlates with a high cell cycle fraction and a low immunodeficiency fraction. Radiogenomic analyses, which are repeatable and noninvasive, may offer a powerful surrogate for difficult-to-repeat invasive genomic analyses.Unlike prior studies, we derived prognostic radiogenomic signatures from tumour gene expression rather than requiring that the analysis be supervised by a directional association with patient outcomesThe quality of the MRI data used in this study may be suboptimal because they were collected in the past, their use was an unavoidable necessity because of the requirement for up to a decade of clinical follow-up to collect the OS outcomes data. The follow-up time for data from TCGA (Cohorts 1 and 2) is shorter than that of Cohort 3 but we do not see a significant impact on the main outcomes of this work. In our study, Cohorts 1 and 2 are used solely to identify the prognostic radiogenomic features by associating the multiscale key components of intratumour heterogeneity, that contributes mechanistically to the poor outcomes in patients. To achieve this unique objective, we selected TCGA/TCIA dataset for the following two reasons. First, TCGA/TCIA is currently the largest publicly available dataset containing the matched genomic and the clinical follow-up information needed to complete the study. Second, this dataset provides the matched genomic and DCE-MRI data that allow us to uncover clinically useful associations between radiomic features and genomic signatures. The innovative data analytics methodology and pipeline developed here are readily applicable to more recently obtained, higher-quality MRI data for further validation once adequate clinical follow-up information becomes available.In conclusion, the current study identified the intratumoural heterogeneity of genomic subclones with cancer-related biological functions and prognostic power. This molecular-level heterogeneity was modelled noninvasively by radiogenomic signatures that reflect imaging heterogeneity. The radiogenomic strategy we developed using an unsupervised method to identify genomic subclones can be extended to other cancers to explore tumour heterogeneity and for further use in clinical practice.The study was approved by the institutional review board (IRB) at Hangzhou Dianzi University IRB-2019001). In the three-phase analysis, 1310 samples were used for (1) genomic subclone identification and prognostic power assessment; (2) radiogenomic analysis of associations between DCE-MRI features and genomic subclones; and (3) radiogenomic signature assessment and validation for prognosis prediction  and the remaining data (n = 1010) were included in Cohort 1. Seven samples were excluded because there was no clinical report, and 14 samples were excluded because they had insufficient survival data, resulting in 989 samples for analysis. We randomly separated the dataset into a genomic development dataset  and a genomic testing dataset . Within the genomic development dataset (n = 660), 567 censored patients had a mean follow-up time of 3.147 years; the remaining patients (n = 93) had a mean follow-up time of 3.769 years. For the genomic testing dataset (n = 329), 283 patients were censored with a mean follow-up time of 3.150 years and the remaining patients (n = 46) had a mean follow-up time of 3.801 years. Cohort 2  contains matched imaging and genomic data and was used to establish the associations between radiomic features and the prognostic genomic signatures . The genomic data was obtained from TCGA-BRCA and the matched imaging data was obtained from TCIA55. The dataset initially comprised 137 samples. Thirty-six samples were excluded due to the variation in scan protocols, one sample was excluded because of absent gene expression data, 6 samples were excluded due to missing clinical information, and 7 samples were excluded because they had incomplete DCE-MRI data. Thus, the final dataset included 87 patients for analysis. Cohort 3 contains matched DCE-MRI and follow-up data and includes two datasets; the prognostic assessment dataset 56 and the prognostic testing dataset (collected from the Breast-NACT-pilot in TCIA)58. The prognostic assessment dataset initially included 222 samples56. A total of 173 samples remained for the analyses after excluding 10 samples with no visible tumour, 8 samples with diffuse tumours, 5 samples with poor imaging quality, and 28 samples with incomplete DCE-MRI data. The prognostic testing dataset initially included 64 samples, but three samples were excluded because of incomplete imaging, leaving 61 samples for study. The optimized prediction model trained in Cohort 2 was used to classify the patient samples into good-survival and poor-survival groups in the independent test sets .Three data cohorts with unique and complementary strengths were purposely organized and used in the three-phase analysis respectively for our radiogenomic signature discovery and prediction model building pipeline. Cohort 1 contains matched genomic and follow-up data from TCGA-BRCA59. In brief, the imaging was performed using a T1-weighted gradient echo sequence, including one precontrast image and three to five postcontrast images after injection of the gadolinium-based contrast agent. The in-plane resolution varied from 0.53 to 0.85 mm, the slice thickness ranged from 2 to 3 mm, and the flip angle was 10°.For the radiogenomic dataset, DCE-MRI protocol was described elsewhere56. DCE-MRI was acquired sagittally at 1.5-T using a T1-weighted fat-suppressed sequence and a dedicated breast coil. A gradient echo sequence was acquired with a precontrast sequence, followed by early-phase and delayed-phase sequences at 2.5 mins and 7.5 mins after injection of the contrast material. The imaging parameters were as follows: repetition time (TR), ≤ 20 ms; echo time (TE), 4.5 ms; flip angle, ≤45°; field of view, 160–180 mm; matrix, 256 × 192; 64 slices; slice thickness, ≤2.5 mm; and in-plane resolution, ≤1 mm.For the prognostic assessment dataset, DCE-MRI protocol was described elsewherehttps://wiki.cancerimagingarchive.net/display/Public/Breast-MRI-NACT-Pilot). The DCE-MRI data were acquired with the patients placed in the prone position using 1.5-T MRI . T1-weighted fat-suppressed MRI was performed under the following parameters: TR, 8 ms; TE, 4.2 ms; matrix, 256 × 192 × 60; flip angle, 20°; field of view, 180–220 mm; in-plane resolution, 0.7–0.9 mm; and slice thickness, 2–2.4 mm. A series of postcontrast images were obtained following the intravenous injection of a bolus of 0.1 mmol/kg gadobutrol. The time interval between the first postcontrast series and the contrast agent injection was 2.5 mins, while the time interval between the second and first postcontrast image series was 7.5 mins.For the prognostic testing dataset, imaging protocol was described in TCIA (Breast-MRI-NACT-Pilot) and can be expressed as a nonnegative linear combination of the subtype-specific component sk, weighted by the relative subclone proportions aj (i) in that sample, as defined by the following equation:aj is the vector notation of the expression values of matrix A and J is the number of subclones.The gene expression profile for each sample xm], using affinity propagation clustering and expectation-maximization mixture model fitting61. To identify the vertices of a convex set This method first clusters genes into an optimal number of representative and robust clusters [J vertices were estimated by optimizing the sum of the margin between the convex hull and the remaining exterior cluster centres to reach the minimum:The most probable K subclone, while K is determined by the MDL as defined by Chen et al.62.Each sample of gene expression data can be decomposed by weighted linear combinations of the latent pattern of gene expression for a specific genomic subclone and the corresponding proportions. The indices of the subclone are based on the genes assigned to the gene cluster at a vertex. A model is selected with the optimal A and the marker genes, the proportion matrix S is estimated from matrix S.On the basis of the expression levels of subclone-specific marker genes detected by the CAM method, the relative proportions of constituent subtypes are estimated using standardized averaging. Based on the reference matrix 63. Specifically, pixel values were normalized by the mean of the interquartile values of the gland tissue in the precontrast MR image, ensuring that the signals inside the tumour and from the parenchymal region were normalized comparably. DCE-MRI data were resized to the same resolution prior to feature extraction with a common in-plane resolution of 0.8 mm and a common slice thickness of 2 mm. The centre of the tumour was first annotated by a radiologist with more than 10 years of experience. The breast tumour was segmented through a spatial fuzzy C-means (FCM) algorithm to segment a volumetric breast tumour from the background tissue64. The DCE-MRI series was registered to reduce the effect of possible body movement during imaging65. Fibroglandular tissue that surrounded the tumour was segmented using FCM clustering, excluding the skin and fatty tissue from the breast image. Imaging tissue that was 2 cm wide surrounding the tumour was identified. Specifically, peritumoural shell that surrounds the tumour margin were identified by manual annotation16.DCE-MRI data were normalized and resized68. We extracted features inside these regions on the image series of the precontrast, the subtraction images between the second postcontrast image series and precontrast series, and between the late postcontrast and precontrast series, which were termed S-0, S-1 and S-2, respectively. We obtained 10 histogram-based features, 10 morphologic-based features, and 19 Haralick features that measure textural heterogeneity based on the grey-level co-occurrence matrix (GLCM). Statistical features were calculated using standard statistics based on the histogram of pixel values. Texture features were extracted using the publicly available, open-source and validated PET Oncology Radiomics Test Suite (PORTS) package69. Both the standard histogram-based and Haralick features were obtained for S-0, S-1, and S-2. Morphological features were evaluated on S-0 using standard shape analysis methods. Comparative experiments using our method and Pyradiomics software produced almost identical sets of statistical and morphologic features. All image processing and feature extraction processes were performed in MATLAB .Feature extraction was performed for each sample; details are provided in Supplementary Table Our study framework was performed in three phases on four datasets Figs.  and 2. I60. The hypergeometric test was used to evaluate the significance of the marker genes enriched in each cell subclone with reference to KEGG pathways. GSEA was used to identify enriched biological pathways using the KEGG pathway database. The volcano plot and the display of the relationship between genes and terms for the illustrations of differentially expressed genes were obtained using R GOplot.For each genomic subclone, biological mechanisms were identified with pathway analyses of the marker genes that were exclusively enriched in the subclonep value. The hazard ratio (HR) and its 95% confidence interval were obtained to assess the differences in survival between the stratified groups. A multivariate Cox regression model was used to determine whether the radiogenomic features were independently associated with OS or RFS after adjusting for the available clinical variables of age, ER, PR, HER2 and tumour size. Patients who did not have an event by the end of 10 years were censored at that time. A likelihood ratio test was used to evaluate whether a survival model including the radiogenomic signatures as an explanatory variable significantly improves the model fit compared with a survival model using only the clinical variables.Kaplan–Meier analysis was used to visualize differences in RFS and OS. A log-rank test assessed significant differences between curves; the cutoff point was determined by the optimal threshold value that yielded the smallest log-rank 64. A support vector machine with a radial basis function kernel was used as the base classifier in this global optimization step. L1 regularization was applied to the base classifier to control for complexity. Prediction performance was evaluated using the AUC (the area under the ROC curve) criterion and 10-fold cross validation. The cutoff ROC value was determined at the maximum Youden index (sensitivity + specificity − 1).To build an optimal model with limited samples, we conducted cross validation-based optimization in each of the major steps in our model building pipeline. In addition to the general rule of thumb for controlling model complexity, we also considered the complex interactions (joint-effect) among the radiomic features and the orthogonal, complementary nature of the texture, morphological, and statistical features. We conducted extensive 10-fold cross validation procedures to optimize both feature selection and model building . To address the collinearity problem in subsequent variable selection, correlation-based clustering of the initial features was used to remove redundant features and to select the most representative radiomic features. A global optimization step used the Evolutionary Algorithm to select the most informative radiomic features to build our prediction modelsp values < 0.1 were considered significant. All statistical analyses were performed using MATLAB  and R .To control for false discovery rates (FDRs), the Benjamini-Hochberg method was used in the survival analysis for individual subclones. FDR-corrected Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


Sequencing-based identification of tumor tissue-of-origin (TOO) is critical for patients with cancer of unknown primary lesions. Even if the TOO of a tumor can be diagnosed by clinicopathological observation, reevaluations by computational methods can help avoid misdiagnosis. In this study, we developed a neural network (NN) framework using the expression of a 150-gene panel to infer the tumor TOO for 15 common solid tumor cancer types, including lung, breast, liver, colorectal, gastroesophageal, ovarian, cervical, endometrial, pancreatic, bladder, head and neck, thyroid, prostate, kidney, and brain cancers. To begin with, we downloaded the RNA-Seq data of 7,460 primary tumor samples across the above mentioned 15 cancer types, with each type of cancer having between 142 and 1,052 samples, from the cancer genome atlas. Then, we performed feature selection by the Pearson correlation method and performed a 150-gene panel analysis; the genes were significantly enriched in the GO:2001242 Regulation of intrinsic apoptotic signaling pathway and the GO:0009755 Hormone-mediated signaling pathway and other similar functions. Next, we developed a novel NN model using the 150 genes to predict tumor TOO for the 15 cancer types. The average prediction sensitivity and precision of the framework are 93.36 and 94.07%, respectively, for the 7,460 tumor samples based on the 10-fold cross-validation; however, the prediction sensitivity and precision for a few specific cancers, like prostate cancer, reached 100%. We also tested the trained model on a 20-sample independent dataset with metastatic tumor, and achieved an 80% accuracy. In summary, we present here a highly accurate method to infer tumor TOO, which has potential clinical implementation. Worldwide, almost one in three cancer patients is clinically diagnosed with distant metastases. In most cases, primary and metastatic lesions are identified simultaneously; however, some primary tumors cannot be found after systematic clinicopathological diagnosis . Cases wTo identify the primary lesion of CUP, a systematic assessment is performed which consists of physical examination, patient-history analysis, serum markers, radiological imaging; as well as immunohistochemical analysis. Immunohistochemical markers are very important for determining tissue-of-origin TOO; ; howeverIn recent years, cancer classification based on gene expression data such as RT-PCR has attracted great interest and has been implemented in different studies . Single Support vector machines (SVMs) based on the recursive feature elimination (RFE) algorithm represent embedded methods used for feature selection and classification modeling based on microarray gene expression data, which mined 11,925 genes to 154 genes with definite biological significance . More thIn the present study, genome-wide gene expression profiles were established based on comprehensive RNA-Seq data. The gene expression data of ∼8,000 tumor samples were used to identify gene signatures for 15 common human cancer types . To screen gene features and evaluate cancer classifiers, the Pearson correlation Neural Network (NN) algorithm was implemented in this study to identify tumor origins.1 and the tissue origins of those samples were confirmed through histopathological analysis. The downloaded data offered RNA-seq data of 21 cancer types that belongs to projects from United States, which is sequenced using the same protocols. Among them, melanoma had a distinct distribution from other cancer types (80 samples were sampled from primary tumor and 352 were sampled from metastatic tumor) and was excluded. Thus, the expression profiles of 15 common cancer types  were studied in this work. The normalized expression value of expression data was downloaded from TCGA and provided the expression levels of 20,501 unique genes for the 15 chosen cancer types.NGS-based gene expression profiling data of 7,480 tumor samples were collected from The Cancer Genome Atlas ,m’ rows and ‘n’ columns, such that ‘m’ represented 7,480 tumor samples and ‘n’ represented the expression levels of 20,501 unique genes.To perform the bioinformatics analysis in this study, the transcript level of genes was normalized again to form a matrix with rows of sample numbers and columns of gene numbers. The normalization was done by dividing the sum of the gene expression value of each sample. Normalized gene expression data were extracted and represented as a matrix with ‘2 to transform the original dataset after replacing zeros to global minimum × 0.1. No normalizations were done after feature selection.For log transformation, we used logAmong all the samples, 7,460 samples were sampled from primary tumors, remaining 20 samples sampled from the metastatic tumors.C columns) for the m tumor samples, labeling the sample as “true” if the sample belongs to the cancer type, otherwise the sample was labeled as “False,” where C is the total cancer types and m is the sample number; (ii) calculate the correlation of gene expression level with samples labeled “true” for each cancer type, then sort in decreasing order according to their correlation; (iii) take the most important signatures, appeared top N of the list, for each cancer type, where N is an integer; and (iv) combine C lists of the top N genes and remove the redundant genes, generating a gene set. Gene expression values from the gene set will be extracted for further usage.To identify an optimal gene signature, we introduced a strategy of feature selection and multi-class classification modeling in this study. According to the mechanism of feature selection, the sets of genes were screened by the Pearson Correlation algorithm . This stN units, the hidden layer has 50 units, and output layer has 15 units corresponding to each cancer where N is the gene number of the input matrix. The output layer of the NN was used as the input for the Softmax function to obtain the probabilities for each cancer type. To prevent overfitting, L2 penalty was set to 0.0001. For comparison, we used logistic regression as a baseline method. The parameter C was set to 10,000 for logistic regression. The algorithms were implemented using scikit-learn package  analysis of the identified gene features, GO consortium  was usedThe main objective in this study is to identify putative gene biomarkers to classify cancer type. The workflow of the present study is shown in Around 20 of the 7,480 samples were sampled from metastatic tumors, whereas 7,460 were sampled from primary tumors. Thus, we split the dataset into the 7,460-sample training dataset and the 20-sample test dataset according to the sampling tumor type. All cancer types in the training dataset had more than 100 samples; the largest sample size was that of breast cancer , whereas, the smallest sample size was that of pancreatic cancer (142 samples). A classification modeling database of 15 common cancer types was established based on the expression data of 20,501 unique genes obtained from TCGA. However, having a large number of samples per cancer type might result in variations due to intra-tumor heterogeneity; hence, it is critical to identify the gene expression features from high-dimension datasets. Pearson correlation-based feature selection represents a multivariable filter method for high-dimension data analysis , which iThe regression model is an important mathematical model for classification. NNs, as types of deep learning algorithms, are advanced techniques that can analyze complex and high-dimensional data. NNs have been applied in protein classification  and anomN genes using Pearson correlation from the 9/10 training set, where N is the gene number which might be 15, 30, …, 300 with a step of 15. (d) Train a model using the selected genes using the 9/10 training set. (e) Use the remaining one part as test set as the validation set of the previously trained model. (f) Repeat b–e 10 times with each part being the test set, until all the samples are predicted once. Finally, (g) merge the results from the test parts and evaluate the metrics.Usually, 10-fold cross-validation is used for minimizing the over-fitting issues and obtaining good performance. Hence, to avoid overfitting of the NN algorithm, we ran a 10-fold cross-validation 10 times using the 7,460-sample training dataset to obtain relatively stable and reliable results, possibly minimizing the percentage of false positives and false negatives. The 10-fold cross validation was performed as follows. (a) Split the whole training dataset into 10 disjoint parts randomly. (b) Use 9 parts as the training set (9/10 training set). (c) Choose The cross validation was done using different gene number and the accuracies from each 10-fold cross validation are plotted. For comparison, we also used logistic regression as a baseline model . We achiWe also attempted to use the log-transformed data for in the cross validation since log-transformation was a common transformation for gene expression profile. For a reasonable comparison, we selected 10 genes for each cancer in each fold of cross validation. However, the overall accuracy by 10 times of 10-fold cross validations only reached 80.90% , which iA 150-gene set was identified using the whole training dataset for subsequent processing . To undeWe further sought to validate our model on the 20-sample metastatic dataset as a test set. We trained the NN model and the logistic regression model on the whole training dataset using the 150-gene set, which was then used for predicting the test set. The prediction accuracy of NNs was 80%, while the prediction accuracy of the logistic regression model was 70%. The detailed predictions are shown in Inferring cancer TOO is important for CUP patients and might serve well for minimizing misdiagnosis, even if the cancer origin is diagnosed by pathological observation. Hence, it is critical to develop a method to classify TOO of common cancer types. This study was possible because of the great advancements in NGS technologies and the general application of NGS in clinical experiments, along with the efforts made by researchers who have contributed to the TCGA, from where huge gene expression datasets can be obtained. In the present study, we utilized the NN method to comprehensively analyze high-dimensional RNA-Seq datasets of 15 common cancer types. The 150-gene panel of cancer classifiers demonstrated an average accuracy of 94.87%, corresponding to the actual numbers of cancer samples.Several hallmarked studies indicated that the cellular origin signatures that are expressed in primary tissue are sufficiently retained even after primary cancer cells undergo dedifferentiation and colonization in different tissue types . A recenGRHL3 (Grainyhead-Like Transcription Factor 3) encodes a cancer suppressor that is a member of the grainyhead-like transcription factor family  are genes that encode serine proteases that exhibit a deregulated expression in prostate cancer. In our study, KLK2, KLK3, and KLK4 were identified as gene signatures for prostate cancer; KLK3 is a prostate-specific antigen that is a gold-standard clinical biomarker widely employed in the diagnosis and monitoring of prostate cancer  Co., Ltd. The remaining 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.