Administration of poly (ADP-ribose) polymerase (PARP) inhibitors after achieving a response to platinum-containing drugs significantly prolonged relapse-free survival compared to placebo administration. PARP inhibitors have been used in clinical practice. However, patients with platinum-resistant relapsed ovarian cancer still have a poor prognosis and there is an unmet need. The purpose of this study was to examine the clinical significance of metabolic genes and focal adhesion kinase (FAK) activity in advanced ovarian high-grade serous carcinoma (HGSC).https://portal.gdc.cancer.gov/). In addition, tumour tissue was sampled by laparotomy or screening laparoscopy prior to treatment initiation from patients diagnosed with stage IIIC ovarian cancer  classification, 2014) at the Saitama Medical University International Medical Center, and among the patients diagnosed with HGSC, 16 cases of available cryopreserved specimens were included in this study. The present study was reviewed and approved by the Institutional Review Board of Saitama Medical University International Medical Center . Among the 6307 variable genes detected in both The Cancer Genome Atlas-Ovarian (TCGA-OV) data and clinical specimen data, 35 genes related to metabolism and FAK activity were applied. RNA-seq data were analysed using the Subio Platform . JMP 15  was used for statistical analysis and various types of machine learning. The Kaplan-Meier method was used for survival analysis, and the Wilcoxon test was used to analyse significant differences. P < 0.05 was considered significant.The RNA sequencing (RNA-seq) data and clinical data of HGSC patients were obtained from the Genomic Data Commons (GDC) Data Portal and analysed (p = 0.0444). These groups were significantly associated with platinum sensitivity/resistance in clinical cases  and showed significant relationships with progression-free survival (p = 0.0307).In the TCGA-OV data, patients with stage IIIC with a residual tumour diameter of 1-10 mm were selected for K means clustering and classified into groups with significant prognostic correlations (In the TCGA-OV data, 2 groups classified by clustering focusing on metabolism-related genes and FAK activity were shown to be associated with platinum resistance and a poor prognosis.The online version contains supplementary material available at 10.1186/s12885-021-09148-x. Gynecological malignancies include cervical cancer, uterine cancer, and ovarian cancer, among others. Ovarian cancer is the 5th leading cause of cancer deaths among women worldwide and is considered to have an extremely poor prognosis –3. One oRecently, clinical trials have shown that administration of poly (ADP-ribose) polymerase (PARP) inhibitors to ovarian cancer patients after achieving a response to platinum-containing drugs significantly prolonged relapse-free survival compared to placebo administration. PARP inhibitors are used in actual clinical practice –17. ThusThe involvement of cancer stem cells (CSCs) in cancer relapse and treatment resistance has been reported in recent years, indicating that cancer tissues are heterogeneous and that some cancer cells, such as CSCs, are involved in relapse and treatment resistance –23. EvenTherefore, the purpose of this study was to examine the clinical significance of metabolic genes and FAK activity in advanced ovarian high-grade serous carcinoma (HGSC). Specifically, RNA-seq was performed on cancer specimens before treatment initiation to examine relationships with the effects of platinum-containing drugs with an emphasis on metabolic genes and FAK activity. Machine learning including cluster analysis was used for analysis.Using machine learning, predicting prognoses for cancer patients and the therapeutic effects of platinum-containing drugs can be widely performed –36. In tThe present study was reviewed and approved by the Institutional Review Board of Saitama Medical University International Medical Center . Patients diagnosed with ovarian cancer stage IIIC  classification 2014) who started treatment at Saitama Medical University International Medical Center between November 2008 and August 2016 were targeted. There were 101 patients with HGSC who had stage IIIC tumours in that period, and tumour tissue sampling was performed during open surgery or exploratory laparoscopy before treatment initiation. Among them, representative 16 cases with available cryopreserved specimens were analysed.Tumour specimens were collected by surgery and immediately cryopreserved at -80 °C. Total RNA was extracted as previously reported . In brieThe clinical information of the 16 cases were obtained from the electrical health record, and is shown in Table Homo sapiens (hg19) and annotation data were downloaded from the UCSC table browser (http://genome.ucsc.edu). The results of sample qualities were shown in Figs. RNA sequencing was performed using the Illumina NovaSeq 6000 platform with a standard 100-bp paired-end read protocol as previously described . Librarihttps://portal.gdc.cancer.gov/) [The RNA-seq data and clinical data of ovarian cancer patients were obtained from the Genomic Data Commons (GDC) Data Portal (er.gov/) –51.RNA seq data for ovarian cancer patients available at TCGA were extracted on October 30, 2019. The RNA-Seq dataset consisted of 378 samples. A total of 373 primary tumour samples and 5 recurrent tumour samples were included.RNA-seq data were analysed using the Subio Platform  .The read count value data were analysed. Normalization/preprocessing was performed as follows. For log transformation, the read count value was converted to a logarithm with a base of 2. If the read count was 0, a missing value was documented. Subsequently, global normalization was performed with the 90th percentile. Then, for the low signal cutoff, if the value after normalization was less than 50, it was replaced with 50 and used as the cutoff value. To account for missing values, original read counts of 0, indicating a missing value, were assigned a value of 2 to the 5th power.For centring, the expression level of each gene was converted to the ratio against the average value. The value generated by applying the above normalization and preprocessing is displayed as a value called the Processed Signal on the Subio Platform and is the log2 ratio against the average value of the expression levels of all samples for each gene.Measurement values with a read count less than 100 were considered to be unreliable, and genes with a read count value less than 50 were excluded from the analysis in 189 samples, reflecting half of the 378 samples. Thus, 16,485 genes were extracted.Similar to the TCGA-OV data, the clinical specimen data were normalized and preprocessed. However, the processing method is fine-tuned on the basis of sample size and the distribution of read count values.For log transformation, the read count value was converted to a logarithm with a base of 2. However, if the read count value was 0, logarithmic transformation was not possible, and the result was replaced with a missing value. Subsequently, global normalization was performed through alignment with the 75th percentile. Then, when the value after normalization was smaller than 100 , it was replaced with 100. To account for missing values, sites with a missing value due to an original read count of 0 were assigned a value of 2 to the 6th power.The value generated by applying the above processing is displayed as the Processed Signal on the Subio Platform as well as the TCGA-OV data. Measurement values with a read count value less than 100 were considered to be unreliable, and these genes were removed. To exclude genes whose expression did not change and genes whose expression changed randomly, genes whose average Processed Signal was in the range of -0.3 to 0.3 were removed. Thus, 6840 genes were extracted.Finally, the Processed Signal of 6307 genes, which was extracted from TCGA-OV data and clinical sample data, was selected as a candidate of the variable to be used in the machine learning analysis. There are many genes related to FAK pathways and metabolism, however, selecting many variables for machine learning could result in overfitting . And we P < 0.05 was considered significant.JMP 15  was used for statistical analysis and various types of machine learning. The Kaplan-Meier method was used for survival analysis, and the Wilcoxon test was used to analyse significant differences. TCGA-OV data included data from ovarian cancer patients with advanced stage I to stage IV disease, but since the prognosis differs depending on the stage of advancement, in this study, we analysed the data for the patients with stage III ovarian cancer. However, in the treatment of ovarian cancers, the prognosis differs depending on the amount of residual tumour at the time of surgery . In otheIn 130 cases obtained as described above, cluster analysis was performed for gene expression, as shown in Table p = 0.0444). The mean value and manifestation of each gene in these groups are shown in Fig. A total of 130 cases were classified into 2 groups .Subsequently, similar clustering including clinical specimen data was performed with the TCGA-OV data. Only 4 cases among 130 cases were classified differently from the abovementioned clustering Fig. . The relp = 0.0307). In other words, the group classified as cluster 2 had a significantly shorter PFS than the group classified as cluster 1 in the clinical data. Further, cluster 2 had a worse prognosis tendency with respect to the overall survival (OS) in the clinical data. However, a significant difference was not observed .In this classification, progression-free survival (PFS) after platinum-containing drug administration was examined, and a significant correlation was found . The effects of platinum-containing drugs can be accurately predicted by homologous recombination deficiency (HRD) scores [By using machine learning including deep learning, in recent years, many studies on applying machine learning in cancer research have been performed , 62, 63.) scores , 68. In ) scores . This exIn recent years, metabolism in cancer has received considerable attention with the development and popularization of metabolomic analysis –76. MetaThe same is true for the FAK pathway. Gene expression related to the FAK pathway was incorporated as a variable in this examination based on reports and previous research indicating that recurrence of ovarian cancer, treatment resistance, and CSCs are related to FAK activity , 77–80.Thus, sensitivity and resistance to platinum-containing drugs can be predicted by focusing on metabolic genes and groups of genes related to FAK activity. As a result, the possibility of predicting the prognosis was shown in this examination. Based on this study, metabolism and the FAK pathway may be potential therapeutic targets in the future. In fact, in the test case, the examination using ovarian clear cell carcinoma cell lines, which are likely to be chemotherapy-resistant, showed a synergistic effect of inhibiting glutamine metabolism and the FAK pathway . Howeverin-vitro studies. However, there is a possibility that mechanisms of platinum resistance in serous carcinoma is different from that in clear cell carcinoma. In the future, new targets for drug discovery are expected to be found by focusing on metabolism-related genes and FAK activity in treatment-resistant ovarian cancer.We believe CSC-like properties are a useful model which gives us insight into chemo-resistance. Especially, we assumed that investigating CSC-like properties of clear cell carcinoma could give us insight into platinum resistance because most of the patients with ovarian clear cell carcinoma are platinum-resistant. We conducted this study to ensure the results we obtained from our previous Additional file 1: Figure S1. Throughput output of raw and trimmed data.Analyses were successfully performed on all 16 paired-ends samples.Additional file 2: Figure S2. Q30 score of raw and trimmed data. Figure shows the Q30 percentage  of each sample’s raw and trimmed data.Additional file 3: Figure S3. Overall read mapping ratio. Trimmed reads are mapped to reference genome with HISAT2 [h HISAT2 . Figure Additional file 4: Figure S4. Distribution of the Expression of Each Gene in Each Cluster. (a) The distribution of the expression of each gene in cluster 1. (b) The distribution of the expression of each gene in cluster 2. (c) The mean expression level of each gene in each cluster. Regarding metabolic genes, both high and low expression levels and the overall balance were involved in the metabolic phenotype. Therefore, in this examination, the difference between these 2 groups was unclearAdditional file 5: Table S1. Clinical Specimen Data.


Constructing gene coexpression networks is a powerful approach for analyzing high-throughput gene expression data towards module identification, gene function prediction, and disease-gene prioritization. While optimal workflows for constructing coexpression networks, including good choices for data pre-processing, normalization, and network transformation, have been developed for microarray-based expression data, such well-tested choices do not exist for RNA-seq data. Almost all studies that compare data processing and normalization methods for RNA-seq focus on the end goal of determining differential gene expression.Here, we present a comprehensive benchmarking and analysis of 36 different workflows, each with a unique set of normalization and network transformation methods, for constructing coexpression networks from RNA-seq datasets. We test these workflows on both large, homogenous datasets and small, heterogeneous datasets from various labs. We analyze the workflows in terms of aggregate performance, individual method choices, and the impact of multiple dataset experimental factors. Our results demonstrate that between-sample normalization has the biggest impact, with counts adjusted by size factors producing networks that most accurately recapitulate known tissue-naive and tissue-aware gene functional relationships.https://krishnanlab.github.io/RNAseq_coexpression to make appropriate choices for coexpression analysis based on the experimental factors of their RNA-seq dataset.Based on this work, we provide concrete recommendations on robust procedures for building an accurate coexpression network from an RNA-seq dataset. In addition, researchers can examine all the results in great detail at The online version contains supplementary material available at 10.1186/s13059-021-02568-9. Constructing gene coexpression networks is a powerful and widely used approach for analyzing high-throughput gene expression data from microarray and RNA-seq technologies . CoexpreNevertheless, multiple experimental factors impact the quantification of the expression of individual genes and the coexpression between pairs of genes, making it necessary to normalize and transform high-throughput gene expression data before downstream analysis. For RNA-seq data, examples of factors that affect the number of reads mapped to a gene include gene length, gene sequence, sample RNA population, and sequencing depth. Some factors have a greater effect on comparisons of gene counts within a single sample (“within-sample” effects) while others have a greater effect on comparisons of the same gene’s counts in different samples (“between-sample” effects) . Many daHowever, the best practices for normalization when building a coexpression network from a raw gene-expression dataset have been developed and compared only for data from microarrays , 12. OveThe most relevant prior work focuses on establishing best practices that reduce the introduction of artifacts in coexpression networks built from RNA-seq data . This stIn this work, we present the most comprehensive benchmarking of commonly used within- and between-sample normalization strategies and network transformation methods for constructing accurate coexpression networks from human RNA-seq data. We tested every possible combination of methods from different normalization and network transformation stages. Our primary interest is in identifying robust combinations of methods that consistently result in coexpression networks that accurately capture general and tissue-aware gene relationships across a large variety of datasets. This will allow us to propose general recommendations useful for experimental research groups analyzing their own RNA-seq data as well as computational researchers seeking to build many coexpression networks from publicly available data for the purposes of data/network integration. Towards this aim, we use hundreds of datasets, generated by a consortium and by individual laboratories, covering multiple experimental factors. We then test the resulting networks on both tissue-naive and tissue-aware prior knowledge about gene functional relationships. Based on these extensive analyses, we finally provide concrete recommendations for normalization and network transformation choices in RNA-seq coexpression analysis.To test various within-sample normalization, between-sample normalization, and network transformation methods (and their combinations) on a large data collection, we started with gene count data from the recount2 database . RecountM values (TMM), and upper quartile (UQ); in addition, we tested two new variations of TMM and UQ—counts adjusted with TMM factors (CTF); counts adjusted with upper quartile factors (CUF)—that directly adjust counts by the size factors but does not correct by library size; and (c) network transformation: weighted topological overlap (WTO) and context likelihood of relatedness (CLR). To systematically examine these methods and their interactions, we built 36 different workflows covering all possible combinations of choices . The Counts workflow uses no within-sample normalization, between-sample normalization, or network transformation, but is still transformed with the hyperbolic arcsine function.After preprocessing each dataset using lenient filters in order to keep data for as many genes and samples as possible see the “”, we comces Fig. . For claSince this entire workflow is unsupervised, i.e., not reliant on prior knowledge about gene relationships, we evaluated the resulting coexpression networks by comparing them to gold standards of known gene functional relationships. The gold standards were built using experimentally verified co-annotations to specific biological process terms in the Gene Ontology . These cIn total, for each of the 287 datasets from GTEx and SRA, we built one coexpression network per dataset using each of the 36 workflows, resulting in 8610 coexpression networks. Later on, we created 2430 additional datasets generated by resampling GTEx that, when run through all the workflows, resulted in another 72,900 networks. Each GTEx network contains 20,418 genes while each SRA network contains 22,084 genes, and all networks are fully connected with edges weighted by their strength of correlation. Each of these networks were evaluated using the tissue-naive gold-standard and, whenever applicable, the tissue-aware gold-standard. Finally, we replicated the analysis of the top-performing workflows using as many matched SRA datasets as possible from another RNA-Seq repository, refine.bio , where rCTF_CLR and CUF_CLR) results in top-tier workflows for the GTEx datasets regardless of gold standard. However, CLR transformation is only among top-performing methods for SRA datasets in recovering tissue-aware gene relationships. Though CTF_CLR and CUF_CLR still perform quite well on the tissue-naive standard for SRA, there is a clear gap from the top tier. Despite CTF- and CUF-containing workflows resulting in top performances, workflows that include other between-sample normalization methods are absent among the top ten workflows for both GTEx and SRA. Workflows with TMM or UQ seem to be more comparable to workflows using within-sample normalization methods.For all 36 workflows, Fig. The next noteworthy observation is that the top-tier workflows do not include a within-sample normalization step. Yet, workflows that do include within-sample normalization methods  can perform better than many other workflows depending on other choices made in the pipeline, the best choice often is to be paired with no other method or CLR alone. For GTEx datasets, CLR seems to generally result in slightly improved performance, while the WTO transformation almost exclusively makes up the bottom tier of workflows. For building networks from SRA datasets, although workflows including WTO do not exclusively end up in the bottom tier (as is the case with GTEx data), adding WTO to a particular workflow always hurts performance. The worst workflows for SRA in either standard are quantile normalization (QNT) paired with CLR or WTO.p value < 0.01; Fig. CTF outperforms CTF_CLR, CUF, and CUF_CLR on 58%, 61%, and 58% of GTEx networks, respectively. The CTF workflow is also significantly better the most number of times compared to other workflows in the SRA networks using the naive standard, although Counts and CUF are only slightly behind CTF  values to CTF_CLR and CUF_CLR , utilizing any within-sample normalization method results in worse overall performance than not using it Fig.  and S6. The reason we included SRA data in this study is that SRA datasets are very representative of expression datasets typically generated by numerous individual laboratories. Accordingly, these datasets vary considerably in terms of multiple factors including sample size, sample similarity, number of mapped reads, and tissue type. Though these factors impact the quality of coexpression networks derived from the individual datasets, it is hard to tease out the effect of each of these factors (controlling for others) on the accuracies that we observed using different workflows on SRA data. Therefore, using the large GTEx datasets, we created a collection of SRA-like datasets to more closely examine the impact of each experimental factor. First, we determined the nine sample sizes  that are representative of SRA datasets. Then, from each GTEx tissue dataset with at least 70 samples, we randomly selected samples to create ten datasets for each sample size see the “” sectionCTF was significantly better than all other workflows for sample sizes 5 through 40 when using the naive standard for assessment  is surprisingly effective, especially at lower sample sizes, while CTF_CLR and CUF_CLR improve performance with increasing sample size. In fact, when all samples from a given GTEx tissue are used (≥70 samples), there is no significant difference between CTF, CUF, CTF_CLR, and CUF_CLR. CLR is the next best workflow after those top four. The only other workflows that are ever ranked in the top five are CTF_WTO and CUF_WTO and that too only at low sample sizes (5–7). Based on the tissue-aware standards, CTF_CLR is the most effective workflow on all sample sizes except 5, where CTF and CUF are the top workflows , but CTF and CUF significantly outperform more workflows than any other ). These trends also hold when network accuracy is measured using precision at low recall, which focuses on maximizing the number of functional gene pairs among the high-scoring gene pairs instead of focusing on recovering all functional gene pairs. Put another way, the trends described above hold even when a threshold is applied to the coexpression network to retain just the high-scoring gene pairs for subsequent analysis. For the sake of completion, we have also evaluated all networks using the area under the ROC curve (auROC). All these results based on three different evaluation metrics (log2(auPRC/prior), precision at 20% recall, and auROC) are available as a consolidated webpage at https://krishnanlab.github.io/RNAseq_coexpression that researchers can explore to easily examine the performance of various workflows based on the properties of their RNA-seq dataset.The general trends presented above are all based on network accuracy measured using a metric based on the area under the precision-recall curve  leads to the largest improvement in coexpression accuracy. These methods are designed to make expression values across samples more comparable to one another, an aspect critical for coexpression analysis. However, QNT, a between-sample normalization method that is most commonly used with microarray data, performs very poorly for RNA-seq data. This is likely because QNT forces the distribution of samples to be exactly the same, meaning that each gene value is forced to be a particular quantile value. Consequently, it does not suit situations where there truly are different numbers of genes that are expressed outside of the typical ranges across samples , 30, an CTF_CLR and CUF_CLR improve with increasing sample size on the naive standard  before taking the log ). However, adding a constant pseudocount to all genes is disadvantageous because low gene counts are disproportionately increased compared to high gene counts before log transformation . The hyperbolic arcsine (asinh) transformation—log( x + √(x2 + 1))—mitigates this effect [Counts workflow performs well despite not incorporating any within- or between-sample normalization but only an asinh transformation. We speculate that this good performance is due to the variance stabilization provided by the asinh transformation along with the across-sample normalization of gene expression vectors inherent within the calculation of the Pearson correlation coefficient.RNA-seq data analyses typically benefit from a data transformation that stabilizes the variance across mean values, i.e., renders the data more homoskedastic, because, in its untransformed form, the expected variance grows with the mean for gene counts . A stands effect . The asis effect . Due to , logx + ). HoweveThe popular R package for differential expression analysis, DESeq2 , offers Counts) leads to good performance in our study, applying the additional normalization step is prudent to ensure robustness against variabilities specific to a new dataset.If gene counts are available, use CTF or CUF to normalize the data. They consistently give the best performance regardless of various factors. Between the two, CTF seems to be slightly more consistent in yielding top performance. Even though no normalization  and calculate coexpression using Pearson correlation coefficient.If the dataset has greater than 40 samples, use CLR to transform the pairwise gene correlations. CLR may also help certain cases where the main interest is interactions that are specific to a given tissue.QNT and WTO hurt performance in combination with every other method, in all cases, and should not be used.By constructing coexpression networks for diverse datasets from both GTEx and SRA, we were able to evaluate workflows on large, homogeneous datasets as well as smaller, heterogeneous datasets to identify methods that are robust to differing technical and biological factors. Although there is some variation in performance between GTEx and SRA data, and slightly more variation introduced by tissue-aware gold standards, many trends are consistent across datasets and evaluations. Based on all our results, we make the following recommendations for building coexpression networks from RNA-seq data using Pearson or Spearman correlation:https://krishnanlab.github.io/RNAseq_coexpression.To enable researchers to explore all our analyses in a streamlined manner and find the results most relevant to their own RNA-seq datasets of interest, we have made them available as a rich webpage written with R Markdown: Going forward, we can leverage this comprehensive benchmarking framework for coexpression analysis to answer newer and subtler questions about data quality and sample composition. For example, many studies have found that removing unwanted variation, i.e., noise caused by technical rather than biological factors, in the RNA-seq data has led to improvements in downstream analysis including the calculation of coexpression networks , 40. Suchttps://krishnanlab.github.io/RNAseq_coexpression. Researchers can use this website to easily examine the performance of various workflows and make appropriate choices for coexpression analysis based on the properties of their RNA-seq dataset of interest. All the scripts to reproduce our results are available at https://github.com/krishnanlab/RNAseq_coexpression [We have performed an extensive benchmarking and analysis of how data normalization and network transformation impact the accuracy of coexpression networks built from RNA-seq datasets. Based on this work, we have arrived at concrete recommendations on robust procedures that will generally lead to best coexpression networks. Specifically, using Counts adjustment with TMM Factors (CTF) and Counts adjustment with Upper quartile Factors (CUF) normalizations to construct coexpression networks results in the most consistently high accuracy networks, and using CLR to transform the network can further increase accuracy in select cases. All the results from this study—for GTEx, SRA, and GTEx resampling datasets, based on tissue-naive and tissue-aware gold standard, using three different evaluation metrics—are available as a consolidated webpage at pression , along wpression .Read counts for both SRA and GTEx datasets were downloaded from the recount2 database  and procAs a form of quality control, we excluded experiments that recount2 identified as having a misreported paired-end status. Experiments that contained “cell line,” “celll line,” “passage,” “cultured cells,” or “cell culture” in the characteristics metadata were also removed so as to retain primary tissue samples, which left 341 SRA datasets. Next, we discarded low-coverage samples that had zero expression (counts) in at least half of all genes of interest  and subsequently excluded entire datasets that no longer contained five or more samples. Any dataset that had a sample removed under these criteria was not retained due to dropping below five samples. Retaining only tissues that still had at least 5 separate experiments left 256 datasets. Finally, we removed genes with very low expression across the board by filtering out those that did not have at least one read per million sample reads in at least 20% of the samples in at least one dataset. This resulted in 22,084 genes in the SRA networks and 20,418 genes in the GTEx networks. Our filtering steps are intentionally relaxed, to retain as much data as possible without keeping large amounts of completely uninformative data.Recount2 stores quantified expression as base pair counts per gene. We converted these values into gene counts by dividing these base pair per gene counts by the average read length in the sample and accounted for paired-end read samples by further dividing by a factor of two.To evaluate the workflows on RNA-Seq data processed with different read alignment and counts quantification methods, we matched as many SRA datasets in our final recount2 data corpus as possible to data in refine.bio. In some cases, not every sample in a recount2 dataset was available in the refine.bio database. If the number of missing samples dropped the dataset to less than 5 samples, we did not use that dataset to construct a network. This procedure brought the total number of usable refine.bio datasets to 188, most of which (120/188) contained all of the samples that were used in the recount2 datasets. These datasets were downloaded from refine.bio as unnormalized transcript counts. Because some data in refine.bio was aligned using Ensembl release 93 and the rest was aligned using Ensembl release 96, we first subsetted all refine.bio transcripts to only the common transcripts between releases. The transcript counts were summed to gene counts , transcripts per million (TPM), and reads per kilobase million (RPKM) for performing within-sample normalization of the original raw gene counts , 50. NotM values (TMM) [preprocessCore package available from Bioconductor, which implements the quantile normalization described in Bolstad et al. [edgeR package [Between-sample normalization transforms the expression levels of genes across a group of samples so that gene counts from the same gene in different samples can be more accurately compared to each other. We tested quantile (QNT), trimmed mean of es (TMM) , and uppes (TMM) . In addid et al. . TMM nor package  to calcuWe chose to keep only long RNA gene types (mRNA (protein-coding), lncRNA, antisense RNA) as those are the most common gene types used in coexpression analysis and shorter reads make mapping and identification more difficult , 55. TheA log transformation is standard procedure when working with RNA-seq data, as the expected variance grows with the mean for gene counts . A pseudWe also compared asinh to variance stabilizing transformation (VST)  and reguDistancer tool in the Sleipnir C++ library [A coexpression network was constructed for each individual dataset by calculating the Pearson correlation coefficient between every pair of genes in that dati ‘aset using the  library . These c library , 48. Sini, j) based on how different the original weight of that edge is relative to all of the connections to gene i and all connections to gene j (to the rest of the genes in the network). For instance, CLR will upweight an edge between two genes if the edge weight is high compared to all of the other connections of both genes. WTO was implemented using the wTO function with the “sign” method in the wTO package [Dat2Dab function in the Sleipnir C++ library.We tested two common methods of network transformation, weighted topological overlap (WTO)  and cont package , and CLRSupplemental Note). Specifically, curators were considering the question “if unknown gene/protein G were predicted to be annotated to GOBP term T, would that be enough to consider experimentally testing this relationship between G and T?” Then, any pair of genes that were co-annotated to the same specific GOBP term was set as a positive edge in the gold standard. We only used annotations based on experimental  or curated evidence (IC). We explicitly ignored gene-term annotations made based on expression (GO evidence code: IEP) to avoid circularity when comparing coexpression-derived interactions to this gold-standard. We next had to determine which pairs of genes among the ones with at least one positive edge could be declared as negative edges, i.e., gene pairs that are unlikely to be functionally related based on prior knowledge. To be clear, “positive” and “negative” are used here based on machine learning parlance to indicate interactions and non-interactions, respectively, and do not correspond to the sign of the relationship. This way, the terms are consistent with how we refer to true/false positive/negative edges. Following previous work, we ignored gene pairs not co-annotated to any specific term but still interact with many of the same genes in the gold standard . We also ignored gene pairs that were not co-annotated to any specific term but were co-annotated to certain general GOBP terms, thus introducing ambiguity in whether they are functionally related or not. All remaining gene pairs were considered negatives. We built the naive gold standard using the Answerer function in the Sleipnir C++ library.The goal of coexpression networks is to capture true functional relationships between genes in the cellular context of the original dataset. Therefore, we evaluated the accuracy of each coexpression network by comparing it to two gold standards, one representing known generic (tissue-naive) functional relationships and the other representing known tissue-aware gene functional relationships. We assembled these gold standards by beginning with a set of manually-selected Gene Ontology Biological Process (GOBP) terms , 57 thatWe created the tissue-aware gold standards for as many tissues as possible by subsetting the naive gold standard based on genes known to be specifically expressed in a particular tissue. We obtained tissue-aware genes from the TISSUES 2.0 database Knowledge channel . The knoDChecker function in the Sleipnir C++ library to compare each coexpression network to each gold-standard and return the number of true positives, false positives, true negatives, and false negatives at various edge weight thresholds. These numbers were used to calculate the area under the precision-recall curve (auPRC) using the trapz function in the pracma package. Since gene functional relationship gold-standards of different tissues have different proportions of positives to negatives, the original auPRC scores are not directly comparable to each other. Therefore, we divided each auPRC by its “prior”—the auPRC of a random predictor, equal to the fraction of positives among all positive and negative edges—and expressed the performance as the logarithm of this ratio to enable tissue-to-tissue comparisons.We used the Supplemental Note contains more details on the (i) gene functional relationship gold standard, (ii) additional gold standards that we explored  andp values, we performed a correction for multiple testing with the Benjamini-Hochberg procedure and declared workflows with FDR ≤ 0.01 as being significantly different. Further, each workflow is a combination of method choices at multiple stages. So, to determine the impact of including a particular method in a workflow, we across aggregated workflows to calculate the proportion of times that including a particular method in a workflow resulted in the workflow being significantly greater than one that did not include the method. As it is not possible to do within-sample normalization and then do TMM, UQ, CTF, or CUF, any workflow including CPM, TPM, or RPKM was excluded when assessing between-sample normalization methods so that method being compared to each other based on the same number of aggregated workflows. For similar reasons, workflows involving TMM, UQ, CTF, or CUF were not considered for the analysis of within-sample normalization methods.To assess whether two workflows resulted in coexpression networks that were significantly different in quality, we used a paired Wilcoxon rank sum test to compare the auPRC scores across all coexpression networks generated by those two workflows. After calculating To simulate uniformly processed datasets that have sample sizes similar to datasets from SRA, we chose nine sample sizes  based on the distribution of SRA dataset sample sizes. Then, from each GTEx dataset with at least 70 samples, we randomly sampled a “dataset” of each sample size, repeating this sampling ten times to create 10 datasets per sample size from each GTEx dataset. One coexpression network was constructed and evaluated from each of these GTEX-resampled datasets in the same manner outlined above.In addition to dataset size , the quality of the coexpression network reconstructed from a dataset could also depend on the similarity between the samples in that dataset as well as the total number of mapped reads. We performed an analysis to determine this impact using the GTEx-resampled datasets and the original SRA datasets. Since SRA datasets are not large enough to do resampling for sample size analysis, we split them into five groups with equal number of datasets, with datasets in each group having similar sample sizes. We define sample similarity for a given dataset as the median spearman correlation between all samples using the 50% most variable genes in the GTEx tissue they came from for the resampled GTEx datasets, or the median spearman correlation between all samples using the 50% most variable genes in each individual dataset in the case of the SRA networks. Read count diversity is calculated by summing the gene counts of each sample in a given dataset and taking their standard deviation. Based on each of these measures—sample similarity and read count diversity—we divided the datasets into five groups of equal size while taking care to check that each group contained datasets with similar sample sizes. For the tissue analysis, we could only determine significance in SRA tissues that had at least 15 datasets.Additional file 1: Supplemental Figures and a Note. This file contains supplemental figures S1-S16 and a Supplemental Note describing various aspects of the gold standard.Additional file 2. Review history.


Robust methods for modelling and estimation of cancer survival could be relevant in understanding and limiting the impact of cancer. This study was aimed at developing an efficient Machine learning (ML) pipeline that could model survival in Lung Adenocarcinoma (LUAD) patients. Image transformations of multi omics data were employed for training a machine vision-based model capable of segregating patients into high-risk and low-risk subgroups. The performance was evaluated using concordance index, Brier score, and other similar metrices. The proposed model was able to outperform similar methods with a high degree of confidence. Furthermore, critical modules in cell cycle and pathways were also identified.The utility of multi-omics in personalized therapy and cancer survival analysis has been debated and demonstrated extensively in the recent past. Most of the current methods still suffer from data constraints such as high-dimensionality, unexplained interdependence, and subpar integration methods. Here, we propose SurvCNN, an alternative approach to process multi-omics data with robust computer vision architectures, to predict cancer prognosis for Lung Adenocarcinoma patients. Numerical multi-omics data were transformed into their image representations and fed into a Convolutional Neural network with a discrete-time model to predict survival probabilities. The framework also dichotomized patients into risk subgroups based on their survival probabilities over time. SurvCNN was evaluated on multiple performance metrics and outperformed existing methods with a high degree of confidence. Moreover, comprehensive insights into the relative performance of various combinations of omics datasets were probed. Critical biological processes, pathways and cell types identified from downstream processing of differentially expressed genes suggested that the framework could elucidate elements detrimental to a patient’s survival. Such integrative models with high predictive power would have a significant impact and utility in precision oncology. Molecular biology and high-throughput technology have significantly advanced in the past few decades, resulting in novel solutions for diagnostic and prognostic challenges in the way of personalized cancer therapy ,2,3. It Though multi-omics data can reveal significant insights into the mechanism of a disease like cancer, the form in which it is fed to a model is a decisive hyperparameter for its performance ,14. The Apart from these conventional data-integration approaches, bright ideas like iCluster, CoxPath, and CNAmet have tried to mitigate the issue of high dimensionality and heterogeneity in omics to an extent, by consolidating the principles of mathematics and statistics in an effective manner ,20,21,22ciations ,24.With a similar goal in mind, we intended to provide machine learning algorithms with some prior knowledge about the local interactions among the features (genes). Here, a simple yet efficient way to transform omics datasets into their image representations has been presented. Such images try to represent gene-associations, in addition to the numeric values already provided by omics datasets . Further, these image representations of omics data types can be plugged in state of the art computer vision architecture such as Convolutional Neural Networks (CNN), which are tailor-made for learning such data and estimate the survival prognosis of a cancer patient . The novThe underlying idea behind SurvCNN was to transform numeric omics data into an image form and feed it into a CNN with a custom loss function to predict survival probabilities for different time intervals. The calculated survival probabilities were used to fit a Kaplan–Meier curve for segregating patients in risk groups based on their conditional probabilities at different time intervals. The relative effectiveness of different combinations of omics data in estimating survival prognosis was also probed. The proposed workflow’s modular nature enabled the incorporation of multiple combinations of omics data types without drastically altering the underlying framework. For clarity, a detailed description of the twelve omics combinations analyzed is summarized in Semi-parametric proportional hazards regression (Cox-PH) is considered to be the most common strategy for generating survival estimates, where the relative risks of the patients (hazard ratios) are explained by the model covariates . Howeverhttp://firebrowse.org/ access date: 17 February 2020) of The Cancer Genome Atlas (TCGA) database. While firebrowse provided z-scaled RSEM values of mRNA expression, log2-RPM values for miRNA were retrieved and z-scaled. Common patients from the three datasets were extracted and the necessary processing  was done. While patients with more than 20 percent missing features were discarded, missing values (if any) in the rest were filled using R package impute [We employed three omics data types of LUAD, along with their clinical information in this study. All three data types, namely, mRNA-seq , methylation and miRNA-seq (illuminahiseq_mirnaseq-miR_gene_expression) were retrieved from firebrowse utility  corresponding to every gene/feature value in the original dataset  were assigned to every element on the 2D feature matrix. For example, to build a survival prediction model using two omics data types and ttempted . AverageMany hyperparameters such as perplexity, number of neighbors, distant metrics, and minimum distance were associated and needed to be optimized for these feature transformation methods. As an indirect measure of evaluating the goodness of projections, few genes involved in pathways reported to be dysregulated in cancer were mapped on the projections. t-SNE and UMAP plots mapped with 83 cancer-associated genes were analyzed with silhouette analysis and parameters that led to significant clustering were selected . The lisAiming for a modular framework, a parallel network architecture where different omics types can be simultaneously plugged into the model was constructed. This modularity allowed us to test for various combinations of omics datasets without altering the underlying architecture drastically. For each omics set the training and testing datasets were split in an 80:20 ratio. For example, the omics set I has 515 samples, so the training set and testing set contains 412 samples and 103 samples, respectively. Each convolution block contains one convolution layer with 256 nodes with a 3 × 3 kernel. It is followed by a batch normalization layer, ReLU activation layer, and a max-pooling layer with a 2 × 2 kernel. Batch normalization helps accelerate the training of large networks while max-pooling down-samples of the image at every layer . The outThe proposed model provides flexibility in opting for the proportional hazards assumption versus its violation. For instance, with the proportional hazard assumption, the final dense layer was setup as a single neuron with no bias. Then it was connected to the n-dimensional model output where ‘n’ is the number of time intervals. On the other hand, in the case of large datasets where the proportional hazard assumption may get violated, the single node proportional hazard layer is skipped and the output of the fully connected dense layers is directly connected to an n-dimensional output layer. Every model has an n-dimensional output where n is the number of time intervals, in which total survival time  is split. We opted for a bin width of 3 months for a 10-year survival analysis that gave us a 39-dimensional output layer.The Cox-PH model is usually incorporated into deep neural networks as a final layer to give survival estimates ,36,37. HTo mitigate these issues, a discrete-time survival method for modeling omics data and estimation of survival prognosis was employed. For the approach to work, a custom loss function was based on the negative partial likelihood, assuming the PH criteria had to be defined (Equation (1)). It was critical as major deep learning frameworks like TensorFlow did not have the required loss function built in. The discrete-time survival models are flexible as they do not assume the validity of the PH assumption. These models could easily be trained with SGD, which was attractive as this enabled rapid experimentation for optimizing the model hyperparameters. In discrete-time survival models, the total time frame  was divided into a set of intervals with a fixed duration . For each interval, the conditional probability of survival was estimated, given that an individual has survived up to the beginning of an interval. It was later used to classify the given patient into a high/low-risk class.Negative log-likelihood was adapted as a loss function for the survival model . For eact was the number of time intervals. Given a set of time intervals, SurvCNN predicted the conditional probability of survival at every interval, i.e., The proposed survival prediction model, with the custom loss function, naturally integrated non-proportional hazards and time-varying baseline hazard rates. The baseline hazard probability is allowed to vary freely with a time interval, but the effect of input data on hazard rate does not vary with follow-up time. In other words, if a specific combination of input data results in a high rate of death in the early follow-up period, it will also result in a high rate of death in the late follow-up period. This was implemented by setting the final hidden layer to have a single neuron and densely connecting the prior hidden layer to the final hidden layer without any bias weights. The neural network gave a separate hazard rate for each time interval The Kaplan Meier (KM) survival curve estimated the survival rates and hazard for a given time interval D. The sup-values. In survival statistics, the log-rank p-value was calculated to estimate the statistical significance among the segregated risk groups [The KM survival curves were generated by segregating patients into two risk groups based on the median survival probability after a definite amount of time . The two survival populations were statistically compared by testing the null hypotheses and calculating the associated k groups .Three performance metrics were employed to quantify the goodness of the proposed survival models. The first metric used was Harrel’s concordance index (C-index) that evaluates the relative ordering of events in time-series data . C-indexDifferentially expressed gene clusters among the two classes of patients were identified and exported for functional analysis. Enrichr, a web-based open-source enrichment toolbox, was employed for the analysis ,45. StatTo generate robust representations of omics datasets with predictive ability, we proposed a workflow that transforms numerical omics datasets into an image form while retaining critical information about feature dependencies. Multiple CNNs with different omics combinations were trained to predict survival statistics of LUAD cancer patients effectively. Irrespective of the omics data types included, the performance of all the experiments was evaluated by three metrics C-index, Brier score, and IPCW. To minimize the chances of over-fitting, five-fold cross-validation was performed for every run. Ultimately, differentially expressed genes were derived among the two risk groups and used for further analysis A.Contrary to the conventional practice of feeding numerical omics data into machine learning frameworks, the independent values were converted into well-organized images. These images performed exceedingly well in predicting the patient-specific survival probabilities with a high degree of concordance. The complete set of performance metrics evaluating twelve omics-combinations each for two methods (t-SNE and UMAP) are compiled in p-value < 0.005 was not considered for the results. Though most omics combinations did well to segregate prognostic subtypes significantly, a combination of mRNA-seq and methylation performed exceedingly well  and low-risk (C2) subgroups based on these probabilities. The two risk groups were stringently checked for significance and any experiment with log-rank gly well B,C. Moregly well .Among all the multi-omics combinations tested, an upward trend for mean-concordance values was observed as more omics-types were included. However, for the instances where miRNA-seq data were included, the performance dipped significantly . The exaOur approach was compared with existing methods such as Cox-PH, RF-S, and Cox-nnet ,36,49. FThe comparison of performance in terms of the C-index of omics data among the four methods over twelve omics datasets is shown in While our best model  registered a C-IPCW in the range of 0.68–0.73, Cox-nnet stayed in the 0.58–0.65 range throughout the omics combinations tested. This was in line with a previous work wherein it was around 0.6 (range: 0.55–0.59) for the LUAD dataset . SimilarIt should be noted that while C-indices for Cox-PH, RF-S and Cox-nnet were computed on LUAD data in-house, the Brier score (as 1-Brier score for compatibility with other performance metrics) for Cox-nnet was adapted from its original publication as both used the same (LUAD) dataset. Moreover, to verify if the performance improvement depicted by SurvCNN is statistically significant, a paired t-test was performed on every omics combination. As tabulated in p-value < 0.005, odds-ratio > 4.0) enriched terms associated with Pathway, Biological process, and cell type. More cell cycle and DNA replication-associated genes like CDK1, MCM4, CHEK1, and RFC5 were upregulated in C1 than in C2 [+, CD71+, and CD34 endothelial such as RAD51, KIAA0101, PRC1, POLE2, CDK2, CDK1, CKS2, CENPN, and TAF5. Interestingly, anti-angiogenetic treatment targeting such tumor endothelial cells provides a survival advantage in the treatment of NSCLC [Differential expression levels among the two prognostic subtypes were quantified by averaging out the images corresponding to the two subclasses and filtering out the common pixel locations. As depicted in an in C2 ,51,52,53of NSCLC . On the The proposed SurvCNN method produced promising results and cemented the utility of multi-omics data in the lung cancer survival prognosis. Unlike other algorithms, it integrates Cox-PH regression and CNN models seamlessly into a single package. It not only makes the pipeline robust but also adds a modular aspect to it. This modularity has been exploited to test for various combinations of multi-omics datasets without drastically altering the underline architecture. Although most of the omics combinations tested outperformed the competition, the combination of mRNA-seq, miRNA-seq, and their clinical features proved to be the most effective omics-combination among the twelve sets tested. It also reinforced the utility of multi-omics in cancer research instead of a more traditional single-omics approach. Though only PH models were considered for the final comparison, model performances for PH and non-PH models are summarized in p-value < 0.005, odds-ratio > 6) for the overexpressed genes in C1. On the other hand, regulation of histone acetylation (GO:0090240), chemical homeostasis within a tissue (GO:0048875) and amino-acid transport (GO:0089718) were found to be downregulated in C1. These observations underline the cancerous characteristics that differentiate C1 from C2. It also reinforces the criticality of these processes that lead to aggressive cancer metastasis, tumor development, and possibly the ultimate fate of an individual [It should be noted that creating image representations of omics-datasets was one of the fundamental requirements for this approach to work. The effectiveness of these representations is reflected in above-average prognosis results quantified by the C-index and log-rank test. It should be emphasized that all the performance metrics results are reported for the test-set only. The detailed record of all the training and testing results, along with comparative analysis, are compiled in dividual .Though most of the multi-omics combinations tested in the study were found to have above-average predictive ability, a few combinations did not perform as expected (This work successfully demonstrated that numerical multi-omics data, transformed into their image representations, could extract meaningful information about the individual’s genomic profile. These representations of genomic information also simplify the process of identifying genetic clusters that are coregulated in a diseased individual and predict its likelihood of survival in terms of hazard ratios. SurvCNN also fared well against other machine learning-assisted survival prognosis models. Though we have primarily focused on its application on cancer prognosis detection, one can extrapolate the algorithms for use in a wide variety of applications.As an immediate follow-up, given the encouraging results with LUAD datasets, we propose to scale this method into a holistic cancer prognosis prediction system in a future study. It would include data for a variety of cancer subtypes as opposed to the current single cancer multi-omics. The system would provide prognostic predictions to cancer patients based on their genomic profile and disease history. With more sophisticated CNN architectures and powerful hardware, our method and its derivatives can harness the full potential of recent advances in computer vision and prove to be a stepping-stone in the development of personalized therapy.


Disclosure of patients’ genetic information in the process of applying machine learning techniques for tumor classification hinders the privacy of personal information. Homomorphic Encryption (HE), which supports operations between encrypted data, can be used as one of the tools to perform such computation without information leakage, but it brings great challenges for directly applying general machine learning algorithms due to the limitations of operations supported by HE. In particular, non-polynomial activation functions, including softmax functions, are difficult to implement with HE and require a suitable approximation method to minimize the loss of accuracy. In the secure genome analysis competition called iDASH 2020, it is presented as a competition task that a multi-label tumor classification method that predicts the class of samples based on genetic information using HE.We develop a secure multi-label tumor classification method using HE to ensure privacy during all the computations of the model inference process. Our solution is based on a 1-layer neural network with the softmax activation function model and uses the approximate HE scheme. We present an approximation method that enables softmax activation in the model using HE and a technique for efficiently encoding data to reduce computational costs. In addition, we propose a HE-friendly data filtering method to reduce the size of large-scale genetic data.We aim to analyze the dataset from The Cancer Genome Atlas (TCGA) dataset, which consists of 3,622 samples from 11 types of cancers, genetic features from 25,128 genes. Our preprocessing method reduces the number of genes to 4,096 or less and achieves a microAUC value of 0.9882 (85% accuracy) with a 1-layer shallow neural network. Using our model, we successfully compute the tumor classification inference steps on the encrypted test data in 3.75 minutes. As a result of exceptionally high microAUC values, our solution was awarded co-first place in iDASH 2020 Track 1: “Secure multi-label Tumor classification using Homomorphic Encryption”.Our solution is the first result of implementing a neural network model with softmax activation using HE. Also, HE optimization methods presented in this work enable machine learning implementation using HE or other challenging HE applications. Cancer is a disease caused by the unlimited proliferation of certain cells in the human body, and the exact cause of cancer is not yet known. In 2020 alone, 19.3 million new cases were reported worldwide, and 10 million people died because of cancer 40], respThe dataset consists of total 3,622 samples  and 25,128 genes, and each sample has one cancer type out of 11 types of cancer, consists of two types of data: Copy Number (CN) data and Variants data. The dataset is available in  which isCN data consists of the copy number of the genes. The copy number data show the copy number variations (CNVs) of the genes as numbers, representing the state of the gene on the corresponding sample, whether the gene has duplication or deletion of a considerable number of base pairs. The data consist of 5 different levels 0, ±1,±2 where the negative and positive values represent deletion and duplication of the corresponding gene from the sample, respectively. Copy number with 0 means that the gene has no considerable variation on the corresponding gene from the sample.Variants data consists of mutation data of selected pairs of samples and genes for each tumor type with various features: gene’s location on chromosomes, mutation type, whether the mutation is Single Nucleotide Polymorphism (SNP), and mutation’s effects separately predicted by two different methods.For the training step, we first downsize each sample by using our proposed filtering algorithms, and used it for the training of our neural network model. More precisely, we feed the downsized samples into our shallow neural network model, which consists of one hidden layer with 64 nodes and linear activation function and output layer with 11 nodes. During the training step, we used batch size of 32, number of epochs of 50 and dropout rate of 0.9.dcn,kvar), the parameters for CN and variants dataset respectively, until the size of downsized data are less or equal to 2B for each B from 9 to 12. In our algorithm, the size of model is determined by the size of filtered data under two parameters. For each B, we seek the best pair of parameters, dcn among {0,0.01,⋯,0.24} and kvar among {0,10,⋯,590}; more precisely, we use 10-fold cross validation to find the  pair with best microAUC such that the size of model is less or equal to 2B. After selecting the parameters, dcn and kvar, we train the model on the entire training dataset, and feed it into the inference step over encrypted data.To suitably use the trained model in downstream tasks over encrypted data, we varied = for B=9,10 and  for B=11,12, respectively. All experiments were performed on Intel Xeon CPU E5-2620v4 at 2.10GHz processor and used 8 threads. The detailed description of CKKS parameters is stated in For the approximation of Softmax, we use Goldschmidt algorithm with https://github.com/jaihyunp/iDash2020, and those for the inference step can be found in docker repository swanhong/idash2020.Our codes for the training step can be found in dcn,kvar) pair determines the size of model. The model tends to show the best performance in terms of microAUC on dcn≈0.08, and larger kvar tends to show a better performance. However, to optimize the computational cost on the privacy-preserving inference step based on homomorphic encryption, we seek the best parameters (dcn and kvar) for the model of size less or equal to 2B for each B=9,10,11, and 12.Gradually changing two parameters, our results are presented in Figs. dcn,kvar) pair for each size of model, 2B, and its performance on 10-fold cross validation is given in Table The best  in the HE track of iDASH 2020 competition. Unlike other award winners who obtained relatively low microAUC values (close to 0.95) by performing linear activation within a very short time, our result shows a high microAUC value by proposing the only method for applying softmax activation within a practical time. In addition, our preprocessing method has scalability, making it possible to obtain a higher microAUC value through additional time consumption, which is different from other teams.dcn for each dataset. Variants data filtering can be also applied to other types of datasets that have a lot of empty information. Since various genetic datasets are ‘empty-sparse’, not sparse with lots of 0s but no information, our filtering technique can be used to efficiently extract the relevant features. However, since our method focused only on the filtering method to select meaningful genes, it cna be expected that the high microAUC values can be obtained through other methodologies that perform simple operations. In future studies, combining our method with other HE-friendly preprocessing methods n be the number in {1,⋯,n} satisfying [x]n=x mod n.All logarithms are base 2 unless otherwise indicated. The vectors are denoted with upper arrow. We denote an entry of the vector by using the same character with index. We denote Hadamard multipcation between two vectors by A, A means the i th row and j th column element of A. Also, we denote the submatrix of A with i∈I th rows and j∈J th columns from A by A. In this case, the colon(:) indicates the whole index set.For a matrix Since HE enables anaylsis of encrypted data while preserving the privacy of message from operators, it is considered as one of the beneficial tool to delegate operations that requires sensitive data without revealing any information. Unlike other popular cryptographic tools including multi-party computation, which require protocol participants to continuously interact to each other through the scenario, HE has the advantage that no additional actions or online processes are required for the message owners after they encrypts and transmits data to the operator. Through these characteristics, HE has been exploited in various field such as ML that requires computation using sensitive information such as genomic data , 42, 43 Since Gentry firstly suggested in his blueprint  in 2009,The approximate HE scheme, namely as CKKS scheme, is proposed by Cheon et al. . The maiapproximate does not mean that the homomorphic operations contain large errors and result in data loss, but rather that the very small errors are allowed in the message to increases efficiency of the operations in the scheme. In machine learning applications, such errors does not ruin the message as the scheme guarantees a sufficiently large precision if practical parameters are used.We remark that the word L be a level parameter that a fresh ciphertext is equipped with a modulus qL=(2Δ)L, and qℓ:=(2Δ)ℓ for 1≤ℓ≤L for some scaling factor Δ. Let N and Rq be a modulo-q quotient ring of R, i.e., Rq=R/qR. The distribution χenc and χerr denote the discrete Gaussian distribution with some fixed standard deviation. The distribution χkey outputs a polynomial of {−1,0,1}-coefficient. We denote the rounding function ⌊·⌉ and modulo-q operation [·]q.For the rest of this section, we formally describe CKKS scheme. Let KeyGen(params).s←χkey and Set the secret key as sk=.Sample e←χerr. Set the public key as Sample Encpk(m). Given a message m∈R, sample v←χenc and e0,e1←χerr. Output the ciphertext Decsk(ct). Given a ciphertext ′=〈ct,sk〉.Add/Sub. Given two ciphertext Multevk. Given two ciphertexts Rotrk. For a ciphertext ct encrypting a plaintext vector ct′ encrypting a plaintext vector ct by r positions.CKKS scheme uses a plaintext vector Add=ct1+ct2 or For the remind of the paper, we may denote the operations between ciphertexts or ciphertext and plain vector by common symbols, such as Given more than 25,000 genes, meaningful gene selection is essential for efficient ML using HE. Therefore, we introduce a new data preprocessing technique consisting of a feature selection method modified from  to obtais and G and the number of types of tumor by T. In our dataset, these notations contain values s=2,713(train) or 909(test), G=25,128 and T=11. Using the abstract notation, the CN and Variants data can be understood as a matrix of the size s×G and the T number of set of information. Since the number of genes G is too large to handle with HE efficiently, we propose the preprocessing method which is easy to compute both client-side and server-side in our scenario to reduce the number of filtered gene less than fixed bound.In the rest of paper, we denote the number of samples and genes from original data by Our main approach for CN data filtering is to filter out the irrelevant genes with cluster analysis based on the similarity of the neighboring genes. Modified from CGF in , we intrC∈{0,±1,±2}s×G be the matrix of copy number data, where the s rows correspond to the s samples, and the g columns correspond to G genes; C is a copy number that corresponds to gene j of sample i . For two gene columns pi and qi are the i th entry of vectors ith sample. Starting from the first gene in C, say a representative of the first group, we calculate the hamming distance with the following genes in order. Until the distance is less than the predetermined threshold dcn, we merge each corresponding gene to the first group. If the distance first reached the threshold dcn, the first group ends and the corresponding gene becomes a representative of the second group. Then start from the new representative, calculate the hamming distance with the following genes.where Repeating this algorithm until the genes are all clustered, each gene is in a unique group with neighboring genes. Finally, we filter the CN data with the representative genes, the first gene in each group, resulting in a matrix For Variants data filtering, the feature selection mechanism uses only a mutation’s effect data classified in 4 different levels: LOW, MODERATE, MODIFIER, and HIGH. The Variants data filtering works based on the effectiveness of the mutations. It filters out the genes with less effective mutations.In the Variants data, for each sample, only a few mutation effect data of individually selected genes are given. So the raw Variants data for whole samples and genes is almost empty, which cannot be used immediately as a neural network input. Hence our Variants data filtering is separately applied to each cancer type to reduce the empty spaces and fill in yet remaining spaces with zero.Vt be the matrix of the raw data with mutation’s effect corresponding to the tumor type t (1≤t≤T). Vt is a st×G matrix with mutation’s effect as strings, where st rows correspond to st samples and G columns correspond to whole G genes for each t. Vt is the effect of the mutation in j th gene of i th sample with t . The column-wise summation jth gene to the st samples, so the selected genes in list can be regarded as genes with considerable mutation effects. The union of the selected genes from each tumor type t is the set of filtered genes.Secondly, we sum t, resulting in a matrix Finally, we filter the whole Variants data with the filtered genes for each s×g where Y, we train a neural network model from  in plain while transform Y as the one-hot encoded label matrix with size s×T. Here, we note that T is 11 in our dataset, which is relatively small than s and g. Our neural network model consists of one hidden layer with 64 nodes and linear activation function and output layer with 11 nodes. In the output layer, we use softmax activation function to output their predicted value. During the training phase, we used Keras library [After preprocessing for CN and variants data, we get the data matrix  library  in Pythodcn and kvar, for the preprocessing on the given train dataset, we train and evaluate shallow neural network models using 10-fold cross validation with filtered data based on each pair of parameters. After selecting the best parameters, we train the shallow neural network model on the entire train dataset using the best parameters, and we use the trained model for the inference step over encrypted test dataset.To select the best parameters, X with size s×g and weight matrix W with size g×T are given . Since T is relatively small than s and g in practice, we consider the matrix-matrix multiplication Y=X·W as matrix-vector multiplications i<T, where i+1)th column of W. Then, for each row Yj of Y (0≤j<s), we compute the softmax function to get final score of our model. Since the matrix Y is still encrypted, we need to compute an approximate function of softmax. In short, our Method can be divided into three steps: X to a number of ciphertexts {cti}.Data Packing : encrypt the matrix cti} and W, compute matrix-vector multiplication to get the ciphertext ctY that contains Y=X·W.Matrix-Vector Multiplication : using {ctY to obtain softmax output for each row of Y.Softmax Evaluation : compute approximate softmax function for From now on, we state the method to compute inference step from our model with encrypted data. Precisely, input data matrix We break the method down into the first two steps and the other, and explain the main ideas in each section.Although CKKS scheme supports SIMD operation between vectors, the SIMD operation cannot be directly applied to the matrix-vector multiplication operation. Therefore, in order to efficiently perform a matrix-vector multiplication operation using HE, a process of mapping a matrix to a number of vectors is required. In this section, focusing on the matrix multiplications in our scenario, we first state the naive approach and then suggests our optimization method.n times of slot-wise vector multiplication between diagonal part of X and wi. Concretely, we define j-th diagonal part of X so that j<g. For the repeated rotation of each column W, we define with superscript with parentheses as j<g. Then, the matrix-vector multiplication can be computed as The main idea of mapping a matrix to vectors for this computation is suggested in , which is=8,g=4, and T=4, and assumsing that the number of slots in one ciphertext is 4 times larger than the size of vector s. Then our goal is to compute i<4. In the naive approach, we encode and encrypt i. Then we can compute Hadamard multiplication by s slots in Before we state our explicit method for encodings and matrix-multiplications, we start with a toy example, simplifying the parameters as T number of the matrix-vector multiplication, so that the CMult and Rot should be computed T and 2T times, respectively. Here, the implementation cost of Rot is larger than CMult, so we suggest new packing method to reduce the number of rotation in the whole algorithm. Our main idea is to duplicate and encode X multiple times in each ciphertexts, which reduces the number of rotations since the number of summation between the slots in one ciphertexts is reduced.From the naive approach, we need Now, we propose a new approach for matrix-vector multiplication to reduce the number of constant multiplications and rotations. Our main idea is that we copy each entclass1pt{minimak,l<2. Then we get for 0≤ in Eqs.  and 4),,k,l<2. TCMults and 2 Rots, while 2 ciphertexts are required for encryption instead of 1 (c−id), where In , the autRotSum algorithm, which repeatedly computes rotation and addition to get summation of desired slots in a ciphertext.For the matrix-vector multiplication, the addition between data packed in one ciphertext is needed. We use RotSum outputs the ciphertext ctout that is obtained by computing ctout←ct and ctout←ctout+Rotrk for j=0,1,⋯,d−1 in order. As a result, if ct was an encryption of the message vector ctout contains the message vector Precisely, we define the algorithm r times). Also, we can embed matrices X and W into large matrices with row and column lengths of power-of-2, respectively, so we assume that s,g are power-of-2’s. Recall that our goal is to compute j<t while Combining all of the above methods, we explain the explicit method used for our implementation. For the rest of this section, we denote the concatenation of vectors by m times when encoding, where m is a power-of-2. Since each vector has the size s and the number of slots in a ciphertext is n, each ciphertext will contain As explained before, we copy each cti and plain vector cti sequentially contains m copies of vector q. Here we define jm+r≥T. Precisely, we encode  by Eqs.  and 6)  \documenj, we multiply cti and j. Next, we compute the multiplication step. For each r in Eq.  for eachRotSum so that the first ms slots contain the desired sums and are copied to the remaining slots. The Eq. (i·ℓ+wq+k)’s for all indices q,i, and k works as the summation for all indices from 0 to q−1. Hence, the result is the desired vector Finally, we compute the following summations using  The Eq.  indicate The Eq.  since thj, we compute the result ctY,j that contains jth group of m outputs RotSum operation. From Eq. . Since the number of multiplication does not change asymptotically for m, our method provides a time cost trade-off between the number of rotations and encryptions. In our implementation environment, we can reduce the total time cost by using more memory to encrypt data since the rotation cost is the significant part in total matrix-vector multiplication algorithm.In summary, if we duplicate While softmax layer substantially enhances the performance of the classification, it cannot be directly computed by CKKS scheme since it comprises several non-polynomial operations. Recall that the softmax of a real vector d as Eq. . 10\docBoth exponential function and division are not polynomial, so we should replace them by their polynomial approximation. We introduce a proper polynomial approximation technique for each of exponential and division function. In general, in order to approximate a non-polynomial operation by a polynomial, minimax method that minimizes the maximum error value within an interval or Chebyshev approximation that express the function by the series of Chebyshev polynomials are mainly used. However, the minimax approximation loses the increasing property of exponential and the division function, because the sign of the error is not constant. Hence, this method is not suitable in terms of calculating microAUC score. Instead, we suggest an approximation method of the softmax layer that is more suitable for microAUC score. In particular, our approximation method consists of a less number of squaring operations, so it has an advantage to be evaluated over homomorphically encrypted data.x). Precisely, for some r, we approximately compute exp(x) as Eq.  is monotone on [−2r,∞), so it is more appropriate to approximate softmax functions in terms of getting a high microAUC score compared to other polynomial approximation techniques such as minimax and Chebyshev approximation.Note that this formula can be computed by squaring r,L(x) as Eq.  as Eq. . From thx∈, Goldschmidt’s algorithm uses the property as in Eq. , instead of , by using the equation M should be carefully chosen since the error accompanied by Goldschmidt’s algorithm becomes non-negligiblly large as the input is near 0. Therefore, if we select an overly large M, the input values become smaller, resulting in an error that cannot be ignored.Moreover, we can easily exploit Goldschmidt’s algorithm Gol(·) to approximately evaluate 1/To put approximate exponential function and Goldschmidt’s algorithm together, we now can approximately compute the softmax layer by using HE operations. Denoting  the Eq.  to compuThe detailed algorithm is described in Algorithm 4.