Gene expression data provide molecular insights into the functional impact of genetic variation, for example, through expression quantitative trait loci (eQTLs). With an improving understanding of the association between genotypes and gene expression comes a greater concern that gene expression profiles could be matched to genotype profiles of the same individuals in another data set, known as a linking attack. Prior works show such a risk could analyze only a fraction of eQTLs that is independent owing to restrictive model assumptions, leaving the full extent of this risk incompletely understood. To address this challenge, we introduce the discriminative sequence model (DSM), a novel probabilistic framework for predicting a sequence of genotypes based on gene expression data. By modeling the joint distribution over all known eQTLs in a genomic region, DSM improves the power of linking attacks with necessary calibration for linkage disequilibrium and redundant predictive signals. We show greater linking accuracy of DSM compared with existing approaches across a range of attack scenarios and data sets including up to 22,288 individuals, suggesting that DSM helps uncover a substantial additional risk overlooked by previous studies. Our work provides a unified framework for assessing the privacy risks of sharing diverse omics data sets beyond transcriptomics. The growing availability of large-scale genomic data repositories has led to increasing concerns for the privacy of the individuals from whom the data were collected . Althoughttps://www.ncbi.nlm.nih.gov/geo/) (expression quantitative trait loci (eQTLs)—that is, genetic variants correlated with expression levels of a gene (referred to as eGenes)—could be used to extract genotypic information from gene expression profiles, the full extent of such leakage largely remains unknown. A key concern is that a malicious actor may exploit this leakage to carry out a linking attack, in which one links an individual's gene expression profile to their genotype profile in another data set (or vice versa), potentially reidentifying the individual's data and subsequently associating it with a sensitive attribute such as disease status.Transcriptomic data, such as gene expression measurements broadly shared in databases such as the NCBI Gene Expression Omnibus   and Arraov/geo/) , are a pov/geo/)  have shoLinking attacks require some criterion, which we call a match score function, to score and rank possible candidate matches between the gene expression and genotype data sets. The core challenge in accurately assessing the risk of a linking attack is therefore in devising the best possible match score function that could be leveraged by an attacker. Existing proposals for this function suffer from the key limitation that they account for only a small subset of (nearly) independent eQTLs as required by the simplified probabilistic models used in those approaches . As we wdiscriminative sequence model (DSM), which jointly models all known eQTLs in a genomic region to enable sequence-level inference of genotypes given a gene expression profile. DSM provides more accurate probability estimates for each candidate genotype profile originating from the same individual as the expression profile by calibrating for both correlation among genetic variants and redundant eQTL association signals. Using these probabilities as match scores, DSM leads to substantially greater success in simulated linking attacks than existing strategies in a wide range of scenarios, including (1) linking an expression profile against a large-scale candidate genotype set  representing a population whose ancestry background differs from the training set, (2) linking when the membership of the target individual in the genotype set is unknown, and (3) linking in the reverse direction, namely, from a genotype profile to a panel of candidate expression profiles. Our work provides an essential tool for gaining a deeper understanding of privacy risks of transcriptomic data and their linkage with protected genetic information.Here, we introduce the We developed DSM based on the framework of conditional random fields  to modelgenerative distribution over gene expression given genotypes , instead allowing us to work with discrete genotype distributions. Second, DSM learns to calibrate the predictive probabilities during training to adjust for linkage disequilibrium among nearby genetic variants as well as redundant predictive signals across different eQTLs and eGenes. This feature allows the model to leverage the full range of information captured by eQTLs without being limited to a filtered set of independent eQTLs. Third, DSM introduces eQTL probabilistic factors that are generalized to include any number of eGenes for each eQTL rather than separately considering each eQTL–eGene pair. When considering genes with correlated expression levels, combining information across a set of genes can enhance the quality of the predictive signal. Lastly, we developed an efficient haplotype-based approximate inference scheme for DSM to enable the use of the sufficiently large reference panels (which are used to capture genotype correlations) required for accurate prediction.DSM incorporates a number of novel strategies for joint modeling of genotypes and gene expression (Methods). First, instead of defining a enotypes , we takeTo evaluate the DSM, we compared the success of linking attacks based on DSM against that of two published Bayesian linking strategies, which we refer to as Gaussian naive Bayes (GNB)  and extrWe then used the trained models to attempt a linking attack on a separate, nonoverlapping data set, including both genotype and gene expression profiles, shuffled to obscure the links between the two data types. Our primary evaluation setting emulates an attack scenario in which the attacker holds a gene expression profile of interest and tries to identify a genotype profile from the same individual from a pool of candidate genotype profiles in another data set. To this end, we independently assigned the best-matching genotype profile to each gene expression profile using each method and measured the overall accuracy of the attack by the number of individuals for whom we could correctly link their gene expression profiles to their genotypes. As we show below, we considered a range of attack scenarios and different choices of the candidate set to assess the robustness of our method. We evaluated the methods on Chromosomes 19 to 22.Note that, after observing EBL's poor performance in our experimental setting , we instead analyzed our extension of EBL, where EBL collapses to GNB for genes with nonextreme expression values. We observed that this hybrid model outperforms the original EBL model, which relies only on predicted genotypes based on extreme gene expression values see . HyperpaWe first considered the setting in which the training and test data sets are both sampled from the same data set cohort. Such a scenario may occur when an attacker obtains access to training data consisting of individuals from the same population as the target individuals. For this analysis, we used a subset of gene expression and genotype profile pairs of 450 individuals in the GTEx muscle tissue data set  for traiDSM was able to link all 138 test individuals using all four chromosomes and 135 using Chromosome 19 alone . AlthougWe next assessed our method in the setting in which there is a mismatch between the populations of the training data set and the target data set. Here, we used all 588 pairs of gene expression and genotype profiles available in GTEx for training. For the test data set, we used gene expression and genotype profiles of 292 individuals in the Finland–US Investigation of NIDDM Genetics (FUSION) data set . The genUsing DSM, we were able to link 289 of 292 individuals from Chromosome 19 alone . CompareTo evaluate the ability of each method to distinguish the true match from a larger set of candidates, we next added 292 additional genotype profiles (584 phased haplotypes) from the GOT2D consortium data , of whicOur results show that DSM is still able to link all 292 individuals combining the four chromosomes ; Fig. 2.gap in the match score between the true match and the remaining mismatching pairs. Intuitively, if the gap is large, then we should expect the model to remain accurate for longer as additional samples are added to the candidate set, as it would be less likely that random samples of other individuals’ genotype profiles will result in match scores as extreme as the true match.To gain a deeper insight into DSM's robust performance on larger sets of candidate genotype profiles, we aimed to assess the P-value representing the strength of the identifying signal of each matching xi)( and ei) and 239 (81.8%) individuals compared with GNB and EBL, respectively, suggesting greater separation of the true match  from HRC that did not overlap with FUSION, GTEx, or the DSM reference panel and additionally included this cohort as part of the candidate set together with the FUSION individuals. We observed that DSM displays remarkable robustness to such large data sets, linking 260 of 292 FUSION individuals (89.0%) compared with just 129 (44.1%) and 147 (50.3%) by GNB and EBL, respectively, for Chromosome 20 ; Fig. 4BP-values, calculated on a subsampled candidate set  using our model of null distribution  provides further evidence that the enhanced identifying signals obtained by DSM  truly reflect more robust linking performance in general.Furthermore, testing the linking attack on a much larger candidate set allowed us to validate our model-based ribution , by compdate set C. IncreaWe thus far have evaluated the accuracy of linking attacks when the genotype profile of the same individual as the query gene expression profile is included in the target data set. In an attack scenario in which the membership of the matching individual in the target data set is unknown to the attacker, the attacker must make an additional decision about whether to draw a link between an expression profile and the top-matching genotype profile. For instance, this can be achieved by imposing a threshold on the match scores such that only the high-confidence links above the threshold are called. To assess the performance of DSM in this setting, we performed a holdout experiment based on the expanded FUSION data set , in which the matching genotypes of half of the query expression profiles (146 out of 292) were excluded from the target set before the linking procedure. For each method, we evaluated the linking results across a range of match score thresholds with respect to the standard performance metrics for binary classification, such as false-positive rate (FPR), precision, and recall, which we adapted for the linking problem see .Our results show that linking based on DSM provides a significantly better tradeoff between identifying true matches and minimizing false positives compared with EBL and GNB . For exareverse linking to distinguish it from our main attack scenario. In this setting, the attacker could directly leverage an existing method for predicting gene expression from genotypes to compare with the candidate expression profiles. To this end, we compared our method—using the same scores from DSM as before but performing linking in reverse—against linking based on MetaXcan  poses the linking attack as a sequence-level probabilistic modeling problem, one in which the attacker jointly predicts the entire genotype sequence instead of independently predicting each eQTL. Our results show that DSM reveals greater linking attack risk than previous methods over a range of evaluation settings, including cross–data set prediction and linking attacks involving a massive candidate set. We also illustrated how the P-values calculated based on the match score distributions can be a proxy for the strength of identifying signals captured by the model, representing a promising new approach for quantifying privacy risks.We have shown that existing models for transcriptomic linking attacks overlook a substantial number of predictive signals captured by eQTLs. Our Our framework unifies QTL privacy analyses, because it allows joint prediction of genotypes from any source. It would be interesting to explore incorporating other sources of phenotypic data that could leak genotype information into the DSM, including protein abundance (pQTLs) , methylaThere are a few limitations of our work. Training the DSM requires substantial memory (75 GB) and time (∼6 h) per window. These requirements depend on the size of the eQTL window and reference panel size see . In contAlthough our work reveals that gene expression data contain more identifying information than previously known, we acknowledge that further investigation is needed to ascertain the real-world implications of our findings in the context of existing transcriptomic databases. For instance, when the target genotype set does not include the individual associated with the gene expression profile, the risk of a successful linkage is reduced as only the matches with especially high match scores can be called with sufficiently low false detection error, as we illustrated in our experiments . Furthermore, there are other key factors that modulate the success of potential linking attacks, including ancestry, assay platform for gene expression measurements, and the tissue of origin of the samples. When the target set is different than the training set in these aspects, eQTL-based linking may have reduced accuracy but would still remain feasible . Thus, aBeyond standard access control mechanisms, other tools for consideration to enhance data protection include data sanitization , differeWe consider the setting in which a malicious actor (attacker) wishes to link an individual's gene expression profile to his or her genotype profile in a different data set . Both gehttps://www.ncbi.nlm.nih.gov/gap/])  a publicly available list of known eQTL associations  , (2) a tv/gap/])  and are For the purpose of comparing the effectiveness of different match scores, we primarily consider the setting in which the attacker knows that a given query gene expression profile matches one of the genotype profiles in the target data set. In practice, the attacker may not know the membership of the individual in the target data set and thus might need to make an additional decision about whether the best possible match found truly represents the same individual . In the section “Additional linking attack scenarios,” we also address the performance of our method in this setting, as well as for the closely related problem of matching a genotype profile across a set of candidate gene expression profiles .xi), , , }V, where V is the number of variants considered. Any unphased genotype data set can be preprocessed using standard phasing algorithms to obtain a phased data set .We first provide a formal definition of the transcriptomic linking problem. The attacker has access to two data sets et e.g., . Each e(M(xi). This function must return a high match score if xi)( and ej) refers only to the eQTL subset of the genotype profile. Also, let Q(s) ⊂ [G] denote the set of genes associated with eQTL s, and eQs)( denote the corresponding subset of e. independence assumption across eQTLs to express p(xi)(|ej) as a product of probabilities for individual eQTLs:p(eQ(s)|xs) (with a singleton Q(s) in the setting of s and standard deviation σs, whereas the prior distribution From here onward, Q(s)), for xj and eQ(s) are strongly correlated, for suitable thresholds for extremity and correlation. The match score is then computed by comparing the predicted genotypes and the given candidate genotype profile.Given the noisy nature of gene expression measurements, the strongest predictive signals often lie in the extreme values of gene expression levels, for which a Gaussian model may not lead to reliable probability estimates. Both GNB and EBL approaches treat each SNP independently. To ensure that this assumption is justifiable, the set of eQTLs used by previous models is pruned to a smaller set of mutually independent eQTLs. However, this approach omits all other eQTLs, which collectively provide far richer information about the genotypes than a pruned set would provide, as we show in our work. Simply including all eQTLs in the prediction, disregarding the correlations and redundant predictive signals, lead to poor predictive performance owing to miscalibrated probabilities see , which nOther works have explored reidentification attacks based on sparse and noisy genotypes , where a HMM is used to infer matches while considering the haplotype structure . These wHere, we summarize the modeling techniques we newly leverage to improve upon the existing models of genotype prediction based on gene expression.M in terms of p(x|e) to obtain a ranking over candidate genotype profiles x given a particular expression profile vector e. As we described, existing methods use the relation p(x|e) ∝ p(e|x)p(x) to instead model the conditional distribution over expression given genotypes. This is considered a generative approach to probabilistic modeling, in which the prediction is made by hypothesizing different values of the unobserved variable (x) and choosing one that most likely has generated the observed data (e). However, because e is high-dimensional and has a continuous domain, any parameterization of p(e|x) must make strong assumptions about its distribution , which most likely introduces inaccuracies. Also, when multiple genes are associated with an eQTL, modeling the joint distribution discriminative approach, whereby the target distribution p(x|e) is directly parameterized and learned. This obviates the need to model the distribution over e, significantly simplifying the problem. In addition, x is a vector of discrete values, which requires fewer parametric assumptions.Recall that our goal is to learn a match score function Previous models assumed that equences , based oQ(s). In reality, multiple genes can be associated with a particular eQTL, and the full set of associated genes may provide richer and more accurate information about the genetic variant than only considering the most significant gene. For example, one could reduce the experimental noise in gene expression data by averaging information across correlated genes. Our model allows any number of genes to be used in calculating the predictive signal for a particular eQTL, captured by the following probabilistic factor in our model, instantiated for each eQTL s:xs  without overly increasing model complexity.Another shortcoming of previous models is that they could only consider single eQTL–eGene pairs at a time, that is, x from e by combining the insights described above. More precisely, we model the conditional distribution p(x|e) as a conditional random field (CRF)  , includix as hm  and hp . DSM models the prior over each haplotype using the Li and Stephens’ HMM , which indicate, at each position, the index of reference panel haplotype from which the observed genotype is copied with a small probability of error; this copying distribution is captured by an emission factor, ɛ(hs|zs)ss, which relates the probability of the observed genotype at position s (hs) conditioned on the indexed reference panel haplotype at that position (zs). Each adjacent pair of hidden states are related through a transition factor, τ(zs|zs−1), which defines the probability of crossover between the haplotypes at positions s − 1 and s based on position-specific recombination rates  defined analogously to pHMM. π represents the prior distribution over the first hidden state, typically a flat (uniform) prior.The full joint probability distribution  can be written asx to use for the match score:s as a noisy observation of the corresponding genotype variables To apply the model, we wish to compute the marginal distribution over ver HMMs . This iszm and zp, the aforementioned inference procedure can be computationally expensive given a large reference panel. Using a large panel is necessary to accurately model the linkage disequilibrium patterns. Thus, we introduce the following modification of the QTL factors:s and βs are shared between the two haplotypes. The consequence of this modification is that now we have the factorizationGiven the quadratic state space at each position when jointly considering ered see .x given an expression profile e, in which the adjustments informed by eQTLs are encoded by the ϕ factors. To ensure that the ϕ factors are calibrated with respect to redundant predictive signals and genotype correlations, we jointly learn all ϕ factors to directly maximize pDSM(x′i)(|e′i) across all matching pairs (x′i) in the training data set. This is in contrast to splitting the learning procedure to first separately training ϕs for each s to predict individual eQTLs and then using these predictions to compute a sequence-wide matching score, an approach followed by all of the existing works to our knowledge (DSM provides a way to compute the probability of observing genotypes nowledge . Neglectnowledge .pHMM(x) is as follows. Because we take a particular expression profile e and match it across candidate x’s, p(e|x) is our desired choice for the score so as not to bias the match toward x’s that are more likely just based on the prior. Note that p(e) and the normalization factor for e, this is equivalent to matching using the above score M.For evaluating the linking performance of DSM, we use the following match score:We implemented the forward–backward inference algorithm for DSMs in PyTorch , leveragFor the baseline methods (GNB and EBL), we implemented the pruning of eQTLs by greedily selecting the most significant eQTL (as reported in the training data set) and then removing any other eQTLs that are correlated with it. The choice of correlation threshold was a hyperparameter we optimized, and we found that removing eQTLs with correlation greater than 0.1 to the significant eQTL consistently led to best linking accuracy on FUSION individuals. We thus adopted this threshold for comparison with our approach. Correlation was calculated as the Pearson correlation coefficient of observed genotypes between each pair of eQTLs in the training set.For EBL, we additionally optimized the eQTL–eGene correlation threshold (for determining the inclusion of eQTLs) and the extremity threshold (for assinging extreme gene expression levels to the corresponding homozygous genotypes) over the range of values considered in the software provided by the original publication. Notably, the original approach evaluates the linking performance for fixed thresholds and does not require a separate training phase. Nevertheless, we optimized these parameters on our training set to compare with other approaches that do leverage such training data.https://ega-archive.org) (We obtained our data sets through the NCBI dbGaP  and the ive.org) . From dbive.org)  and the ive.org) . We downive.org) . Genotypive.org)  using thive.org) . Gene exive.org) .We included in our models all eQTL associations reported in the GTEx data set that overlapped with the genotype data in FUSION, which consisted of following: 47,322 eQTLs and 735 eGenes for Chromosome 19; 21,685 eQTLs and 254 eGenes for Chromosome 20; 11,740 eQTLs and 118 eGenes for Chromosome 21; 19,241 eQTLs and 264 eGenes for Chromosome 22; and 99,988 eQTLs and 1011 eGenes for all four chromosomes combined.https://github.com/shuvom-s/DSM).Our Python implementations of DSM training and linking algorithms and example data formats and scripts are provided as Supplement 1Supplement 2


Epstein-Barr virus (EBV) causes lifelong infection in over 90% of the world’s population. EBV infection leads to several types of B cell and epithelial cancers due to the viral reprogramming of host-cell growth and gene expression. EBV is associated with 10% of stomach/gastric adenocarcinomas (EBVaGCs), which have distinct molecular, pathological, and immunological characteristics compared to EBV-negative gastric adenocarcinomas (EBVnGCs). Publicly available datasets, such as The Cancer Genome Atlas (TCGA), contain comprehensive transcriptomic, genomic, and epigenomic data for thousands of primary human cancer samples, including EBVaGCs. Additionally, single-cell RNA-sequencing data are becoming available for EBVaGCs. These resources provide a unique opportunity to explore the role of EBV in human carcinogenesis, as well as differences between EBVaGCs and their EBVnGC counterparts. We have constructed a suite of web-based tools called the EBV Gastric Cancer Resource (EBV-GCR), which utilizes TCGA and single-cell RNA-seq data and can be used for research related to EBVaGCs. These web-based tools allow investigators to gain in-depth biological and clinical insights by exploring the effects of EBV on cellular gene expression, associations with patient outcomes, immune landscape features, and differential gene methylation, featuring both whole-tissue and single-cell analyses. Epstein-Barr virus (EBV) is a gamma-herpesvirus estimated to infect 90% of the world’s population . EBV infIt is estimated that EBV is the causative agent of around 10% of all gastric cancer (GC) cases worldwide, though relative proportions differ by region . FurtherIndeed, a large recent meta-analysis reported that individuals with latent epithelial EBV infections exhibit an 18-fold increased risk of gastric cancer development . Other rAs no licensed prophylactic or therapeutic EBV vaccines exist , understhttps://www.cancer.gov/tcga; accessed on 29 August 2022). The outcome of this endeavor is a massive, publicly available, and comprehensive dataset of multidimensional maps of genomic changes in over 11,000 tumor samples from 33 different types of human cancer. Most samples collected to construct the TCGA have complete mRNA and miRNA sequencing and DNA methylation profiling. Additional work has systematically estimated numerous immune landscape features for each TCGA cancer sample [The Cancer Genome Atlas (TCGA) is a comprehensive, publicly available atlas of genomic, epigenomic, and transcriptomic data from primary, surgically resected human cancers  samples from nearly 400 cancer patients . All TCGhttps://mymryklab.ca/EBV-GCR/ebvgcr-home/, and the standalone version can be downloaded from the GitHub depository at https://github.com/msaland/EBV-GCR-Suite (deposited 5 March 2023).We recently developed a suite of tools to compare human papillomavirus (HPV)-positive cancers from the TCGA cervical cancer and head and neck cancer cohorts with their HPV-negative counterparts, providing improved access to these important clinically relevant resources . In thishttps://www.charlesbordet.com/en/guide-shiny-aws/, accessed on 25 August 2022). The following packages, along with their respective dependencies, have been installed: corrplot version 0.92, corto version 1.1.11, cowplot version 1.1.1, dplyr version 1.0.10, DT version 0.27, gdata version 2.18.0.1, ggplot2 version 3.4.0, ggpubr version 0.5.0, RColorBrewer version 1.1.3, scales version 1.2.1, Seurat version 4.3.0, shiny version 1.7.4, shinyjqui version 0.4.1, shinyjs version 2.1.0, shinythemes version 1.2.0, survival version 3.5.0, survminer version 0.4.9, and tidyverse version 1.3.2. The service is available 24 h/day, 7 days/week at https://mymryklab.ca/EBV-GCR/ebvgcr-home/, excluding downtime for maintenance and software updates. Tutorial videos for tools are available on the home page, under the section titled “Video Guides”. A standalone version of EBV-GCR for the Windows operating system can be downloaded from https://github.com/msaland/EBV-GCR-Suite.The web server has been deployed on an Amazon Elastic Compute Cloud (EC2) virtual machine instance running Ubuntu version 22.04, available through Amazon Web Services (AWS). The backend of the server is running Shiny Server version 1.5.20.1002, as well as R version 4.2.2. The server setup was performed in agreement with the methods outlined by Charles Bordet  or other publicly available sources as noted below; as a result, no ethical approval was needed. All data were downloaded from The Cancer Genome Atlas (TCGA) via the Broad Genome Data Analysis Center’s Firehose server , with the data normalized using the RSEM algorithm. The mRNA datasets feature expression patterns for 20,531 unique genes, whereas the miRNA datasets feature 1046 unique genes. The mRNA dataset is comprised of 30 EBVaGC, 353 EBVnGC , and 35 normal (noncancerous) control tissues. The miRNA dataset comprises 29 EBVaGC, 315 EBVnGC , and 41 normal control tissues. Boxplots were generated using the ggplot2 package (version 3.4.0). The maximum and minimum boxplot values were calculated as the 1.5× upper and lower quartile ranges, respectively. The correlations between the cellular gene mRNA or miRNA expressions and the GC subtypes were determined by sorting the datasets into their respective subsets, with subsequent calculations performed with R’s built-in wilcox.test function, with the conf.level parameter set to 0.95. Patient cellular gene mRNA and miRNA expressions with >50% zero or null values were marked as nonsignificant regardless of the calculated p-values. q-values were calculated for each comparison group with a false-discovery rate (FDR) of 5%.Level 3 mRNA and miRNA expression data for the TCGA STAD datasets were obtained from the Broad Genome Data Analysis Center’s Firehose server . The maximum and minimum boxplot values were calculated as the 1.5× upper and lower quartile ranges, respectively.The EBV viral mRNA expression datasets were obtained from Chakravorty et al. . The EBVp-values. q-values were calculated for each comparison group, with an FDR of 5%. Boxplots and scatterplots were generated using ggplot2 (version 3.4.0). The maximum and minimum boxplot values were calculated as the 1.5× upper and lower quartile ranges, respectively.Immune landscape features for the TCGA STAD dataset were obtained from Thorsson et al. , which ip-values. q-values were calculated for each comparison group, with an FDR of 5%. Kaplan–Meier survival plots were generated using the ggsurvplot function available through the survminer package (version 0.4.9).The TCGA STAD overall survival (OS) datasets were obtained from Liu et al. . Based ohttps://gdac.broadinstitute.org/, accessed on 2 March 2017). The datasets feature the methylation beta values for 395,405 different probes, along with chromosome number and genomic coordinates. The dataset features methylation data for 303 STAD samples, with 29 EBVaGC, 313 EBVnGC , and 18 non-cancerous, normal control tissues. Correlations between the probe methylation beta values and the genomic loci were determined via R’s built-in wilcox.test function, with the conf.level parameter set to 0.95. Probe methylation beta with >50% zero or null values were marked as nonsignificant regardless of the calculated p-values. q-values were calculated for each comparison group, with an FDR of 5%. Boxplots and line plots were generated using the ggplot2 package (version 3.4.0). The maximum and minimum boxplot values were calculated as the 1.5× upper and lower quartile ranges, respectively.Level 3 Infinium HumanMethylation450 BeadChip array datasets for the TCGA STAD cohort were obtained from the Broad Genome Data Analysis Centers Firehose server , with the logfc.threshold and min.pct parameters set to 0, and the densify parameter set to true. Violin plots were generated with the VlnPlot function, dimensional reduction plots with the DimPlot function, and feature plots with the FeaturePlot function, all of which are available through Seurat (version 4.3.0). Dimensional reduction plots were generated using the t-distributed stochastic neighbor embedding (t-SNE) reduction algorithm. A total of 12 t-SNE reduced datasets are available: the filtered dataset grouped by the patient histopathological type of the cell subpopulation, and subsets of the filtered dataset for the following 11 cell types: T, epithelial, B, plasma, erythroid, fibroblasts, macrophages/DCs, endothelial, endocrine, granulocyte, and parietal cells. With multiple selected genes, the gene signature was calculated by averaging the transcript levels for each cell, and the p-values were combined via Fisher integration of the p-values using the fisherp function available through the corto package (version 1.1.11).The gene expressions of 48,000 cells obtained from newly diagnosed, treatment-naïve patients were obtained from Zhang et al. . The datThe EBV-GCR web suite is a collection of six unique tools, with each created to explore a variety of molecular or clinical characteristics that may be impacted by the EBV status in GC patients. Such characteristics include differential mRNA and miRNA expression, changes in immune landscape features, overall patient survival, and gene loci methylation. By employing the tools present in the EBV-GCR suite, each of these characteristics can be correlated with EBV status, viral or cellular gene expression, genomic loci, GC histopathological subtype, and cell subpopulations. A hallmark of EBV is the ability to reprogram gene expression-infected epithelial and B cells, allowing for its prolonged survival within host cells . In a smp-values and associated q-values are shown for each comparison, with significant values highlighted. A table containing descriptive statistical information, including the sample size, minimum, maximum, and quartile values, is generated for each of the STAD subtypes. The generated boxplots can be resized via a grey triangle in the corner of the figure, and the figure itself can be downloaded as a raster (PNG) or vector (PDF) graphic. Statistical tables can be downloaded as CSV files, allowing for local data storage and analysis. Comprehensive master lists summarizing the gene expressions of all mRNAs and miRNAs are also downloadable through a link provided on each tool’s webpage.The DEG tool is available in two versions: one for cellular mRNA genes and one for miRNA gene expression. For either tool, users can select a GOI, upon which two different boxplots are generated, showing the distribution of the expression levels of the GOI for EBVaGC, MSI, CIN, GS, POLE, and normal control samples. Pairwise The vast number of DEGs observed between EBVaGCs and EBVnGCs may be the result of the interaction between EBV-associated viral factors and human genes. Given the ability of EBV to impact gene expression ,38, we cp-values and the corresponding q-values are also calculated, with significant values highlighted. The generated heatmap can be resized via a grey triangle in the corner of the figure, and the figure itself can be downloaded as a raster (PNG) or vector (PDF) graphic. Tables summarizing the correlations and significance values can be downloaded as CSV files, allowing for local data storage and analysis. Downloadable lists summarizing the correlations of viral and cellular mRNAs/miRNAs are also available through a link provided on each tool’s webpage.The EBV-GCR suite has four tools for analyzing the correlations between cellular and viral gene expressions. These include the correlations of cellular mRNA with viral mRNA, cellular miRNA with viral mRNA, cellular mRNA with viral miRNA, and cellular miRNA with viral miRNA. For any of these tools, users select a GOI, for which a heatmap is generated, showing both the Spearman correlations and the significance levels of the GOI’s gene expression against 34 miR-BARTs and 3 miR-BHRF genes for the viral miRNA tools and 19 unique viral genes for the viral mRNA versions of the tool. TP53) is shown in The availability of patient outcome data for a number of TCGA cohorts, including STAD , providep-values and associated q-values is generated, with significant values highlighted. The generated Kaplan–Meier survival curves can be resized via a grey triangle in the corner of the figure, and the figures can be downloaded as a raster (PNG) or vector (PDF) graphic. Tables summarizing the significance values can be downloaded as CSV files, allowing for local data storage and analysis.There are two versions of the EBV-GCR tool to explore the impact of cellular gene expression on overall patient survival. One explores the impact of cellular mRNA gene expression levels on overall patient survival and the other explores the impact of cellular miRNA gene expression levels on overall patient survival. For either tool, users can select a GOI, as well as the number of comparison groups, with users being limited to 2–4 different comparison groups, and each selection splitting the dataset equally into the number of desired comparison groups. Two comparison groups are titled low and high expression. Three comparison groups are low, mid, and high. Four comparison groups are low, mid-low, high-mid, and high. Upon the selection of both the GOI and the number of comparison groups, a Kaplan–Meier survival curve, along with a risk table, is generated for each of the STAD classifications; EBVaGC, MSI, CIN, GS, and POLE patient groups. Additionally, a table summarizing the pairwise With the rising clinical emphasis on cancer immunology and immunotherapy in the past decade, it is important to understand the interplay between the immune system in cancer progression and its effects on clinical outcomes ,44. The p-values. The tool featuring viral genes does not generate either the boxplot or the associated table. Additionally, a table containing descriptive statistics, such as the sample size, minimum, maximum, and quartile values, is generated for each of the subsets exhibited within the correlation plots and boxplots. The generated boxplot and correlation plot can be resized via a grey triangle in the corner of the figure, and the figures can be downloaded as a raster (PNG) or vector (PDF) graphic. Tables summarizing correlations, detailed statistical information, and significance values can be downloaded as CSV files, allowing for local storage and analysis. An example of the sample output of this subset of tools is provided in There are three versions of the tool to correlate cellular and viral gene expressions with the immune landscape. These are: the correlation of cellular mRNA with immune landscape features, the correlation of cellular miRNA with immune landscape features, and the correlation of viral mRNA and miRNA with immune landscape features. For any of the tools, users select a GOI, which generates a table showing both the Spearman correlation and significance level of the GOI’s gene expression with the 53 immune landscape features . The tooEBVaGCs are considered to be one of the most hypermethylated tumors, with genome-wide hypermethylation of promoters and genes associated with tumor suppressor functions ,46 likelp-values, q-values, the names of genes associated with the probe, and their chromosomal coordinates is generated, displaying all probes within the selected region. Significant values are highlighted and indicate significant differences in probe methylation. Users then have the option of choosing a probe from the selected region, via an additional dropdown menu, in order to generate a boxplot displaying the methylation beta values across EBVaGC, MSI, CIN, GS, POLE, and normal control samples. The generated line plot and boxplot can be resized via a grey triangle in the corner of the figure, and the figures can be downloaded as a raster (PNG) or vector (PDF) graphic. Tables summarizing the genomic information and significance values can be downloaded as CSV files, allowing for local storage and analysis. A downloadable master list summarizing all differentially methylated probes is also available on each tool’s webpage, which can assist users in identifying DMPs.The tool facilitating differential probe methylation analysis can be used for both the mRNA and miRNA STAD datasets. When users select a GOI, the genomic region and 100,000 base pairs 5′ and 3′ around both sides of the GOI are searched for methylation marks across the encompassed probes. A line plot summarizing the average methylation beta values across EBVaGC, MSI, CIN, GS, POLE, and normal control samples is generated. The line plot displays an arrow representing the coding strand for the GOI, with the left-to-right strand representing the forward orientation and the other strand representing the reverse strand orientation. A comparison table with the Bulk RNA sequencing is a technology that allows researchers to look at general expression patterns across tumors but suffers from sampling bias due to intra-tumor heterogeneity, lack of data regarding tumor cellular composition, and lower data fidelity ,52. Singp-values and associated Bonferroni-adjusted p-values is generated, with significant differences in gene expression highlighted. The generated dimensional reduction, violin, and feature plots can be resized via a grey triangle in the corner of the figure, and the figures can be downloaded as a raster (PNG) or vector (PDF) graphic. Tables summarizing the significant values can be downloaded as CSV files, allowing for local storage and analysis. An example of the sample output of this tool is provided in The single-cell analysis tool is based on our analysis of the raw data available from Zhang et al.  to compaTFF1, a trefoil family gene encoding a secretory protein expressed in gastrointestinal mucosa. Multiple reports indicate that TFF1 expression is downregulated by the EBV infection of AGS or MKN7 gastric cells [TFF1 mRNA levels were similarly reduced in non-TCGA cohort-based EBVaGC samples compared to their EBVnGC counterparts [TFF1 expression was also observed in the TCGA bulk sequencing data , the accessibility of such data to researchers without significant computational and bioinformatics skills is limited without substantial investments in time, money, and resources to make these resources easily usable. To help fill this niche, a number of web-based tools have been developed [The vast scale of data provided by the TCGA is an invaluable resource for cancer research, including the study of viral oncogenesis. Although the processed data is freely available via the Broad GDAC Firehose (eveloped ,58,59. TEBV-GCR also provides the invaluable opportunity of easily downloading both graphical and tabular interpretations for each tool. At the press of a button, users can either download either a vector or raster version of the generated graphic, which users can resize prior to download. The same applies to tabular data, where users can download an easily readable file, which can be used for further analyses and figure generation. Additionally, comprehensive master list files of DEGs, DMPs, and cellular/viral gene expression correlations can also be downloaded for further analysis or reference and allows for the narrowing down of a GOI for further experimental analysis.https://mymryklab.ca/EBV-GCR/ebvgcr-home/.To sum up, the EBV-GCR provides an intuitive and data-rich interface for the exploration and interpretation of EBV-dependent changes in gene expression, immune landscape features, patient outcomes, and DNA methylation using molecularly annotated STAD datasets from the TCGA. Single-cell gene expression data can also be examined by the GC histopathological subtype and/or cell subpopulations using datasets from Zhang et al. . Compari


L0-pseudonorm approach to learn sparse solutions in multivariable regression. The model sparsity is maintained by restricting the number of nonzero coefficients in the model with a cardinality constraint, which makes the optimization problem NP-hard. In addition, we generalize the cardinality constraint for grouped feature selection, which makes it possible to identify key sets of predictors that may be measured together in a kit in clinical practice. We demonstrate the operation of our cardinality constraint-based feature subset selection method, named OSCAR, in the context of prognostic prediction of prostate cancer patients, where it enables one to determine the key explanatory predictors at different levels of model sparsity. We further explore how the model sparsity affects the model accuracy and implementation cost. Lastly, we demonstrate generalization of the presented methodology to high-dimensional transcriptomics data.In many real-world applications, such as those based on electronic health records, prognostic prediction of patient survival is based on heterogeneous sets of clinical laboratory measurements. To address the trade-off between the predictive accuracy of a prognostic model and the costs related to its clinical implementation, we propose an optimized  L1-norm (LASSO), L2-norm (Ridge Regression) and their hybrid (Elastic Net) dominate the field. In this paper, we present a novel methodology that is based on the L0-pseudonorm, also known as the best subset selection, which has largely gone overlooked due to its challenging discrete nature. Our methodology makes use of a continuous transformation of the discrete optimization problem, and provides effective solvers implemented in a user friendly R software package. We exemplify the use of oscar-package in the context of prostate cancer prognostic prediction using both real-world hospital registry and clinical cohort data. By benchmarking the methodology against existing regularization methods, we illustrate the advantages of the L0-pseudonorm for better clinical applicability, selection of grouped features, and demonstrate its applicability in high-dimensional transcriptomics datasets.Feature subset selection has become a crucial part of building biomedical models, due to the abundance of available predictors in many applications, yet there remains an uncertainty of their importance and generalization ability. Regularized regression methods have become popular approaches to tackle this challenge by balancing the model goodness-of-fit against the increasing complexity of the model in terms of coefficients that deviate from zero. Regularization norms are pivotal in formulating the model complexity, and currently  PLOS Computational Biology Methods paper.This is a Current cancer incidence is more than 19 million new cases per year and rapidly rising globally [Prostate cancer is one of the most common cancers diagnosed in men and among the top causes of cancer mortality . AlthougRisk classification models for prostate cancer are traditionally applied either at the diagnostic phase or primary treatment phase. Most of the current prognostic models contain Gleason score, which is considered the most significant factor for early disease course estimation . In contL0-pseudonorm to restrict the number of nonzero coefficients. Such cardinality constraint complicates the optimization, since this constraint is discontinuous and nonconvex, which makes the problem NP-hard  [L0-implementations have been developed for generalized linear models, such as linear and logistic regression [L0-penalized least squares solutions, thus being applicable only for linear regression models. To the best of our knowledge, there is only one L0-implementing Cox’s proportional hazards model, the augmented penalized minimization-L0 (APM-L0) [L0 approach, and iterates between a coordinate descent-based convex regularized regression and a simple hard-thresholding estimation. However, since the APM-L0 method incorporates also L1- and L2-norms, it is unclear whether or not it performs fundamentally differently compared, for example, with LASSO.Our prognostic modelling framework for prostate cancer is based on the Cox’s proportional hazards model , 10, whial hard) . Previougression –14, but (APM-L0) , which aL0 approach. First, we rewrite the cardinality constraint with its exact DC (Difference of two Convex functions) representation, after which the constraint is added to the objective function utilizing a penalty function approach [Our implementation differs from the APM-approach . This leapproach , 18 for approach , 20 for L0 regularization method OSCAR  and exemplify it with Cox’s proportional hazards model in prognostic prediction of prostate cancer. The OSCAR method is tested in multiple data cohorts: TYKS  [L0-augmented APM-L0 [In this work, we present a new ry data) , VENICE,ry data) , and TCGry data) –23. We ury data)  in this ry data) , L0-augmd APM-L0 , smoothld APM-L0 , and greIn the OSCAR method, we refer to cardinality as the number of predictors or groups of predictors (i.e. kits) in the model. Schematic illustration of the OSCAR methodology is presented in n is the number of observations, p features, δi ∈ {0, 1} is the label . In addition, we let t1 < t2 < … < tm be increasing list of m unique failure times, and Di be the set of indices of observations failing at time ti, meaning that ties are also allowed to happen.Our modelling interest is mainly in the patient survival prediction, where we investigate the relationship between patient features (see subsection “Prostate cancer data for testing”) and survival time . In the general form, this type of data can be stated as a sethazard for the patient i at time t is given with the formulah0(t) is a shared baseline hazard and β by maximizing the Breslow approximation of the partial likelihood . In thescaled log partial likelihood of the formRi = {j : yj ≥ ti} is the set of indices at risk at time ti and di = |Di| is the number of failures at time ti. The function −l is convex, since it is a sum of linear and log-sum-exp functions [l, it is equivalent to minimize the convex function −l. In the following, we concentrate on solving the minimization problemInstead of maximizing the partial likelihood directly, it is also possible to maximize the scaled log partial likelihood, since this leads to an equivalent solution . This mounctions . TherefoL1- and L2-norms. In particular, approaches relying on the L1-norm ensure sparsity to a certain extent.In many real-world applications, it is beneficial to have sparse solutions for the partial likelihood function. To favor sparse solutions, a regularization term is typically added to the optimization problem. For example, the elastic net penalization is used in  by combiβ. The strength of this approach is that it provides us an effective tool to seek solutions with a predetermined model complexity. Instead of considering each feature separately, we may also want to group some features together, if they are always measured together (i.e. they belong to the same measurement kit). Therefore, we also generalize the cardinality constraint-based feature subset selection to a case where we restrict the number of selected kits   largest-ρ > 0 is a positive penalization parameter. In this reformulation, we are balancing between feasibility and optimality. By selecting a too small value for the parameter ρ, we do not obtain a feasible solution for the original problem ,where ρ raint in  to hold.f is nonconvex and nonsmooth, it is a DC function (Difference of two Convex functions). This means that f can be represented in the form f = f1 − f2 with two convex functions f1 and f2. This way we can better control the nonconvexity than in the general case. In addition, these convex functions can be selected, for example, asOne major benefit of the formulation in  is that,L1-norm based penalization since the only difference is the largest-k norm term Another interesting aspect of the penalized reformulation  is that In this section, we introduce the new algorithm OSCAR  to solve the cardinality-constrained problem formulated in . Since tp < 100 features. Due to this, we have also incorporated into the R-package of OSCAR the possibility to use the limited memory bundle method (LMBM) [p ≥ 100. In addition to boosting calculations with high-dimensional data, we introduce an acceleration procedure that utilizes a one-dimensional subproblem and a reduced-sized original problem  , 20. LMB problem  .However, since DBDC and LMBM are local optimizers, the quality of solutions for a nonconvex problem strongly depends on the choice of starting points. For this reason, the algorithm OSCAR combines the DBDC and LMBM methods with an incremental type of an approach to generate multiple starting points with higher likelihood of leading to most promising parts of the search space. The idea in our incremental approach is to start with solving the cardinality-constrained problem, where only a single predictor (or kit) is allowed to be used initially, and then to increase the number of predictors (or kits) one at a time until the maximal number of predictors is achieved. In particular, we utilize the solution of the cardinality-constrained problem with Algorithm 1: OSCARInput: The values of features xi, the survival times yi, the labels δi ∈ {0, 1} and the maximal number of predictors Kmax ∈ {1, 2, …, p} until which the cardinality-constrained problem is solved.Output: For i = 1, …, Kmax, gives the solution i predictors.Step 0:  Solve the convex problem (i = 1. problem  with DBDStep 1: (Starting points) For the cardinality-constrained problem with i predictors, initialize the set of starting points Si = ∅. For j = 1, …, p construct the point Si.Step 2:  Do the following steps A–C for all Step A: Select a positive initial value for the penalization parameter ρ. Step B: Solve the problem (  problem  with theStep C: If ρ and go to Step B. Step 3: (Solution) Select the best solution i predictors using the formula problem  with i pi = i + 1. If i ≤ Kmax, then go to Step 1. Otherwise go to Step 4. Update Step 4: Return i = 1, …, Kmax.Kmax, defining how many predictors maximally can be selected in the densest cardinality-constrained problem. As an output, the method provides incrementally a solution to each cardinality-constrained problem with i predictors for i = 1, …, Kmax and, thus, one obtains as a by-product a solution also for each cardinality-constrained problem with a smaller number of used predictors (or kits). This means that one can control how many different sparse solutions are generated. Naturally, it is also possible to select Kmax = p, in which case the problem . This guarantees that the obtained solution does not diverge too much from the previous solution and maintains its best predictors. In addition, this way the method does not become too sensitive to the selection of ρ, since too small values of ρ are basically omitted.In Step 2B of Algorithm 1, we always use the original starting point. The reason for this is that if the parameter For testing the new algorithm for survival prediction, we used one prostate cancer cohort from real-world hospital registry data, three prostate cancer cohorts from randomized clinical trials (see Table A in n = 590). Median imputation has been previously tested and found adequate [The real-world hospital registry data were collected from the advanced prostate cancer patients treated at the Turku University Hospital . Patients with castration resistance were selected and data processed as in . Furtheradequate , 9. One https://www.projectdatasphere.org/). These data come from three prostate cancer patient cohorts  with metastatic castration-resistant prostate cancer [n = 132, n = 150 and n = 119 for MAINSAIL, VENICE and ASCENT, respectively). Features with over 50% of missing values were eliminated. Missing values in each cohort were imputed separately using median values calculated from the corresponding training datasets . Patient characteristics are presented in Table A in The randomized clinical trial data included in the analyses were previously constructed in the DREAM 9.5 competition , hosted by Project Data Sphere  and Taylor et al.  datasets were used while examining how the computational burden increased as a function of data dimensionality. Since Sun et al.  provided only the recurrence as a binarized outcome, it was not included in the computational benchmarking of the Cox model fitting with OSCAR, but it was included in the validation of the generalization ability of identified models when using OSCAR and the other benchmarking methods.For analysis of computational cost, the full TCGA . Lastly, in order to make the identified genes as comparable as possible across the datasets, genes were subset to common gene names. This resulted in a validation data dimensionality of p > 10 000 and disease recurrence as the prediction end-point.We first investigated the performance of our OSCAR method in four clinical patient cohort-based prostate cancer datasets, which portrait two very distinct archetypes of biomedical data. First, we applied the method to the advanced prostate cancer cohort obtained from Turku university hospital (TYKS), representing a highly heterogeneous real-world hospital registry patient cohort. Second, we applied the method to three prostate cancer cohorts obtained from randomized clinical trials, which had been part of a DREAM prostate cancer modelling challenge and had been homogenized previously by the challenge organizers. Lastly, to investigate the method performance in high-dimensional transcriptomic data from prostate cancer patients, we used three additional gene expression-based datasets , which all have data dimensionality above The predictive performance was evaluated with Harrel’s concordance index (C-index)  when theL1-regularization. We included another L0-pseudonorm based method APM-L0 [L0-related methods capable of performing survival analysis. We further compared OSCAR to a SCAD-penalized regression method [L0, and SCAD, the penalization coefficient of the regularization term used is denoted with λ > 0 and thus these methods can be called λ-penalized shrinkage methods. We performed cross-validation (CV) to assess generalization ability, supported by bootstrapping of the data and subsequent re-fitting of the models to assess robustness of the selected features.To benchmark OSCAR performance, we compared its results to a widely used method LASSO , which ud APM-L0 , which wn method . FurtherL0, SCAD, and Greedy FS with respect to the costs calculated with the corresponding number of predictors. This gave us an approximation of the Pareto-front aiming at a good compromise between minimal real-life cost and maximal accuracy, since the underlying problem can be seen as a multi-objective optimization problem of these two objectives.In addition to the model accuracy, we evaluated the cost-efficiency of the models as a function of feature measurement costs obtained from actual clinical laboratory measurement kit reference costs from the Helsinki University Hospital. We evaluated the model performance of the methods OSCAR, LASSO, APM-We also investigated which features were selected as robust predictors. More specifically, we performed bootstrapping (BS), in which the model was fitted 100 times to calculate how often (%) each feature was selected as a predictor when a certain cardinality was set. This enabled us to interpret which features are the most robust predictors that are not sensitive to slight perturbations in the input data.Based on the BS evaluation of the OSCAR method in the TYKS cohort , PSA wasL0, and SCAD methods (p = 22) was relatively low in comparison to the number of patients (n = 590). All the methods selected similar predictors (se1) selected three predictors , which are the same as the most important predictors of OSCAR based on the BS. The penalization coefficient λ in LASSO, APM-L0, and SCAD is typically chosen either based on a local optimum for CV performance (λmin), or when a solution is within a range of the standard error of the local optimum (λse1). In OSCAR, to avoid arbitrary choices for the crucial model penalization, we leverage the use of bootstrapping-based inference to explore feature robustness in addition to the CV generalization ability.In general, OSCAR resulted in improved performance in terms of C-index in CV, when benchmarked against LASSO, APM- methods . Greedy edictors . For exaL0, SCAD, and Greedy FS with respect to the costs calculated with the corresponding number of predictors or the values of λ . This is similar approach to those used in LASSO, APM-While the most typical approach is to choose features one at a time, as presented above, features may be available as groups. In clinical practice, features are often measured together as kits (e.g. complete blood count), and therefore including a single feature from a kit in the model leads to availability of measurements for the rest of the kit’s features as well. As the extra features become available at the same cost, it is economical to consider including all of the kit’s features in the model simultaneously.Such a kit structure can be easily included in the OSCAR method . However, all the methods suggested similar predictors, indicating their importance and robustness.In the VENICE cohort, after the selection of these main predictors that appeared in all the trial cohorts, it became less clear which additional features had the most prognostic power on patient survival. However, based on the model accuracy and the CV results Figs  top rowsand SCAD  top row.L0, and SCAD, OSCAR again resulted in a higher mean C-index  . The comparison methods selected similar predictors within a cohort. In general, the OSCAR method improved the prediction accuracy in training data without increasing the cost when compared to the shrinkage-based methods.As high-dimensional ‘omics data present key features for prognostic and predictive modelling for patient’s recurrence and survival in most cancers, we conducted further analysis across three prostate cancer gene expression datasets. Firstly, The Cancer Genome Atlas (TCGA)  presentsn = 404, total 76 observed recurrence events without censoring) presented the most comprehensive dataset, thus it was used for training all the five methods. One fourth of the data  was set aside as a held-out TCGA validation cohort, while the remaining primary tumor samples  were used for training the models.TCGA  were plotted as a function of λ; of these, SCAD exhibited a non-monotonous number of non-zero coefficients as a function of the penalization coefficient λ. Of note, all the shrinkage methods were closely clustered together, with only minor differences observed between the methods. For the cardinality-based methods (OSCAR and Greedy FS), a spectrum of model fits from k = 1 to k = 50 was inspected, and the results of the shrinkage methods were mapped to the cardinality based scale on their count of non-zero coefficients as a function of penalization coefficient λ.Results for the recurrence predictions with the five methods are presented in k = 50. The shrinkage methods performed best after k > 10, reaching a C-index of approximately 0.7 as more features were introduced into the models. At higher cardinalities, OSCAR performed slightly worse than the shrinkage methods, while maintaining a reasonable C-index of slightly below 0.65.The TCGA held-out dataset was in general well modeled across the spectrum of model complexity, with all models starting with relatively high C-index of 0.65 when using the first few features . After tk = 10 it outperformed the other methods and maintained a C-index of around 0.70. The shrinkage-based methods again performed very similarly, with C-indices ranging between 0.60 and 0.65. Greedy FS maintained a stable performance of C-index of around 0.60 across the cardinality range.The Taylor et al. transcriptomic dataset differentiated OSCAR from the other methods when trained in the TCGA training dataset ; while Ok = 10, performing only slightly better than random (C-index = 0.5) at best. Between k = 10 to k = 20 OSCAR and the shrinkage methods improved in performance, with OSCAR gaining an advantage over the other methods with ROC-AUC reaching above 0.65. This was slightly reduced when more features were introduced into the model, but OSCAR remained above ROC-AUC > 0.6.Sun et al. clearly represented the most difficult prediction task for the TCGA-trained models, possibly because it was the oldest dataset, had the lowest sample size, and it lacked follow-up information; the end-point was a binarized recurrence outcome, with ROC-AUC used as the performance metric . All theL0, and SCAD), which formed a very closely performing model across all three validation datasets as seen in k = 50 for OSCAR and Greedy FS, while for the λ-penalized methods we chose the lowest λ with the first model with 50 non-zero coefficients. A Venn diagram of these variables is presented in L0. However, SCAD somewhat deviated from the other shrinkage-based methods, as it identified 20 genes unique to this method, in contrast to unique gene counts specific to LASSO and APM-L0 of three and four, respectively. OSCAR and Greedy FS identified notably more unique genes, that were specific to each cardinality-based method.In addition to validation performance, we observed that the methods separated into roughly two distinct classes. The first class was constituted by those methods that rely on a λ-penalized shrinkage , we observed that the computational time increased linearly for identifying kmax top features as the desired maximum cardinality k was increased , three datasets from clinical trials  and three high-dimensional transcriptomics datasets . The OSCAR method utilizes the L0-pseudonorm as a penalty term to restrict the number of predictors. Unlike previous approaches trying to tackle the difficult discrete nature of the L0-pseudonorm, OSCAR restructures the problem so that no approximation is required and the original solution can be then obtained in an exact manner. Since the pseudonorm is discontinuous and nonconvex, the optimization problem becomes NP-hard and computationally heavy [L0-pseudonorm based penalty was rewritten for easier management, and this leads to a regularization term in the form of a DC (Difference of two Convex functions) composition. The optimization was done using DBDC algorithm [In this work, we have introduced a new ly heavy . In the lgorithm , 18. ThiL0  [L0-pseudonorm allows the model coefficients to vary freely from zero, unlike, for example, in LASSO, which pushes the coefficients towards zero. LASSO, APM-L0, and SCAD utilize the coordinate descent in optimization, which is more prone to local optima when compared to the DBDC and LMBM algorithms. Despite the L0-approach, APM-L0 performed similarly to LASSO, most likely because it incorporates both L1 and L2.We compared OSCAR to LASSO , APM- method) , SCAD-pe method) , and greIn the TYKS cohort, the OSCAR method suggests PSA, HB, ALP, and age group as the main predictors. Similar trend was also observed if the kit structure was included. PSA reflects the disease severity, especially at disseminated state and in treatment-resistant disease . Thus, PIn the VENICE cohort, ALP prevailed as the most prominent predictor, and AST, CREAT, NA, HB, and ALB followed as additional predictor candidates. As mentioned above, ALP is associated with metastases and thus poor prognosis. AST tests for liver damage, and it has been associated with multiple cancers including prostate, bladder, testicular and small cell lung cancer –46. CREAAlbumin is a protein that maintains fluid balance and osmolality in bloodstream and it is associated with malnutrition and problems in intake of nutrients in the gut . CompromIn the MAINSAIL cohort, HB and ALB were again identified as key prognostic features. In addition, LDH was selected systematically in the BS analysis as a key predictor. LDH is an enzyme participating in energy production in nearly all tissues. Damaged tissues release LDH, which has been linked to cancer burden .Similarly to the VENICE cohort, AST was among the top predictors in the MAINSAIL cohort. In addition, BMI, MG, and WEIGHT had considerable prognostic power, of which MG is a pivotal part of metabolism.In the ASCENT cohort, similar features were selected consistently in the BS analysis: PSA and ALP, along with NEU, CA, LDH, and HB. NEU are white blood cells that kill bacteria and help in wound healing. They have also been associated with cancer, despite the previous belief of neutrality against cancer , 53. EspL0 (despite embedding the L0-pseudonorm), and SCAD penalized models performed almost identically  algorithms that incorporate forward selection, backward elimination, and their adaptive mixture techniques . It is pL0-pseudonorm is highly interesting in the light of our recent application of the OSCAR methodology in the DREAM Anti-PD1 Prediction Challenge. In this crowd-sourced data analysis challenge, the Cox model produced by OSCAR was a top-performer for predicting nivolumab efficacy in non-small cell lung cancer among competing models submitted by over 50 data modelling teams across the world, representing with a diverse set of modelling algorithms ranging from tree-based regression, regularized regression (L1 and L2), to deep learning algorithms. This highlights that there is untapped potential in methods, such as the L0-regularized regression, in various applications where it can outperform competing traditional methods. [The novelty in practical implementations of the methods. L0-pseudonorm, the optimization problem becomes NP-hard and computationally heavy as illustrated in the high-dimensional transcriptomics data  reformulation, bringing the optimization task to the continuous domain. In addition, we have incorporated the kit structure into the method, enabling the selection of grouped features as they are measured in the clinical practice. Since the measurements may have a potentially high costs, the model sparsity allows the selection of the most prognostic features to avoid excessive costs by addition of redundant predictors. The costs were investigated along with model accuracy. This gave us an approximation of the Pareto-front based on the minimal cost and maximal accuracy, since the underlying problem can be seen as a multi-objective optimization problem with two objectives: accuracy and cost. The multi-objective optimization could be regarded as a new way of providing models that are highly relevant to real-world applications, rather than merely optimal according statistical metrics. This way the regularized methodology can also leverage domain-expert knowledge in choosing the final model for real-world applications. Unfortunately, since the transcriptomics data are not collected on a cost-per-gene basis, our Pareto-front approach was not directly applicable to these data. However, simple count of features (i.e. genes in the model) could potentially have applications in designing commercially effective targeted panels using, for example, PCR-based approaches.We have developed, tested and made available a novel approach to the L0-pseudonorm like characteristics. Thus, we observed that the L0-pseudonorm may present similar properties as sequential feature selection algorithms rather than the shrinkage-based methods such as LASSO (L1-norm) or Ridge Regression (L2-norm). We benchmarked our methodology against highly popular regularization methods, readily available for R users, such as LASSO, and demonstrated comparable or improved performance of our L0-approach. The OSCAR methodology has been implemented and distributed as a user-friendly R-package, accompanied by a wide range of useful helper functions and a set of efficient Fortran optimizers called from within the R-package. The OSCAR method is easily accessible through the Central R Archive Network (CRAN).The OSCAR method demonstrated efficient and robust performance in the context of metastatic castration resistant prostate cancer in real-world hospital registry data, as well as in three clinical trial data cohorts, and three publicly available high-dimensional transcriptomics data capturing biochemical recurrence. Our results brought insights into the best markers, which to some extent differ between the real-world registry data and the clinical trial data, possibly due to differences in cohort patient characteristics, missingness patterns, or data reporting practices. Furthermore, exploration of the transcriptomics data revealed that the existing shrinkage-based methods are prone to providing similar solutions, despite some incorporating S1 TextThe file contains sections: 1) Restricting the number of kits in OSCAR, 2) Acceleration procedure for high-dimensional data, 3) Data characteristics, 4) Correlations, 5) Approximated Pareto-fronts, 6) High-dimensional transcriptomics data.(PDF)Click here for additional data file.


Due to the high dimensionality and sparsity of the gene expression matrix in single-cell RNA-sequencing (scRNA-seq) data, coupled with significant noise generated by shallow sequencing, it poses a great challenge for cell clustering methods. While numerous computational methods have been proposed, the majority of existing approaches center on processing the target dataset itself. This approach disregards the wealth of knowledge present within other species and batches of scRNA-seq data. In light of this, our paper proposes a novel method named graph-based deep embedding clustering (GDEC) that leverages transfer learning across species and batches. GDEC integrates graph convolutional networks, effectively overcoming the challenges posed by sparse gene expression matrices. Additionally, the incorporation of DEC in GDEC enables the partitioning of cell clusters within a lower-dimensional space, thereby mitigating the adverse effects of noise on clustering outcomes. GDEC constructs a model based on existing scRNA-seq datasets and then applying transfer learning techniques to fine-tune the model using a limited amount of prior knowledge gleaned from the target dataset. This empowers GDEC to adeptly cluster scRNA-seq data cross different species and batches. Through cross-species and cross-batch clustering experiments, we conducted a comparative analysis between GDEC and conventional packages. Furthermore, we implemented GDEC on the scRNA-seq data of uterine fibroids. Compared results obtained from the Seurat package, GDEC unveiled a novel cell type  and identified a notable number of new pathways among various cell types, thus underscoring the enhanced analytical capabilities of GDEC.https://github.com/YuzhiSun/GDEC/tree/mainAvailability and implementation:  Traditional bulk RNA sequencing measures the average gene expression levels of all cells in a sample, which can mask the diversity and functional heterogeneity of individual cells . Single-However, the identification of cell types in scRNA-seq data has become challenging due to limitations posed by the sparse and high-dimensional gene expression matrix, as well as the high noise caused by low-depth sequencing . To addret al. [et al. [et al. [et al. [The first group consists of traditional clustering methods, with many of them being based on the K-means clustering algorithm. For instance, Sun et al.  introduc [et al.  proposed [et al.  develope [et al. , which i [et al. , which aet al. [et al. [et al. [The second type of method is based on similarity, where these methods rely on similarity measures to determine the similarity between cells. Kim et al.  investig [et al.  introduc [et al.  proposed [et al.  develope [et al.  is also et al. [et al. [et al. [et al. [The most powerful category of methods for cell clustering in scRNA-seq data is based on deep learning. These methods directly utilize autoencoders and decoders, showcasing strong robustness. Kopf et al.  introduc [et al.  proposed [et al.  combined [et al.  presenteTo address these challenges, we have developed a novel method called, graph-based deep embedding clustering (GDEC) that aims to perform clustering of single-cell RNA-seq data across different species and batches. ‘GDEC’ combines the power of graph convolutional networks (GCN) and DEC. Firstly, we use GCN to extract the topology of the gene interaction network, which helps in capturing the relationships between genes and their interactions. Next, we employ DEC, which utilizes a deep autoencoder to learn a low-dimensional embedding of the scRNA-seq data. This low-dimensional representation helps in preserving the essential information while reducing the noise and dimensionality of the data. To fully leverage the wealth of information from previous scRNA-seq datasets and accurately labelled scRNA-seq datasets (Gold Standard Dataset), we apply transfer learning in our method. GDEC can acquire significant prior knowledge from existing datasets, enabling a better understanding of gene expression patterns and cellular relationships between different cell types. The application of transfer learning allows GDEC to achieve cross-species and cross-batch scRNA-seq data clustering effectively. This means that the method can identify and group cells from different species and experimental batches, even in scenarios where labelled data is limited, thanks to the knowledge gained from previous datasets. Ultimately, this contributes to more accurate and comprehensive clustering results in single-cell RNA-seq analysis.The workflow of GDEC is shown in GCN has the capability to capture intricate inter-node information. Thus, we employ GCN to extract inter-gene interaction relationships. We adopt a progressive approach with two consecutive graph convolutional modules to capture the network topological characteristics of genes. The detailed formulation within each graph convolutional block is as follows:where In consideration of the model’s robustness, particularly its ability to train on large graphs with limited computational resources; we have implemented a method of random mini-batch training for the GCN. The process is shown as By employing GCN, it becomes feasible to derive a feature vector for each gene. We use randomly generated features as the initial features of gene nodes. The multiplication of this vector with the sample feature vector from the gene expression profiles yields a feature vector representing the interrelation of genes within the sample. The specific formulation is outlined as follows:where M denotes the gene feature embedding matrix obtained through GCN, S represents the gene expression profile matrix and D signifies the matrix encompassing gene interaction feature embeddings corresponding to each cell within the expression profile. Here, ‘a’ signifies the count of cells in the expression profile, ‘g’ represents the count of genes and ‘d’ signifies the dimensionality of the GCN feature embedding. Depending on distinct contextual scenarios, dimensionality reduction of D to a one-dimensional representation can be undertaken, as elucidated below:Concatenating the GCN-derived features with the gene expression profile data yields the input data for the DEC model. The specific formulation is presented as follows:Gene expression profile data often exhibit high-dimensional characteristics. Common unsupervised machine learning techniques such as K-means and Gaussian Mixture Models may suffer diminished effectiveness when confronted with such data. Hence, we have adopted the DEC approach to effectuate feature representation and cluster assignment on the high-dimensional gene expression profiles. DEC undertakes a mapping of the data space to a lower-dimensional feature space and iteratively optimizes clustering objectives within this feature space.The process commences by conducting pre-training on the dataset using an encoder-decoder autoencoder, yielding a model capable of encoding and decoding data features. Subsequently, the encoder component is extracted for use as the dimensionality reduction model. The reduced feature representation is input into K-means to perform clustering, generating a set of cluster centers for initialization. Lastly, fine-tuning of the encoder model parameters is executed through the utilization of the Kullback–Leibler (KL) divergence loss function.Employing the Student’s t-distribution as a kernel facilitates the measurement of similarity between embedded points and centroids. This choice of kernel serves to underpin the similarity assessment between the transformed embeddings and cluster centroids.where For a given biological organization, there exists a substantial volume of single-cell data spanning diverse species. Leveraging this wealth of data holds the potential to enhance the accuracy of cell type clustering. Consequently, the GDEC method employs transfer learning to predict data with limited sample size, facilitating cross-species cell type clustering.Simultaneously, different library preparation strategies can lead to disparities in sequencing results for the same cell type, thereby influencing downstream analyses. In contrast to conventional techniques like canonical correlation analysis (CCA), transfer learning has the capacity to assimilate latent contextual knowledge, thereby mitigating batch effects and accomplishing tasks across diverse batches.As illustrated in the et al. [et al. [et al. [et al.  The mous [et al.  The mous [et al.  To verifWe employed GDEC to transfer training data from human pancreatic data to mouse pancreatic data. Additionally, Seurat, Moana and scVI were used as comparative models to validate the effectiveness of our proposed model. We identified the intersection of cell types between the source and target datasets and selected the six cell types with the highest coverage across both datasets for our testing.As depicted in As shown in In order to verify whether our model is applicable on different batches of data, we validated it on different batches of mouse brain datasets. As shown in Since the accuracy of Moana is second only to GDEC, we compared the clustering results of the two . GDEC caTo establish the significance of each component within our model, we conducted ablation experiments. We removed the graph neural network feature extraction component from the model, referred to as GDEC_gcn, and omitted the transfer learning portion, making direct predictions on the target data, termed GDEC_transfer. As depicted in Within the same dataset, GDEC_transfer outperforms GDEC_gcn, indicating that graph feature embeddings extract inter-gene relationships, thereby bolstering predictive outcomes. The absence of graph embedding features impedes achieving high accuracy, even when transferring knowledge from a high-quality dataset to the target dataset, underscoring the capability of graph embeddings to capture deeper latent relationships.For the same model, GDEC_gcn exhibits superior performance on pancreatic data, implying that transfer learning excels at learning cross-species information, aligning with expectations as transfer learning is fundamentally designed to tackle similar problems. In GDEC_transfer, enhanced performance on the brain dataset is noted, signifying that graph embedding features more effectively extract intra-species gene relationships, with a slight decrement in cross-species relationships.Through these comparisons, it is evident that graph embedding features excel in capturing inter-gene interaction relationships, while transfer learning adeptly addresses issues of dissimilar data distributions and similarity. The synergy of these two components yields excellent predictive results.et al. [et al. [We acquired single-cell sequencing data from the study conducted by Goad et al. , encompa [et al.  as the sIn the normal tissue samples, myeloid, smooth muscle cells (SMC) and fibroblasts are distributed in a similar proportion across both methods . NK and Within the fibroid tissue, Seurat identifies SMC cells comprising nearly 70% while fibroblasts account for only 1%, contradicting factual observations . ConversHence, it’s evident that GDEC provides a more detailed cell partitioning compared to Seurat. For uncommon cell types, GDEC offers more accurate predictions. With unknown cell types, GDEC can reject assigning them to a specific category instead of obligating a forced judgment like Seurat, offering significant value for exploring unknown cell types.P<0.05 were selected. Some new KEGG pathways were discovered by GDEC in fibroclasts cells and endothelial cells (not found by the Seurat method).We first used the Seurat method and GDEC method to classify cell types in normal and leiomyoma tissues, and then performed gene differential expression analysis based on cell types. By using KEGG to perform pathway analysis on the differential genes obtained, pathways with a New pathways such as proteoglycans in cancer and necroptosis have been discovered in fibroclasts cells, as shown in We also conducted GO and KEGG enrichment analysis on cells classified as ‘unknown’  and 12. Clustering methods play a fundamental role in the analysis of scRNA-seq data by enabling the exploration of cellular heterogeneity, the discovery of novel cell types, and the illumination of biological processes. However, given that each cell captures transcripts from tens of thousands of genes and the sequencing coverage is often low, a substantial number of genes remain undetectable, leading to considerable noise in the data. Consequently, achieving accurate cell clustering presents a formidable challenge.Most of the existing clustering techniques rely on conventional methods like Kmeans, tailored for cell clustering within the specific dataset. Yet, due to the noise and sparsity inherent in single-cell data, some approaches combine imputation methods with clustering techniques. Despite these efforts, limitations persist, and the full potential of numerous established gold standard datasets remains untapped.In response, this paper introduces GDEC, a transfer learning-based clustering algorithm for single-cell data, which integrates GCN and DEC. GCN integrates gene interaction information to address sparse gene expression matrices, while DEC learns cell feature representations in a low-dimensional space to mitigate noise interference. Most notably, GDEC accomplishes cross-species and cross-batch clustering of single-cell data. Leveraging prior knowledge from target datasets, the model parameters are fine-tuned to facilitate transfer learning, harnessing the extensive repository of single-cell data for enhanced clustering precision. This method treats cell types that do not appear in the training set as unknown types, which is a methodological limitation. However, as the training set continues to expand, theoretically it can achieve recognition of all known cell types in humans. At the same time, this method can also provide hints for unknown cell types in humans, which is a significant improvement compared to other traditional methods.To validate GDEC’s prowess, we first established a model using human pancreatic tissue scRNA-seq data and fine-tuned it using mouse pancreatic data, exemplifying cross-species migration learning. Experimental results highlight GDEC’s superior clustering accuracy compared to general toolkits, with the added benefit of easier correction of clustering errors through manual annotation. We extended this validation to a model built on mouse brain tissue data, followed by fine-tuning using another set of mouse brain data for cross-batch transfer learning. Once again, GDEC exhibited enhanced clustering accuracy compared to alternative toolkits. These experiments underscored GDEC’s effectiveness in cross-species and cross-batch clustering of single-cell data.Illustrating GDEC’s utility in downstream analysis of single-cell data, we examined a uterine fibroid dataset. In contrast to clustering using Seurat packages, GDEC demonstrated heightened accuracy in distinguishing epithelial cells from endothelial cells. Additionally, for cell types absent from the training set, GDEC successfully clustered and researchers can identify them accurately by annotation tools. With GDEC’s aid, we unearthed a greater number of differentially expressed genes in specific cell types between uterine fibroids and normal tissues. This insight holds considerable value in elucidating the functional distinctions among cell types.graph-based deep embedding clustering (GDEC) to achieve cell clustering on single-cell RNA-sequencing data.We fused graph convolutional networks (GCN) with deep embedding clustering (DEC) to construct Using transfer learning techniques to fine-tune the GDEC model, GDEC is enable to cluster scRNA-seq data cross different species and batches.Case on uterine fibroids shows that compared with traditional tool, GDEC can identify novel cell type and more accuracy cell type specific genes to discover novel function of cells.