The count table, a numeric matrix of genes × cells, is the basic input data structure in the analysis of single-cell RNA-sequencing data. A common preprocessing step is to adjust the counts for variable sampling efficiency and to transform them so that the variance is similar across the dynamic range. These steps are intended to make subsequent application of generic statistical methods more palatable. Here, we describe four transformation approaches based on the delta method, model residuals, inferred latent expression state and factor analysis. We compare their strengths and weaknesses and find that the latter three have appealing theoretical properties; however, in benchmarks using simulated and real-world data, it turns out that a rather simple approach, namely, the logarithm with a pseudo-count followed by principal-component analysis, performs as well or better than the more sophisticated alternatives. This result highlights limitations of current theoretical analysis as assessed by bottom-line performance benchmarks. This paper compares different transformation approaches for analysis of single-cell RNA-sequencing data and provides recommendations for method selection. Single-cell RNA-sequencing (RNA-seq) count tables are heteroskedastic. In particular, counts for highly expressed genes vary more than for lowly expressed genes. Accordingly, a change in a gene’s counts from 0 to 100 between different cells is more relevant than, say, a change from 1,000 to 1,100. Analyzing heteroskedastic data is challenging because standard statistical methods typically perform best for data with uniform variance.3, but parameter inference can be fiddly and computationally expensive5. An alternative choice is to use variance-stabilizing transformations as a preprocessing step and subsequently use the many existing statistical methods that implicitly or explicitly assume uniform variance for best performance6.One approach to handle such heteroskedasticity is to explicitly model the sampling distributions. For data derived from unique molecular identifiers (UMIs), a theoretically and empirically well-supported model is the gamma-Poisson distribution 7 promise an easy fix for heteroskedasticity if the variance predominantly depends on the mean. Instead of working with the raw counts Y, we apply a non-linear function g(Y) designed to make the variances  more similar across the dynamic range of the data8. The gamma-Poisson distribution with mean μ and overdispersion α implies a quadratic mean–variance relationship α = 0 and α can be considered a measure of additional variation on top of the Poisson. Given such a mean–variance relationship, applying the delta method produces the variance-stabilizing transformationy0 = 1 / (4α) , such that the range of the adjusted counts is about the same as that of the raw counts. The simplest estimate of the size factor for cell c isc, g indexes the genes and An additional requirement is posed by experimental variations in sampling efficiency and different cell sizesL. For instance, Seurat uses L = 10,000, others12 have used L = 106 calling the resulting values ygc/sc counts per million (CPM). Even though the choice of L may seem arbitrary, it matters greatly. For example, for typical droplet-based single-cell data with sequencing depth of ∑gygc ≈ 5,000, using L = 106 and then transforming to y0 = 0.005 in equation  motivated above.Sometimes, a fixed value is used instead for 13 suggested a different approach to variance stabilization based on Pearson residualssc is again the size factor for cell c, and βg,intercept and βg,slope are intercept and slope parameters for gene g. Note that the denominator in equation  of each cell. Sanity MAP (maximum a posteriori) ignores the inferred uncertainty and returns the maximum of the posterior as the transformed value. A related tool is Dino, which fits mixtures of gamma-Poisson distributions and returns random samples from the posterior15. Normalisr is a tool primarily designed for frequentist hypothesis testing16, but as it infers logarithmic latent gene expression, it might also serve as a generic preprocessing method. Normalisr returns the minimum mean square error estimate for each count assuming a binomial generative model.A third set of transformations infers the parameters of a postulated generative model, aiming to estimate so-called latent gene expression values based on the observed counts. A prominent instance of this approach is Sanity, a fully Bayesian model for gene expression4 and applied to biological data by Townes et al.17. Recently, Agostinis et al.18 presented an optimized implementation called NewWave.In this work, we analyze transformations for preprocessing UMI-based single-cell RNA-seq data based on each of these approaches. We will first contrast the conceptual differences between them. In a second part, we benchmark the empirical performance of all approaches and provide guidelines for practitioners to choose among the methods. In the benchmarks, we also include a fourth preprocessing approach that is not transformation-based and directly produces a low-dimensional latent space representation of the cells: factor analysis for count data based on the (gamma-)Poisson sampling distribution. An early instance of this approach, called GLM PCA, was presented by Townesy0 = 1 or y0 = 1 / (4α) and the shifted logarithm with CPM. In addition, we tested the shifted log transformation with highly variable gene selection (HVG), z scoring (Z) and rescaling the output as suggested by Booeshaghi et al.19.Among the delta method-based variance-stabilizing transformations, we considered the mentclass2pt{minimz scoring and an analytical approximation to the Pearson residuals suggested by Lause et al.20.Among the residuals-based variance-stabilizing transformations, we considered the clipped and unclipped Pearson residuals (implemented by sctransform and transformGamPoi) and randomized quantile residuals. In addition, we tested the clipped Pearson residuals with HVG selection, Among the latent gene expression-based transformations (Lat Expr), we considered Sanity Distance and Sanity MAP, Dino and Normalisr.Among the count-based factor analysis models (Count), we considered GLM PCA and NewWave.There are multiple formats for each of the four approaches:y) and the raw counts scaled by the size factor (y / s).Last, we include two methods as negative (Neg) controls in our benchmarks, for which we expect poor performance: the raw untransformed counts  graph as a fundamental data structure that encodes essential information. The next challenge is then the definition of ‘ground truth’. We designed our benchmarks upon reviewing previous benchmarking approaches. For instance, Breda et al.14 and Lause et al.20 employed synthetic or semi-synthetic data. This is operationally attractive, but it is difficult to be certain about biological relevance. Hafemeister and Satija13 and Lause et al.20 used qualitative inspection of non-linear dimension reduction plots. This can be informative, but is difficult to scale up and make objective. Germain et al.24 compared how well the transformations recovered a priori assigned populations, defined either through FACS or by mixing different cell lines. This is conceptually clean, but restricts analysis to a limited range of datasets that also may only offer a caricature view of cell diversity.There is no context-free measure of success for a preprocessing method, as it is contingent on the objectives of the subsequent analysis. For instance, if interest lies in identification of cell type-specific marker genes, one could assess the shape of distributions, such as in Fig. k-NNs of each cell as measured by Euclidean distance and, finally, computed the overlap of the thus obtained k-NN graph with a reference k-NN graph (Consistency. We downloaded ten 10x datasets from the Gene Expression Omnibus (GEO) database. As there was no formal ground truth, we measured the consistency of the results  by splitting the genes of each dataset into two disjoint subsets.Simulation. We used four different previously published simulation frameworks and one adapted by us to generate a diverse collection of datasets for which we had full access to the true k-NN graph.Downsampling. We used five deeply sequenced datasets based on mcSCRB and Smart-seq3, which we downsampled to sequencing depths typical for the 10x technology. We postulated that a proxy for ground truth could be constructed from the k-NN graph inferred from the deeply sequenced data intersected across all transformations which we call reliable nearest neighbors. To our knowledge, this work presents the first instance of such an approach.Extended Data Fig. For all our benchmarks, we applied the transformations to the raw counts of each dataset listed below, computed a lower-dimensional representation of the cells using principal-component analysis (PCA), identified the NN graph . We perfk = 10, 50 and 100 nearest neighbors. In total, we collected more than 61,000 data points. In addition to the results highlighted in the following, we provide an interactive website with all results for all tested parameter combinations.We tested 22 transformations—where applicable with an overdispersion fixed to 0, 0.05 and a gene-specific estimate from the data—across four to eight settings for the number of dimensions of the PCA and measured the overlap with k = 50. Similar results were obtained for k = 10 and k = 100, shown in Extended Data Fig. Figure In the consistency benchmark, the delta method-based transformations performed better than the other transformations Fig. .On the simulated data, the differences between the transformations looked less pronounced in Fig. The results of the downsampling benchmark Fig.  agreed wk-NN overlaps was dataset dependent, ranging from 34 of 50 for the best performing transformation versus 9 of 50 for the negative control for the SUM149PT cell line consistency benchmark, to 2.9 of 50 versus 1.5 of 50 for the HEK downsampling benchmark. For the latter, the overall small overlaps were due to small sets of reliable nearest neighbors  and the adjusted mutual information (AMI) for the five simulation frameworks. Extended Data Fig. k-NN overlap . We found that the delta method-based and residuals-based variance-stabilizing transformations performed as well in this benchmark if we projected the cells to a lower-dimensional representation before constructing the k-NN graph. In fact, Fig. The Random Walk simulation reproduced the benchmark based on which Breda et al.k-NN on the 10x human helper T-cell dataset with 10,064 cells. Sanity Distance took particularly long because its distance calculation, which takes into account the uncertainty for the nearest neighbor search, scaled quadratically with the number of cells  and the count-based factor analysis models were computationally more expensive than the delta method- and residuals-based transformations. Figure lls Fig. . Across In terms of uncovering the latent structure of the datasets, none of the other transformations consistently outperformed the shifted logarithm Fig. , one of 20 and Choudhary and Satija25 debated on how to best choose the overdispersion parameter. We found empirically that, for Pearson residuals and the α > 0, but saw no clear benefits from estimating this parameter from the input data versus using a generic, fixed value such as 0.05  improved the results for identifying nearest neighbors Fig. . Lause e.05 Fig. .k-NN overlap with the ground truth , but our benchmarks showed limited performance benefits for these.We compared 22 transformations, conceptually grouped into four basic approaches, for their ability to recover latent structure among the cells. We found that one of the simplest approaches, the shifted logarithm transformation 19. In our hands .24 benchmarked many steps of a typical single-cell RNA-seq analysis pipeline, including a comparison of clustering results obtained after different transformations against a priori assigned populations. In line with our findings, they reported that dimension reduction was of great importance. They went on to recommended sctransform  based on its good performance on the Zhengmix4eq dataset, which is a mixture of peripheral blood mononuclear cells sorted by surface markers using flow cytometry; however, it is not clear how generalizable this result is and our benchmarks do not support such a singling out of that method. Lause et al.20 considered the related Zhengmix8eq dataset, into which they implanted a synthetic rare cell type by copying 50 B cells and appending ten genes exclusively expressed in the synthetic cell type. They used k-NN classification accuracy of the cell type averaged per cell type  and averaged over all cells . They found a performance benefit for the Pearson residuals over the shifted logarithm with the macro F1 score, but similar performance with regard to overall accuracy. The macro F1 score emphasizes the performance difference for the synthetic cell type, which seems somewhat construed and might not be a good model for most biologically relevant cell type and state differences. Instead of comparing clustering results to discrete cell type assignments, we have focused on the inference of the k-NN of each cell, with the expectation that this enables consideration of more subtle latent structures than well-separated, discrete cell types.Our results partially agree and disagree with previous studies. Germain et al.Pearson residuals- and delta method-based transformations weight genes differently; for example, Pearson residuals put more weight on lowly expressed genes than the delta method Fig. . This ca26.We did not evaluate the impact of alternative size factor estimators. We also did not consider how suitable a transformation is for marker gene selection, because we are not aware of a suitable metric to determine success, as the utility of a marker gene hinges on its biological interpretability. For a recent effort to compare different marker gene selection methods, see Pullin and McCarthyConsiderable research effort has been invested in the area of preprocessing methods for single-cell RNA-seq data. To our surprise, the shifted logarithm still performs among the best. Our bottom-line performance benchmark highlights current limitations of theoretical analysis of preprocessing methods, but also the utility of lower-dimensional embeddings of the transformed count matrix to reduce noise and increase fidelity. Interesting open questions include choosing among the many possible embedding methods and number of latent dimensions.The delta method is a way to find the s.d. of a transformed random variable.g to a random variable X with mean μ, the s.d. of the transformed random variable g(X) can be approximated byg at μ.If we apply a differentiable function X1, X2, … whose variances and means are related through some function v, that is, g by requiring constant s.d., Now consider a set of random variables We compared 22 transformations that can be grouped into four approaches.19 ; the shifted logarithm with subsequent HVG selection ; Pearson residuals with clipping and additional heuristics implemented by sctransform v.2, an analytic approximation to the Pearson residuals with clipping suggested by Lause et al.20 ; randomized quantile residuals implemented by transformGamPoi (Random Quantile); Pearson residuals without clipping implemented by transformGamPoi (Pearson (no clip)); Pearson residuals with clipping and subsequent HVG selection (Pearson → HVG); Pearson residuals with clipping and subsequent z scoring per gene (Pearson → Z); and Pearson residuals with clipping and subsequent HVG selection and z scoring per gene (Pearson → HVG → Z). For each composite Pearson residual transformation (with HVG and/or z scoring), we used the transformGamPoi implementation.The residuals-based transformations were: Pearson residuals implemented with the transformGamPoi package where each residual is clipped to be within The latent expression-based transformations were: Sanity with point estimates for the latent expression (Sanity MAP) and with calculation of all cell-by-cell distances taking into account uncertainty provided by the posteriors (Sanity Distance); Dino as provided in the corresponding R package; and Normalisr with variance normalization, implemented in Python, which we called from R using the reticulate package.α = 0.05. In the figures, we show the results for the Poisson model unless otherwise indicated. We used the avagrad optimizer. We ran NewWave with 100 genes for the mini-batch overdispersion estimation.The count-based factor analysis models were: GLM PCA using the Poisson model and the gamma-Poisson model with s using equation  and computed For α = 0, because these settings worked best for the respective transformations. The latent expression-based transformations and NewWave do not support custom overdispersion settings.In the overview figures Figs. –4, we us21. We filtered out RNAs that were all zero and plotted the first two principal components. Where applicable, we used gene-specific overdispersion estimates. For visualizing the results of Sanity Distance, instead of the PCA, we used multidimensional scaling of the cell-by-cell distance matrix using R’s cmdscale function. We calculated the canonical correlation using R’s cancor function on the size factors and the first ten dimensions from PCA and multidimensional scaling.For the visualization of the residual structure after adjusting for the varying size factors, we chose a control dataset of a homogeneous RNA solution encapsulated in droplets27. Where applicable, we used the gene-specific overdispersion estimates. The panel of Sanity Distance shows the variance of samples drawn from a normal distribution using the inferred mean and s.d.The plots of the mean–variance relationship are based on the 10x human hematopoietic cell dataset28, we filtered out cells with extreme size factors . We also removed cells that did not pass the scran quality control criterion regarding the fraction of reads assigned to mitochondrial genes. To account for the fact that some transformations share information across genes, we applied all transformations to the 100 most highly expressed genes and three genes  known to be differentially expressed in some cell types according to the assignment from the original publication.For the mouse lung datasetThe benchmarks were executed using a custom work scheduler for slurm written in R on CentOS7 and R 4.1.2 with Bioconductor v.3.14. The set of R packages used in the benchmark with exact version information was stored using the renv package and is available from the GitHub repository.k-NN, we used annoy, which implements an approximate nearest neighbor search algorithm. To calculate t-distributed stochastic neighbor embeddings (tSNEs), which we only used for visualization, we used the Rtsne package on data normalized with the shifted logarithm with a pseudo-count of 1.To calculate the PCA, we used the irlba package. To infer the k-NN for all cells.We downloaded ten single-cell datasets listed in GEO browser after searching for the term mtx on 14 October 2021. All datasets are listed in the Data Availability section. To measure the consistency of the transformations, we randomly assigned each gene to one of two groups and processed the two resulting data subsets separately. We calculated the consistency as the mean overlap of the 29 using a consecutive bifurcating mode and the default parameters otherwise. We ran muscat30 with four clusters, a default of 30% differentially expressed genes with an average log fold change of 2 and a decreasing relative fraction of log fold changes per cluster. We ran scDesign2 (ref. 31) with the 10x human hematopoietic cell dataset as the reference input with a copula model and a gamma-Poisson marginal distribution. We simulated the Random Walk by translating the MATLAB code of Breda et al.14 to R and using the data by Baron et al.32 as a reference. For the Linear Walk, we adapted the Random Walk simulation and, instead of following a Random Walk for each branch, we interpolated the cells linearly between a random start and end point. For both benchmarks, we used a small non-zero overdispersion of α = 0.01 to mimic real data.We used five frameworks to simulate single-cell counts in R: we ran dyngenk-NNs to each other. We calculated the overlap as the mean overlap of this ground truth with the inferred nearest neighbors on the simulated counts for all cells. Furthermore, we calculated the ARI and AMI by clustering the ground truth and the transformed values with the graph-based walktrap clustering algorithm from the igraph package.With each simulation framework, we knew which cells were the k-NNs of a cell that were identified with all 22 transformations on the deeply sequenced data (excluding the two negative controls). We used the downsampleMatrix function from the scuttle package to reduce the number of counts per cell to approximately 5,000, a typical value for 10x data. We considered only one setting for the overdispersion per transformation . We ran all transformations that supported the setting, with a gene-specific overdispersion estimate . Finally, we computed the mean overlap between the k-NNs identified on the downsampled data with the set of reliable nearest neighbors for all cells with more than one reliable nearest neighbor.We searched the literature for single-cell datasets with high sequencing depth and found five  that had a sequencing depth of more than 50,000 UMIs per cell on average. We defined reliable nearest neighbors as the set of k-NN graphs. Denoting their no. cell × no. cell adjacency matrices  by N1 and N2, we defined their overlap asFor all three benchmarks, we calculated overlaps between pairs of Further information on research design is available in the Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41592-023-01814-1.Supplementary InformationSupplementary Fig. 1, Supplementary Table 1 and mathematical details A1–A3.Reporting SummaryPeer review file.


Tumor classification based on genomic features may be able to identify new clinically relevant subtypes and disease characteristics. By integrating multiple levels of genetic and epigenetic data, distinct clusters can be defined among tumors with similar histology and previously unknown distinguishing features. Here, we aimed to find prognostic subtypes among high-grade serous ovarian tumors by integrating their transcriptomic and methylomic features. Feature selection was applied to retain only those features most significantly correlated with disease recurrence. By using consensus clustering and machine learning algorithms, we describe four groups of tumors characterized by unique genetic and epigenetic properties which were associated with significant differences in clinical outcomes. By using both techniques in succession, we uncovered both differential features between groups and defining ontologies therein. One such group was associated with stromal and immune diverse cell populations and was associated with poor clinical outcomes. Our findings identify unique contributors to disease recurrence in high-grade serous ovarian cancer.High-grade serous ovarian cancer (HGSOC) is characterized by a complex genomic landscape, with both genetic and epigenetic diversity contributing to its pathogenesis, disease course, and response to treatment. To better understand the association between genomic features and response to treatment among 370 patients with newly diagnosed HGSOC, we utilized multi-omic data and semi-biased clustering of HGSOC specimens profiled by TCGA. A Cox regression model was deployed to select model input features based on the influence on disease recurrence. Among the features most significantly correlated with recurrence were the promotor-associated probes for the NFRKB and DPT genes and the TREML1 gene. Using 1467 transcriptomic and methylomic features as input to consensus clustering, we identified four distinct tumor clusters—three of which had noteworthy differences in treatment response and time to disease recurrence. Each cluster had unique divergence in differential analyses and distinctly enriched pathways therein. Differences in predicted stromal and immune cell-type composition were also observed, with an immune-suppressive phenotype specific to one cluster, which associated with short time to disease recurrence. Our model features were additionally used as a neural network input layer to validate the previously defined clusters with high prediction accuracy (91.3%). Overall, our approach highlights an integrated data utilization workflow from tumor-derived samples, which can be used to uncover novel drivers of clinical outcomes. Ovarian cancer remains among the leading causes of cancer death among women, with an overall 1 in 78 mortality risk . HGSOC iTP53 mutations, a defined subset of tumors displaying BRCA1/2 germline mutations, and characteristic DNA copy number alterations and promoter methylation events. Non-negative matrix factorization (NMF) consensus clustering was conducted using mRNA expression, miRNA expression, DNA copy number, and promoter methylation data as input. Four subtypes were then defined: Mesenchymal, Proliferative, Immunoreactive, and Differentiated, building off a prior analysis which used microarray in isolation [MCM2, PCNA), as well as increased WNT/β-catenin signaling [CXCL11, CXCL12 CXCR3, etc.). The Differentiated subtype displayed high expression of markers of epithelial differentiations, such as MUC1 and MUC16. Other studies have attempted similar “omic” classifications; however, the prognostic and therapeutic relevance of molecular subtypes remains variable between studies and has not drastically influenced treatment decisions [The integrated molecular analysis of HGSOC in The Cancer Genome Atlas (TCGA) yielded a classification of tumors based on histology and genomic features  . This ansolation ,10. The ignaling ,10. Tumoecisions ,10,11,12Advancements in unsupervised learning and multi-omic data integration are allowing for more complex methods of tumor subtyping ,14. Theshttp://gdac.broadinstitute.org), accessed on 17 August 2022. Time to recurrence was defined as days from diagnosis to tumor recurrence. Patients were censored at the last date they were alive and known to be recurrence-free.Paired RNA-seq and 27k Illumina methylation array data were obtained for 374 HGSOC specimens from TCGA, downloaded directly from the Genomic Data Portal (GDC) via a 2011 Legacy dataset available online . Legacy BAM genomic alignment files. Fragments per kilobase of transcript per million mapped reads (FPKM) and expected gene counts were then calculated using RNA-Seq by Expectation–Maximization (RSEM) [RNA-seq data were collected as n (RSEM) . FPKM co27k Illumina methylation array data were collected in a SeSAMe Methylation Beta Value file format. Nine multi-aliquot samples existed, for which the mean beta values were used to represent each sample. Missing beta values were imputed using ChAMP version 2.30.0, using the K-nearest neighbors method (KNN) with k = 5 neighbors . Probes The expression data (count matrix) and methylation data  were unified such that each patient had one representative sample in each dataset. Prior to sample clustering, various feature selection methods were performed to select the most relevant features for cluster distinction. Two main methods were used—mean absolute deviation (MAD) and Cox proportional hazards regression models .p-value. A cutoff value of 0.05 was used for the proportional hazards p-value for each feature. The coxph function in R survival package was used for this analysis [The univariate Cox model was used for each feature  to indiscriminately test its significance in relation to disease recurrence. In this case, the event variable was the binary recurrence or censoring indicator, and the time was the number of days from cancer diagnosis to recurrence, death, or censoring. The Cox-selected features were chosen for downstream analysis. Features were evaluated for selection based on both R-square value and Ward analysis .The MAD method was initially used for feature selection for the 500 most variable features from each dataset but was not deployed in downstream clustering. The following formula was used:In total, 1467 features  were selected for use in the clustering analysis. Various methods of unsupervised clustering were used to identify distinct subtypes using this feature set. The methods used for clustering included Ward hierarchical clustering, partition around medoids (PAM), Clara, and similarity network fusion (SNF). Ultimately, a combined SNF and consensus clustering (CC) was applied . First, n = 370 and expecting to identify 3 or 4 clusters, we expected the cluster size to be approximately n = 100. Assuming approximately 80% event rate , a Cox proportional hazards model comparing time-to-event outcomes between two such clusters would provide 80% power to detect a hazard ratio HR = 1.56 when testing at two-sided α = 0.05. Adjusting for multiple comparisons and testing at α = 0.01, there would be 80% power to detect HR = 1.72.Overall survival and time to recurrence were estimated using the method of Kaplan–Meier and compared between the identified clusters using the logrank test. With a sample size p-value of <0.05 (Benjamini–Hochberg correction) and absolute LFC (|>0.5|) were used as thresholds for significance. To test for methylation differences among the two clusters of interest, differential methylation was performed using limma [p-value of <0.05 (BH) was used as a cutoff for significance with an absolute delta beta value (|>0.10|). Gene annotation for each differential probe was obtained from the Illumina Human Methylation 27k Annotation. Enrichment analysis using differentially expressed and methylated genes was conducted using Enrichr [To test for differences in expression and methylation among the responsive and non-responsive clusters, differential expression was performed using DESeq2 . DESeq ung limma . Limma e Enrichr .n = 1467) used for unsupervised clustering were used as the input nodes for a multilayer perceptron (MLP) artificial neural network. The data were split into 80/20 training and testing sets (by % of samples), respectively. The sample labels were defined as the cluster numbers  previously identified. The model architecture was as follows: one input layer (nodes = 1467), three hidden layers , and one output layer (labels = 4). A layer dropout rate of 0.1 was used in the first layer. For the first four layers, the relu activation function was used. For the output layer, the softmax activation function was used. The adam optimizer function was used, with a learning rate of 0.0001. The categorical crossentropy loss function was used. Model accuracy was calculated based on the confusion matrix of predicted and actual class labels. Machine learning analysis was performed with Keras [The selected features  version 4.8.1 .Three additional downstream analyses were performed on the identified clusters to evaluate further signature differences among them. Correlation analysis was performed for each cluster separately to evaluate the correlation of gene-level methylation with expression, using MethylMix 2.0 . Immune p-value cutoff was applied to Cox feature selection (p < 0.01) to account for the higher number of probes included in the 450k array. All downstream analyses were conducted in the same fashion as the described workflow. To compare methylation probes from 450k array ICGC data to 27k array TCGA data, 450 k probes were limited to only those falling within +/− 1500 base pairs of TSS, representing the promoter region. However, all 450k probes were considered for feature selection.To validate the described workflow and demonstrate its utility on an external dataset, RNA-seq expression and 450k methylation array data were collected from the HGSOC dataset maintained by the International Cancer Genome Consortium (ICGC) . Followip-values of <0.05. Prior feature selection attempts, using features with high variability (mean absolute deviation), were inconclusive.Data were processed and analyzed according to the workflow outlined in NFRKB and DPT genes and the TREML1 gene  showed a higher propensity toward treatment sensitivity; the median time to disease recurrence was 977 days (n = 111 tumors) showed a trend toward treatment resistance; the median time to disease recurrence was 428 days. Cluster 3 (n = 98 tumors) also trended toward resistance and lethality, with a median time to recurrence of 568 days and median time to death of 1248 days. These clusters were selected for downstream differential analyses, as they had the highest disparity in treatment outcomes.Similarity network fusion combined with consensus clustering yielded optimal k = 4 clusters with distinct differences in disease recurrence propensity A. All id977 days . ClusterCluster 1: “Responsive”p-value < 0.05, |log2FC| > 0.50), 26 upregulated and 381 downregulated genes  were downregulated in this cluster vs. all others  were found to be differentially expressed  and immunoglobulin kappa variable chains (IgKV) were identified   A. The pa2, CCR2) B. Groups2, CCR2) C. No cle2, CCR2) D. Due to2, CCR2) . The ove2, CCR2) . DiffereCluster 4: “Non-Responsive|Hypomethylated”GABRA3 and DLL1 genes), Ovarian infertility (CNTN6 and COL9A3), and Nuclear receptors , pointing to a phenotype more dysregulated in hormone signaling . Of these, 6505 features were methylation probes. A four-cluster optimal solution was again identified (p < 0.0001). In total, 56 promoter-region probes and 9 gene features overlapped with those identified in the primary model  neural network was constructed, using the 1467 features selected by the univariate Cox regression model as node inputs. With three hidden layers, the output layer led to a classification into one of four clusters. This feedforward structure combined the selected feature inputs with initial weights and subjected them to an activation function for each layer A. The daAmong the differentially expressed and methylated features of each cluster, a list of overlapping features occurring in both lists was produced A. The hiOur findings have several notable implications, within the context of HGSOC genomic profiling. The semi-biased clustering of samples by integrated transcriptomic and methylomic data was superior to traditional hierarchical clustering, as well as feature selection using variability measures. The immunosuppressive phenotype found in Cluster 3 is distinct; the estimated presence of multiple stromal and immune cell types was associated with a poor response to treatment. Finally, the entire set of selected features was required for accurate subtype prediction using a supervised MLP neural network.Since the wide deployment of next generation sequencing (NGS), several methods have been developed to cluster RNA sequencing data into de novo cancer subtypes. HGOSC, like other tumor types, is genetically and epigenetically heterogeneous . The cluMulti-omics clustering methods used for subtyping have included basic k-means clustering, iCluster, similarity network fusion, and consensus clustering algorithms ,34. SuchSimilarity network fusion (SNF) is a clustering approach which works best for multi-layer data integration . This meWe deem our approach “semi-biased” as the integrated features were selected based on their correlation with disease recurrence. Thus, the de novo clusters have an expected difference in predicted recurrence. However, by conducting downstream differential expression and methylation analysis between the most clinically different clusters, we identified additional features of each which may drive the phenotype. We also captured biological insights based on the differential analyses that were not evident with hierarchical clustering or a two-category definition of platinum response . Finally, we performed a supervised neural network deep learning exercise to confirm the validity of our clusters and ensure the assignments were detectable based on the selected features alone. Each of the clinically distinct clusters  was associated with clinically significant findings.SOX genes which were downregulated . The sex-determining region Y-box (SOX) family of transcription factors has been linked to oncogenic processes, programs related to cell differentiation and stemness [SOX2, SOX5) [p53 activation [SOX11 has been implicated as a factor that can function as both a tumor suppressor and a metastasis inducer [The Cluster 1 “Responsive” group contained multiple stemness . Some of2, SOX5) ,40. In ltivation . The hig inducer .SOX3 was shown to upregulate pro-apoptotic genes in breast cancer and was associated with a poor prognosis. The SOX transcription factors can promote cell proliferation and survival in cancer in a context-dependent fashion. Of the three SOX genes found downregulated in Cluster 1, both SOX11 and SOX3 have been demonstrated to have oncogenic features in ovarian or cervical cancer [In contrast, l cancer ,44,45. WCXCR2 and CCR2 have been associated with chemoresistance in multiple cancer types, including HGSOC [CCL5, CCRL2, CD244, CD28, CD3G, CD48, CD52, CD84). IRAK3 has recently been studied for targeting to enhance pro-inflammatory cytokine signaling in cancer [The Cluster 3 “Non-Responsive|Immunosuppressive” group is noteworthy for its immune cell-type composition differences and its upregulation of multiple chemokine signaling and immunoglobulin heavy and kappa-chain-associated genes. Both ng HGSOC . The tarng HGSOC . Many imn cancer . Macrophn cancer . Tumor-an cancer . InteresIGHV genes and expression response to treatment have been demonstrated as prognostic biomarkers [ELAVL3, GCK, PYY, SSTR3, FGF17, and PLPPR1. Several of these have previously been noted for their varying roles in oncogenesis and cell proliferation [GCK is a glucokinase responsible for glucose metabolism by sensing glucose uptake and encouraging insulin release. GCK is highly expressed in the liver, and its expression is closely related to hexokinase-2 [The RNA-seq findings for Cluster 4 “Non-Responsive|Hypomethylated” were noteworthy in contrast to Cluster 3. The two groups had comparable clinical outcomes regarding both time to recurrence and time to death. Yet, whereas Cluster 3 showed the upregulation of multiple immunoglobulin chain coding genes, Cluster 4 showed the downregulation of this group. Both the mutation status of omarkers . Patientomarkers . That thferation ,56,57,58kinase-2 . Its rolPAGE2, GAGE2A, GAGE13, and GAGE2E. Such tumor antigens have been described in many cancer types, and they represent cancer/testis antigens which are normally expressed in male germ cells and are repressed in cancer [The shared features of both non-responsive clusters (3 and 4) included the overexpression of multiple tumor antigen genes: n cancer ,60. Theynon-responsive groups), compared to Cluster 1. Among the DMPs of Cluster 4, there were multiple anion transporters , as well as multiple altered probes in the promoter region of IL1RN. The latter gene codes for an interleukin 1 cytokine which modulates immune and inflammatory response [Notably, many DMPs within Cluster 4 were hypomethylated—compared to Cluster 1. This finding would imply a lack of epigenetic repression in the treatment-resistant group. We found that there were significantly more overexpressed genes in the DEG groups of both Cluster 4 and 3 (the response .n = 215) indicated high rates of MAPK, BRAF, and NRAS mutation. Notably, the overexpression of CDKN2A was associated with worse disease outcome, and the low expression of CD274 (PDL1) was found in a subset of LGSOC patients. Conversely, other studies have demonstrated that high progesterone receptor expression, correlated with the presence of CTNNB1 mutations, is associated with a favorable prognosis [Finally, our findings are restricted to HGSOC, a distinct entity within the spectrum of ovarian tumors, and confirm that the heterogeneity of clusters within HGSOC are unique to this disease. For instance, multiple studies have examined relapse propensity in low-grade serous ovarian cancer (LGSOC) ,63. LGSOrognosis . While lFurther, the sheer number of features that were significantly correlated with recurrence in our Cox model supports the notion that a small group of genomic features are likely insufficient as a biomarker set for HGSOC prognostic classification. The clinical applicability of such models remains limited at this time; however, a validated signature including multiple genetic and epigenetic features, as we propose here, may become useful in the future to identify patients at high risk for early recurrence.The clinical utility of novel subtyping, even with the introduction of multi-omics integration and newer clustering methods, is still debated. Here, we present a novel workflow used to integrate methylation array data with NGS RNA-seq data. Using our semi-biased clustering approach, we were able to define gene signatures correlating with distinct phenotypes of chemo-response in subsets of HGSOC patients from TCGA and ICGC. We paired this approach with an MLP neural network learning model to ensure that each de novo cluster was predictable from the features selected for it. In so doing, we provide a feature selection, clustering, and deep learning approach which can be applied to any multi-omics dataset with a definable outcome measure . The inclusion of 27k array data presented challenging integration with RNA sequencing data. Firstly, the available probes are limited to the promoter region for this assay (distance to TSS ≤ 1500). Secondly, most genes are represented by only one probe—those with more probes had to be averaged by probe-wise methylation level. Finally, the normalization methods widely available for 450k and EPIC array are not available for 27k array data. Thus, a bespoke workflow had to be created for within-array normalization, probe-level quality filtration, and imputation.Here, we utilize a workflow of integrated ‘omics data, across HGSOC tumors profiled in the TCGA to identify novel subtypes of the disease. Using unsupervised clustering, we present four unique phenotypes which are predictable via MLP machine learning architecture, based upon features most correlated with disease recurrence. Importantly, we identified genetic markers of each subtype, as well as a strong immunosuppressive signature in one cluster enriched for stromal and immune cell types. Our findings underscore the importance for ‘omic integration in single-cancer clustering analysis and can be extended to other layers of data.


The adaptive immune system has the extraordinary ability to produce a broad range of immunoglobulins that can bind a wide variety of antigens. During adaptive immune responses, activated B cells duplicate and undergo somatic hypermutation in their B-cell receptor (BCR) genes, resulting in clonal families of diversified B cells that can be related back to a common ancestor. Advances in high-throughput sequencing technologies have enabled the high-throughput characterization of B-cell repertoires, however, the accurate identification of clonally related BCR sequences remains a major challenge. In this study, we compare three different clone identification methods on both simulated and experimental data, and investigate their impact on the characterization of B-cell diversity. We observe that different methods lead to different clonal definitions, which affects the quantification of clonal diversity in repertoire data. Our analyses show that direct comparisons between clonal clusterings and clonal diversity of different repertoires should be avoided if different clone identification methods were used to define the clones. Despite this variability, the diversity indices inferred from the repertoires’ clonal characterization across samples show similar patterns of variation regardless of the clonal identification method used. We find the Shannon entropy to be the most robust in terms of the variability of diversity rank across samples. Our analysis also suggests that the traditional germline gene alignment-based method for clonal identification remains the most accurate when the complete information about the sequence is known, but that alignment-free methods may be preferred for shorter sequencing read lengths. We make our implementation freely available as a Python library cdiversity. To ensujunctions  are assembled through the rearrangement of the V, D, and J gene segments, coupled with stochastic insertions and deletions of nucleotides at the gene boundaries, i.e. at the V and D, and the D and J gene unctions . The jununctions .Once a BCR has been formed, B cells are exposed to antigens in the secondary lymphoid organs and undergo affinity maturation in microanatomical structures known as Germinal Centers (GCs) . Throughsingletons, and use the term non-singletons to refer to B cells that have other clonally related B cells. Of course, the distinction between singletons and non-singletons depends not only on the random experimental cell sampling and repertoire sequencing depth, but also depends crucially on the user-defined threshold to define and separate clonally related and unrelated cells, as will be discussed in Section 2.2.Because of the stochastic nature underlying clonal selection coupled with the randomness associated with experimental BCR sampling and sequencing, it is common to observe a fraction of B cells without any clonally related B-cell in a repertoire. In this manuscript, we refer to this group of B cells as The rapid change and adaptation of B-cell repertoires in response to antigen stimulation driven by internal and external immune insults makes the sequencing and analysis of BCRs a valuable tool to characterize the immune status of an individual. Furthermore, as memory B cells produced during short-lived immune episodes can survive for a very long time, sometimes for the entire lifetime of a person, their analysis can also reveal information about the past and current pathogens encountered by an individual , 7. BeyoAdvances in Adaptive Immune Receptor Repertoire Sequencing (AIRR-Seq) technologies have considerably increased the amount of repertoire data that is available for analysis and improved our understanding of the dynamics of B-cell repertoires in both individuals and populations. Typical B-cell repertoire analyses start by grouping BCR sequences into clones of related B cells. The reconstruction of phylogenetic lineages of clonally related B cells provides information about the evolutionary paths that led to the development of functional antibodies and it is also useful to understand the progression of diseases such as chronic infections, autoimmune diseases or cancer. In most cases, however, immune repertoire data show significant differences in clonal composition across individuals in humans and mice , and eveA more promising approach to comparing immune repertoires across individuals focuses on the investigation of sequence-independent quantifiers such as clonal diversity indices. These quantifiers offer the possibility of correlating immune repertoire diversity to immunological status and, in doing so, readily allow for immune-repertoire-based comparisons across individuals. Nevertheless, there is still substantial ambiguity and a lack of quantitative understanding of the effectiveness of the diversity metrics to reliably capture status-specific information from immune repertoires. Realistic measures of diversity should reflect not only the relative abundances of clones, but also the main differences between them , 19. FurThe limitations associated with individual metrics have supported the practice of aggregating multiple indices for immunological classification. An example of such aggregation is the Hill-based diversity profile, which integrates a continuum of single diversity indices and can facilitate a global quantification of the immunological information contained in immune repertoires , 23. Nevempirical definition of clone poses several challenges, the first being the arbitrariness of the choice of BCR properties used to define a clone, and second, the subjective choice of metric and threshold used to separate clonally related and unrelated B cells. Importantly, the optimal way to group clones may differ depending on the dataset.In fact, another challenge in the analysis of B-cell repertoire data is the grouping of BCR into clones. Theoretically, a group of clonally related B cells represents a group of B cells descending from the same common ancestor (aka founder cell). In an experimental context, the founder cell has long disappeared, being replaced by better-adapted descendants. Therefore, in most cases reconstructing phylogenetic trees amounts to inferring trees where the founder cell is unknown. In practice, B cells with similar characteristics, such as the same gene segments and similar CDR3, are grouped together in the same clone. This In this context, a variety of methods has been proposed to (semi-)automatically identify clones from a set of BCR sequences. Some are based on probabilistic models that infer a hypothetical unmutated common ancestor to be used as tree root, which enables the inference of rooted trees interpreted as clones , 28. TheOur contribution: Each method for clonal identification depends on arbitrary choices of BCR sequence features, sequence-based distances and thresholds, and therefore, may lead to substantially different clonal groupings – besides displaying high variability in computational complexity and robustness. This variability might affect the estimation of clonal diversity which, as we discussed earlier, is crucial for the global analysis of B-cell repertoire data. In this work, we consider different definitions of clones and investigate the consistency and robustness of commonly used diversity indices at different sequencing depths and across different samples and technical replicates. By objectively comparing the performance and consistency of both clone definitions and diversity indices in various experimental contexts, we aim to investigate how the different empirical clone definitions affect diversity analyses and the biological conclusions extracted from them. Finally, to facilitate the use of the different clonal identification methods and diversity metrics, we make our implementation freely available as a python library (Section 4.4.3).22.1To characterize the influence of the different metric and clone definition choices on repertoire diversity analyses, we collected three different B-cell repertoire datasets from three different biological contexts:Simulated data. We collected artificial repertoires with known clonal relationships  of BCRs into clonal families. In this work, we focus on three clonal identification approaches previously described in the literature.Junction-based methods: In this method, B cells are assigned to the same clone if and only if their receptors share the same CDR3 sequence. This has the advantage of being computationally simple and eliminating any ambiguity when setting arbitrary clustering thresholds. On the other hand, since the junctions of clonally related B cells typically exhibit small sequence differences due to SHM, this approach tends to split branches of the same lineage into different clones, leading to an inflation of the diversity metrics. Sequencing errors further contribute towards artificially increasing the number of clones.Alignment-based methods: A more commonly used approach relies on the junction sequence and the V and J assignments  algorithm  to furthAlignment free methods: As germline gene alignments are error-prone, alignment-based methods might fail to identify clonal relatives accurately, especially when part of the nucleotides are missing in the sequences (as in the GC dataset described in section 2.3). To overcome this limitation, an alignment-free method that leverages NLP techniques has been recently introduced (tf-idf) as a weighting scheme that increases proportionally to the number of times a troduced . In briealignment-based method . To better quantify the similarity of the inferred clonal group across methods, we computed the adjusted mutual information (AMI)  between tf-idfImportantly, additional analysis revealed that these differences are not due to chance or subsampling, as the three methods were found to be giving similar clonal relationships after subsampling even across different sample sizes and shuffling . Intuitively, it is more difficult to rank confidently the samples when their diversity index values are closer to each other. Still, we found that the Chao estimator for Shannon entropy yields the best performance with a Spearman correlation Rather than a single diversity index, the B-cell repertoire landscape may also be characterized in terms of diversity profiles  Figure, the divwhere We computed the Spearman correlation of the Finally, we observe a substantial drop in the correlation in 2.5Another interesting question is the influence of sequencing depth (i.e. sample size) in clonal identification and diversity characterization. It is also worth investigating how effective traditional statistical estimators are, as the Chao estimators for richness and Shannon entropy to minimize the bias associated with sample size variability. To investigate these aspects, we sub-sampled repertoire sequences with sampling ratios from 1% to 100%, and evaluated the changes in clonal identification performance for different subsampling fractions on the simulated data. Interestingly, the clustering performances were not affected by the subsampling, with the AMI between the inferred clusters and the ground truth staying roughly constant for subsampling fractions higher than 2% (SI section 6).αNext, we evaluated the change in diversity indices for different samples sizes when different clonal identification methods are used. For that, we computed the fold change between the diversity index values with and without sub-sampling. The figures also indicate fold changes for the Chao estimators of richness and Shannon entropy . More importantly, we showed that the choice of the method can greatly impact the inferred clonal structure, especially for low-frequency and singleton clones (Section 2.4). This in turns might bias the analysis of immune repertoires in specific biological contexts.Our analysis suggests that the VJ & Junction method remains the most accurate to identify clonal groups and singletons, while the junction-only performed worst on the simulated data. However, the choice of the clonal identification method should be made taking into consideration the experimental design and constraints of each dataset. For instance, we observed that if the V gene assignment is ambiguous, the alignment-free method proposed by Lindenbaum et al.  was a beAnother important aspect we explored in this article is the impact of sequencing depth on the quantification of diversity. As clonal compositions across individual repertoires are highly variable, the analysis of repertoires by means of diversity indices offers the unique advantage of extracting biological information without directly comparing sequences across repertoires. We performed subsampling experiments and characterized the variability of different diversity metrics with sequencing depth and clonal identification methods. We analyzed the change in these metrics when different clonal identification methods were used and found that, while the absolute values were different, the main patterns of variation were conserved. In particular, the analysis of individual samples through diversity indices such as dominance, Shannon entropy, and richness led to high sample rank similarity. Shannon entropy was the most robust index (maximizing the Spearman sample rank correlation across methods) in the datasets and clonal identification methods we analyzed, which might be due to its weighting rare and abundant species similarly. Nevertheless, as different diversity indices provide different information, the best practice remains to combine several indices to gain a global view of diversity. In that respect, Hill’s diversity profiles already encompass information about many different indices, and therefore, already provides a more global understanding of B-cell repertoires than any given index. Finally, the use of Chao statistical estimators did not significantly lower the variability of the diversity estimation, both in terms of sub-sampling and clonal identification methods. As these estimators rely heavily on singletons and doubletons estimation, a potential cause behind these inefficiencies could be the unreliable detection of singletons during the process of clonal identification.Considering the widespread variability we observed across datasets, methods and metrics, we can expect that the characterization of B-cell repertoire diversity will also show great variability in other applications. For instance, repertoires derived from blood or tissues samples typically showcase a high B-cell diversity, which is mostly composed of non-expanded B-cell clones. However, we can expect that more targeted applications, such as for the study of the immune responses induced by a foreign antigen  or the dnegation sequences to estimate the specificity of the clone identification methods, i.e. random sequences extracted from different experimental studies, that are very unlikely to be clonally related to sequences in the considered study. However, negation only helps to set up the threshold between singletons and non-singletons. Quantifying the accuracy of the identified clones still remains a subjective endeavor. Nevertheless, we presented an overview of the different methods’ performances by evaluating the agreement between them (AMI). In particular, we investigated whether different methods agreed in the identification of singletons and found that the agreement was between 80% and 90% for the three datasets (SI section 1).In summary, we presented a quantitative comparison of different diversity metrics for the analysis of B-cell repertoires. We characterized the variability of these metrics when different clonal identification methods were used and for different sequencing depths. One of the main limitations of our analysis is the lack of ground truth in experimental datasets. To partially address this limitation, we included a synthetic dataset for which the ground truth is known by construction, which has enabled us to test the accuracy the different methods. However, addressing this limitation in an experimental context is much more difficult, and cannot be addressed in a fully satisfying manner yet. Rather, we leveraged tf-idf metric. This representation does not exploit potential semantic similarities between tf-idf metric computes frequencies across a corpus. Changing the dataset, i.e. the corpus, might result in changes in In future work, we aim to investigate whether additional improvements to the alignment-free method  can furtmune2vec , ESM . This assumption greatly reduces the computational workload.4.24.2.1The Levenshtein distance  is definwhere 4.2.2A and B, the cosine similarity is defined as:The cosine similarity is a measure of similarity between two vectors. Namely, given vectors encode them. In this paper, we use the term frequency-inverse document frequency (tf-idf) weighting scheme. In brief, we first compute a tf-idf representation is then computed as tf−idf (k) = tf (k) · idf (k). The logic behind this is to emphasize rare and hopefully meaningful terms while reducing the influence of common and uninformative terms.To apply this similarity measure to BCR sequences, we first need to 4.2.3The mutual information (MI) of two random variables is a measure of the mutual dependence between these two variables. More specifically, it quantifies the “amount of information” obtained about one random variable by observing the other random variable. The mutual information of two jointly discrete random variables where ectively .MI can also be used to compare clusters, for instance, by measuring the information shared by the two clustering partitions. In practice, this is done by counting the number of sequences that are shared by each pair of clusters, The adjusted mutual information (AMI) is a modified version of the MI to compare two random clusters.One limitation of the MI to compare partitions is that the baseline value of MI becomes larger when the number of clusters in both partitions increases. To address this limitation, the adjusted mutual information (AMI) can be used instead . Defininwhere 4.3We implemented three clonal identification methods in this article.Baseline: B cells were assigned to the same clone if and only if their receptors shared exactly the same CDR3 sequence.VJ & Junction: We first grouped B cells together if they had the same V and J gene. For each obtained group, we then computed the pairwise normalized Levenshtein distance between each junction in that group, and applied the Hierarchical Agglomerative Clustering (HAC) algorithm  weighting scheme (see section 4.2.2). Following on from previous work  represents the homogeneity of abundances in a sample or a community  be able to include both the Richness (4.4.3Complete knowledge about a system is often not available. Partial knowledge often results in the underestimation of a sample’s diversity, as some species might not have been observed. Specialized statistical tools have been developed to estimate the true richness stimator , 25.where In addition to the Chao1 estimator for species richness, a similar approach can be used to estimate the Shannon entropy with incomplete sample information . DefininEstimators can also be computed for higher orders of diversity, for instance, by using the general Horvitz-Thompson estimator  or otherThe original contributions presented in the study are included in the article/SL wrote the code and analyzed the data under the supervision of AP and MR. SL and AP wrote the manuscript. All authors contributed to the article and approved the submitted version.


Cancer subtype classification is helpful for personalized cancer treatment. Although, some approaches have been developed to classifying caner subtype based on high dimensional gene expression data, it is difficult to obtain satisfactory classification results. Meanwhile, some cancers have been well studied and classified to some subtypes, which are adopt by most researchers. Hence, this priori knowledge is significant for further identifying new meaningful subtypes.https://github.com/lffyd/ForestSubtype.In this paper, we present a combined parallel random forest and autoencoder approach for cancer subtype identification based on high dimensional gene expression data, ForestSubtype. ForestSubtype first adopts the parallel RF and the priori knowledge of cancer subtype to train a module and extract significant candidate features. Second, ForestSubtype uses a random forest as the base module and ten parallel random forests to compute each feature weight and rank them separately. Then, the intersection of the features with the larger weights output by the ten parallel random forests is taken as our subsequent candidate features. Third, ForestSubtype uses an autoencoder to condenses the selected features into a two-dimensional data. Fourth, ForestSubtype utilizes k-means++ to obtain new cancer subtype identification results. In this paper, the breast cancer gene expression data obtained from The Cancer Genome Atlas are used for training and validation, and an independent breast cancer dataset from the Molecular Taxonomy of Breast Cancer International Consortium is used for testing. Additionally, we use two other cancer datasets for validating the generalizability of ForestSubtype. ForestSubtype outperforms the other two methods in terms of the distribution of clusters, internal and external metric results. The open-source code is available at Our work shows that the combination of high-dimensional gene expression data and parallel random forests and autoencoder, guided by a priori knowledge, can identify new subtypes more effectively than existing methods of cancer subtype classification.The online version contains supplementary material available at 10.1186/s12859-023-05412-y. Cancer is a disease closely associated with genetic predisposition, and primarily caused by an imbalance between proliferation and growth-inhibiting apoptosis genes, resulting in abnormal cell proliferation without death .Modern medical research has established that cancer is not a single disease, but rather a collection of hundreds of different diseases. Consequently, cancer can be divided into heterozygous and homozygous cancers. Homozygous cancers can be staged not only according to the stage of cancer development but also according to certain characteristics of the genes in the cancer cells, which allow cancer to be classified into different subtypes . UnderstTraditional cancer subtype classification may have limitations in implementing precise treatments for patients. Cancers with similar clinical and pathological manifestations may exhibit different behaviors, and identifying targeted and precise treatments based on these different behaviors is the key to treating cancer , 7. To tHigh-dimensional gene expression data can be utilized to analyze changes in gene expression, correlations between genes, and gene activity, among other things. Some cancers have been studied to mark subtype categories, which have been used in many areas of research , 9. ConsMethods based on supervised learning. Guo et al.  proposedMethods based on unsupervised learning. Classification of unlabelled data is more in line with the scope of the clustering problem. Currently, some cancer subtype classification methods use unsupervised learning methods and high-dimensional gene expression data for cancer subtype classification, but the problem is that cancer subtype with no clinical value will be identified when there is no a priori knowledge to guide them. Witten et al.  proposedMethods based on a joint supervised learning and priori knowledge. DeepType  is the fCurrently, various methods for cancer subtype have been presented, which can be categorized into three categories.Although a great deal of research work has been done on the identification of cancer subtype, a number of problems remain in this area:First, the problem of the “curse of dimensionality” , which iSecond, existing cancer subtype classification methods do not identify new clinically valuable cancer subtype guided by a priori knowledge. Typically, conventional cancer subtype identification methods tend to assign samples to a known subtype or cluster cancer subtype directly without the use of a priori knowledge guidance.In the face of these two problems, traditional methods of cancer subtype classification tend to select fewer features, and therefore the resulting models are usually prone to bias. How to solve the above problems more effectively will be the focus of this paper.In this paper, we present a combined parallel random forest and autoencoder approach for cancer subtype identification based on high dimensional gene expression data, called ForestSubtype. Random forest (RF) has advantages in dealing with data sets with small sample sizes and high-dimensional , 23. MorForestSubtype adopts high dimensional gene expression data and the prior knowledge about cancer subtype as input. ForestSubtype consists of three modules, which are shown in Fig. i-th sample in j-th subtype in i-th sample belongs to the j-th subtype, Let ForestSubtype aims to discover new subtypes of cancer and guide the subsequent personalized treatment process. For high-dimensional gene expression data, it is important to select significant features and reduce dimensionality. Furthermore, we should retain the biologically and meaningful features associating with cancer subtypes during the feature extraction step.Random forest is an ensemble of multiple decision trees, which is an ensemble model. To extract feature results for accuracy, stability, and lower dimensionality, ForestSubtype uses ten random forests for parallel processing. Two kinds of shuffle processing are performed for sample data set, which can guarantee each random forest can output different features. The first shuffle is to disrupt the order of samples, and the second shuffle is a random division of the sample dataset into training set and testing set based on Pareto’s law.In this module, an RF is a homogeneous integration of all utilized classification and regression tree (CART). In the CART algorithm, its goal is to choose a feature to split samples, which can minimize the cost function (Gini index).i-th class, Given a sample set mentclass2pt{minim S into two parts.a, where a is an value of Suppose sample set entclass1pt{minimaFor one sample set, constructing a node including these samples as current node.Calculate the Gini index for each feature and its values of the current node see Eq. .a with the smallest Gini index is selected as the optimal feature, and the corresponding value a is used as the optimal segmentation point.The feature Split the sample set of the current node into two sample subsets. And, the feature Then the left and right nodes are processed as current node respectively, and the above steps are repeated.For each feature, this process is performed recursively until a tree is built. The steps of the CART algorithm are as follow:X to form one hundred sample subsets, and uses the above CART algorithm to construct one hundred decision trees. These one hundred decision trees together form a random forest. Based on each decision tree, the random forest uses voting strategy to obtain the final classification results.A random forest randomly collects multiple samples from E.Next, we calculate the feature importance of a single random forest using Eqs.  and 4)..4). Featβ (0.001 in default). Then, we can obtain ten feature sets from ten parallel random forests, and next we take the intersection of them .f(x′) is the predicted value of x′. Before performing cluster identification, we use an AE  module tFinally, we output the core layer results i-th cluster, i-th cluster, i-th cluster, and ForestSubtype uses the k-means++  see Eq. and 8)))8)) methThis section contains six parts: (i) dataset preprocessing; we describe how the input dataset is obtained and processed; (ii) classification method selection; we give a performance comparison between random forest and other classification methods; (iii) experimental parameter settings; we illustrate the parameters in our experiments; (iv) related feature gene results; we discuss the important genes associated with cancer found by ForestSubtype; (v) visualizing subtyping results; we visualize the cancer subtyping results to examine their cluster subtype distributions and the distributions of the prior knowledge labels in the clusters; (vi) performance comparison; first, we validate the training performance between ForestSubtype and the other two competing methods; second, we validate the performance of ForestSubtype and the other competing methods on an independent breast cancer dataset; third, we validate the performance of ForestSubtype on two other cancer datasets.Gene expression data concerning breast cancer are downloaded from the Sangerbox 3.0 platform. The original dataset includes 1211 samples and 56,461 genes. Then, we classify these samples with the genefu package in R. All samples are classified into 5 categories. The genefu package is a PAM50 classification kit. Although this classification process is simple and cannot obtain more sophisticated subtypes, it supplies prior knowledge that can guide the subsequent subtyping step. Note that if one gene is expressed in fewer than 500 samples, it is removed. Finally, we obtain a gene expression dataset containing 1211 samples, each sample includes 23,902 genes, and each sample is labeled. The same steps were followed for the other three datasets, the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) , ACC adrThe feature extraction module is the core of the model. Therefore, we compare the performance of parallel RFs with other five classification methods: k-nearest neighbors (KNN), a support vector machine (SVM), logistic regression, a multilayer perceptron (MLP) and the ensemble method.For RFs, there are three important parameters: n_estimators, max_depth, max_feature. To avoid costly 3D parameter grid searches, and avoid overfitting, we choose a compromise value of 100 as the actual value of the parameter n_estimators. To balance the decision tree generation time, max_feature is set to be the square root of the total number of features. For max_depth, we perform a grid search between 0 and 20 and evaluate the results with the precision rate metric. For KNN , we condTable The RF is a parallel integrated model with three main parameters, where n_estimators is 100, max_depth is 14 and max_feature is taken as the square root of the original total number of features. For the feature optimization module, we use the AE to condense the features into a two-dimensional feature. The input and output layers contain 201 parameters, the encoder hidden layer contains  parameters, the core layer possesses 2 parameters, the decoder hidden layer includes  parameters, the number of model epochs is 10,000, and the batch size is 128. For the classification module, we use the k-means++ method to find subtypes, with an initialization value of 10 runs, a maximum number of iterations of 300 and a convergence condition of 0.0001.When using k-means++ to cluster samples, k is an important parameter for clustering result. For obtaining optimal clustering result, we validate different values of k for k-means++. Specifically, we take the value of k in Deeptype as the lower limit and record the silhouette width We identified the genes in F that contributed to our identification efforts. From F, we selected 13 representative genes for discussion, and the gene information are obtained from NCBI  and Google Scholar.PCAT29: PCAT29 regulates the proliferation, migration and invasion of breast cancer cells and may point to a novel therapeutic target in triple-negative breast cancer . ESR1: TWe apply ForestSubtype to the public breast cancer dataset and detect 12 subtypes. Visualizing the high-dimensional clustering subtype results allows us to intuitively feel the effect of the model and the distribution of data for each cluster. To visualize the high-dimensional cluster subtype results, we use the t-SNE method  to visuaFor validating the performance of ForestSubtype, we compared it with other two methods DeepType  and SparFirstly, we train and test the three methods on the public breast cancer dataset to compare their performance.i-th cluster, j-th category, i-th sample and the other samples in its same cluster, i-th sample and the nearest sample in the different clusters, i-th cluster to its cluster center, j-th cluster to its cluster center, i-th and j-th clusters, We divided the public breast cancer dataset into two subsets of 80% and 20% according to Pareto’s law. We used the former for training ForestSubtype and the other two competing methods Deeptype and SparesK, and used the latter for testing these three methods. To compare the advantages and disadvantages of the three models, we first visualize the subtype results of the three methods using the t-SNE method, as shown in Fig. n in Eq. .11\documIn summary, the proposed method has cancer subtyping results with higher quality than those of the other two methods.Next, we further verify the performance of the three methods on an independent breast cancer dataset.We use the public breast cancer dataset preprocessed in “In summary, the proposed method generalizes well to the test set.Finally, we validate the performance of the proposed method on other types of cancer datasets.We select ACC adrenocortical carcinoma with a small sample size and BLCA uroepithelial carcinoma of the bladder with a large sample size from TCGA database to test the ability of ForestSubtype. After performing the steps described in “This paper proposes a cancer subtyping method, named ForestSubtype, based on a parallel RF and autoencoder, which uses the prior knowledge and high-dimensional gene expression data to obtain new subtypes. First, some significant candidate features are extracted by ForestSubtype based on the priori knowledge of cancer subtype. Second, the features with large weights are selected. Third, ForestSubtype uses an autoencoder (AE) to condenses the selected features into a two-dimensional data. Fourth, ForestSubtype utilizes k-means++ to obtain the final clustering results. Our experiments demonstrate that ForestSubtype have a better performance than other two methods. In this paper, we only focus on the gene expression data, but some other types of data (DNA methylation dataset) may play a important role in the mechanism of cancer subtyping . In the In this paper, we propose a parallel RF and autoencoder based cancer subtype identification method, named ForestSubtype, which uses prior knowledge and high-dimensional gene expression data to obtain new subtypes. Our work shows that the combination of high-dimensional gene expression data and parallel random forests and autoencoder, guided by a priori knowledge, can identify new subtypes more effectively than existing methods of cancer subtype classification. This paper focuses on only one dimension, gene expression. In the future, we will combine the gene expression and DNA methylation data to study cancer subtype.Additional file 1. Supplementary materials of ForestSubtype.


Accurate prediction of the survival of bracer cancer will benefit appropriate medical decision-making and patient care. In this study, the breast cancer RNA sequencing (RNA-Seq) data in The Cancer Genome Atlas (TCGA) was first normalized to transcripts per million (TPM). After dimension raising, the differential gene expression data were used for different deep learning architectures testing. Among them, GoogLeNet was selected to build the survival prediction model, SaBrcada. Considering the influence of age on prognosis, it was found that adding stratified random sampling by the patient’s age of 61 could improve the accuracy of SaBrcada up to 0.798. In addition, a website tool of the same name, SaBrcada, was established to provide five kinds of predicted survival periods for clinicians to refer to.(1) Background: Breast cancer is the second leading cause of cancer death among women. The accurate prediction of survival intervals will help physicians make informed decisions about treatment strategies or the use of palliative care. (2) Methods: Gene expression is predictive and correlates to patient prognosis. To establish a reliable prediction tool, we collected a total of 1187 RNA-seq data points from breast cancer patients (median age 58 years) in Fragments Per Kilobase Million (FPKM) format from the TCGA database. Among them, we selected 144 patients with date of death information to establish the SaBrcada-AD dataset. We first normalized the SaBrcada-AD dataset to TPM to build the survival prediction model SaBrcada. After normalization and dimension raising, we used the differential gene expression data to test eight different deep learning architectures. Considering the effect of age on prognosis, we also performed a stratified random sampling test on all ages between the lower and upper quartiles of patient age, 48 and 69 years; (3) Results: Stratifying by age 61, the performance of SaBrcada built by GoogLeNet was improved to a highest accuracy of 0.798. We also built a free website tool to provide five predicted survival periods: within six months, six months to one year, one to three years, three to five years, or over five years, for clinician reference. (4) Conclusions: We built the prediction model, SaBrcada, and the website tool of the same name for breast cancer survival analysis. Through these models and tools, clinicians will be provided with survival interval information as a basis for formulating precision medicine. Breast cancer is the most common cancer in women . In 2020Medical treatments should be decided based on the patient’s goals and expected survival time, the potential benefits and risks of treatment, and the effects on quality of life. Therefore, a comprehensive consideration of these factors determines treatment choices . To predTo analyze gene expression, protein-coding RNAs (mRNAs) and noncoding RNAs, including long noncoding RNAs (lncRNAs), snRNAs, rRNAs, tRNAs, and microRNAs (miRNAs), were considered candidates ,21,22,23The TCGA-BRCA database, most commonly used for bioinformatics prediction of breast cancer survival, records common event dates as the last follow-up date rather than the date of patient death. This may be the key factor affecting the accuracy of previous studies ,29. We tThe SaBrcada modeling process is shown in In this study, we used TCGA version 27 data. RNA-seq data from breast cancer patients were collected in FPKM format. It was noted that the original counts (reads) may be different from the true values due to the sampling environment, experimental methods, or length of each RNA . AlthougBefore preprocessing, we downloaded a total of 1187 RNA-seq data to build the SaBrcada-BPP dataset. After excluding 96 samples with missing clinical data, we obtained 1091 data records containing clinical data. We further excluded the samples that recorded the same survival time and obtained a SaBrcada-APP dataset with 807 breast cancer cases after preprocessing. To ensure that all the samples included actual survival times, we selected 144 RNA-seq data points with actual date of death information to establish the SaBrcada-AD dataset . FurtherTo ensure that there was enough data in the two datasets after stratification, quantiles Considering the reliability and comparability between different patients, we first normalized the 60,483 gene expression data from FPKM into TPM, and consistently arranged the expression data of genes in the order provided by TCGA-BRCA RNA-Seq for comparison of the differential gene expression between patients. According to our previous study, the difference between genes calculated using subtraction improved the predictive model of survival analysis, especially its sensitivity, compared with using traditional fold change . It mighTaking five patients as an example, the data were arranged by the length of survival time from long to short, as N1 to N5, as shown in We obtained 60,483 gene expression data from TCGA-BRCA; this RNA-seq data produces a lot of features that are difficult to directly process by machine learning. CNNs designed to process data with a lot of features are therefore considered. However, CNN is more suitable for processing two-dimensional data with spatial structure. Therefore, the survival analysis data were arranged into a 246 × 246 matrix by dimension, rising from one dimension to two dimensions. Here, the 246 × 246 matrix is the smallest square matrix that can contain 60,483 differential gene expressions. All 60,483 differential gene expression levels were filled in order from left to right and top to bottom and then converted into grayscale pixel values ranging from 0 to 255. Zero represented the maximum negative difference in gene expression, and 255 represented the maximum positive difference. After filling the remaining 33 positions with 0, the survival analysis matrix was generated and finally saved in PNG file format to serve as the survival analysis images. The process is shown in We used CNN, one of the most common deep learning network architectures, implemented in PyTorch 1.9 to build a neural network framework and combined it with a Quadro GV100 32G graphics card (GPU) for model construction. The convolutional and pooling layers in the neural network architecture improve the recognition of pattern identity and the relationship between adjacent data and can learn features independently. Based on these characteristics, we used a CNN to learn features from survival analysis images. The deep learning frameworks, containing 3 inceptions and 22 convolutional layers, were used to learn different features and make comprehensive judgments on all features. For hyperparameter selection, we tested three different sets of hyperparameters by using Adam (the optimizer), Cross Entropy (the loss function), and a dropout value of 0.4.In this study, we tested eight different deep learning architectures to build a survival prediction model. In brief, GoogLeNet, introduced by Google in 2015 , employsTP, or true positive, is the number of positive predictions; TN, or true negative, is the number of negative predictions, and P and N are the numbers of positive and negative predictions, respectively. The accuracy ranges between 0 and 1.0. An accuracy of 0.5 represents a random prediction, and a value of 1.0 indicates that the prediction was completely consistent with the actual value.Accuracy is a common method to evaluate the prediction model . AccuracAs shown in Based on various features, different learning methods were selected for model construction. To detect differences between the e tested . Among tAccording to the results shown in According to the clinical data of breast cancer patients, the survival time of young patients is shorter, and the survival interval of older patients is generally longer , which i testing . The resIn order to provide potential survival intervals via the SaBrcada web tool, suitable patients need to be identified as reference points for comparison based on their accuracy. After testing the accuracy of SaBrcada’s prediction for all patients with different ages in the SaBrcada-AD database, we found that the accuracy was higher than 0.85 for patient ages of 70, 89, and 90 years. Among them, the best performance was an accuracy of 0.92 for the age of 90 years. Patient ages of 63, 84, and 88 years also obtained accuracy values higher than 0.7, with significant differences .http://ncblab.nchu.edu.tw/SaBrcada (accessed on 19 July 2023). It provides a tool for generating survival analysis images and an online analysis of survival time. The outcome of the analysis is the patient’s predicted survival time, which can be classified as less than six months, six months to one year, one to three years, three to five years, or more than five years. The website is freely available at http://ncblab.nchu.edu.tw/SaBrcada (accessed on 19 July 2023). SaBrcada provides preprocessing tools to transfer TPM-formatted RNA-Seq data for survival analysis image generation. After analyzing the survival analysis images uploaded by the user, SaBrcada provides the analysis information for the patient’s survival period. SaBrcada obtains two modules: the first is survival analysis image creation, and the second is survival period analysis. For survival analysis image creation, the user first downloads the preprocessing program packaged by pyinstaller and then inputs the user’s TPM file with.TXT into the corresponding file according to the age of the patient. The tool compares the input data from the user with that from four default reference patients to generate four survival analysis data. The survival analysis data are then raised to a two-dimensional matrix, and four survival analysis images are generated using the png package provided by Python. For survival period analysis, the user needs to upload the four survival analysis images generated by the preprocessing for survival analysis using the established SaBrcada model and then obtain the results. The analysis results will show the predicted patient survival period, with possible values of less than six months, six months to one year, one year to three years, three to five years, or more than five years, as a reference for clinicians to implement treatment strategies.The purpose of developing the SaBrcada tool is to provide users with guidelines for the analysis of the survival time of breast cancer patients. Combining survival analysis and clinical experience may help clinicians choose the most suitable treatment strategies to improve the quality of life of patients. Based on the results shown in In this study, SaBrcada, a CNN-based breast cancer survival analysis prediction model, was established by using RNA-seq data. In brief, the SaBrcada-AD dataset was selected from TCGA-BRCA based on the completeness of RNA-seq and clinical data. The RNA-seq data in SaBrcada-AD were then converted into a TPM data type to represent the relative transcript levels and used to generate the survival analysis image dataset SaBrcada-I after stratified random sampling by age of 61, which is used to build a survival prediction model based on CNN learning. By using the SaBrcada-I dataset and GoogLeNet, SaBrcada achieved the best performance of all examined frameworks with an accuracy of 0.798.In the past, breast cancer survival analysis models typically used deep learning to extract the nonlinear characteristics of RNA-seq data and then predicted linear Cox regression survival times ,17. ReceThe advantage of Sabraca is that it considers three key points that have been overlooked by previous studies on prediction model building. The first is the accuracy of the data collection. Usually, all TCGA data are used directly ,29,30. TIn the past, doctors analyzed the prognosis of patients by using their clinical experience, inevitably causing inconsistencies in accuracy due to individual differences. In the postgenomic era, precision medicine has become a trend. In this study, we combined gene expression and clinical data to establish a reliable survival analysis model, SaBrcada. To enrich the biological information provided, we will integrate characteristics, genetic variants , and coehttp://ncblab.nchu.edu.tw/SaBrcada (accessed on 19 July 2023). We downloaded the gene expression and clinical data from TCGA-BRCA. After normalization of the RNA-seq data into TPM format and dimension raising, survival analysis images were generated by differential gene expression and then subjected to deep learning architecture testing. According to their performance, GoogLeNet was selected to build the survival prediction model, SaBrcada. We also evaluated key factors affecting the performance of the survival prediction model. After filtering out the incomplete data, the performance of SaBrcada-AD-M improved to an accuracy of 0.6. Coupled with the stratified random sampling by patients’ age of 61, the performance of SaBrcada achieved an accuracy of 0.798. These results suggest that the accuracy of date of death recording and stratified random sampling by the medium age of patients will improve the performance of the survival prediction model. We hope this highly reliable survival analysis model and website tool provide information on survival interval periods for clinicians’ reference in precision medicine.In this study, we have established a breast cancer survival analysis prediction model, SaBrcada, and its website,