TP53 signature has a robust predictive performance for prognosis in early-stage breast cancer, but the experiment that reported this relied on public microarray data and fresh-frozen samples. Before TP53 signature can be used in a clinical setting, a simple and low-cost diagnostic system using formalin-fixed paraffin-embedded (FFPE) samples is needed. New treatments based on the biological characteristics of TP53 signature are expected to follow.TP53 signature was evaluated in 174 FFPE early breast cancer specimens using digital quantification via the nCounter technique (NanoString). Patients were classified as TP53 signature mutant type (n = 64) or wild type (n = 110). Predictive power of TP53 signature was compared with those of other gene expression signatures in 153 fresh-frozen samples of the same cohort by RNA-seq. The molecular features of TP53 signature were elucidated using TCGA omics data and RNA-seq data to explore new therapeutic strategies for patients with TP53 signature mutant type.TP53 signature was a strong predictor of prognosis and was also more accurate than other gene expression signatures and independent of other clinicopathological factors. TCGA data analysis showed that risk score of TP53 signature was an index of chromosomal and genomic instability and that TP53 signature mutant type was associated with higher PD-L1 expression, variation in copy numbers, and numbers of somatic mutations.TP53 signature as diagnosed using the nCounter system is not only a robust predictor of prognosis but also a potential predictor of responsiveness to immune checkpoint inhibitors. TP53 gene were seen in 30 percent of whole breast cancer patients and 80 percent of triple-negative breast cancer patients [TP53 structural mutation status is associated with worse overall and disease-free survival, but its predictive value is still debated [TP53 structural mutations are missense mutations, and the function of each mutation was verified using a yeast system [TP53 missense mutations, however, and several comprehensive analyses by next-generation sequencing (NGS) have revealed other key genes associated with the p53 pathway, epigenetic abnormalities and copy number alternations without TP53 missense mutation [TP53 signature, a gene expression profile composed of 33 genes including two housekeeping genes to predict TP53 structure [TP53 signature can be used to classify breast cancer patients into wild type (TP53 signature WT type) or mutant type (TP53 signature MT type) based on the expression pattern of 33 genes. The TP53 status determined by TP53 signature does not completely match to the TP53 status defined by TP53 structural status. There were some samples without TP53 structural mutation in TP53 signature mutant type. Recent reports revealed TP53 signature could also predict prognosis of early-stage breast cancer more accurately than TP53 status determined by DNA sequencing or immunohistochemically examination. Uji et al. reported that TP53 signature was a powerful predictive prognostic indicator for ER-positive breast cancer rather than TP53 structural mutation detected by NGS, Sanger sequence method, and immunohistochemistry [TP53 signature had a robust capacity for predicting prognosis in early-stage breast cancer compared to other gene expression profiles including Mammaprint and Oncotype DX [The functional loss of p53 plays a very important role in oncogenesis , 2. Repopatients . There i debated . Many TPmutation . Becausemutation . Previoutructure . TP53 sihemistry . In addiotype DX , which hotype DX –18.TP53 signature have been based on microarrays. Before the robust predictive ability of TP53 signature can be used in an ordinary clinical situation, a simple and low-cost diagnostic system for TP53 signature using formalin-fixed paraffin-embedded (FFPE) tissue samples is absolutely needed. The nCounter  is a gene expression analysis machine which can analyze a maximum of 800 kinds of gene expression values at the same time without PCR reaction [TP53 signature using the nCounter would provide us with more accurate prognostic predictive ability for early breast cancer in actual clinical situations. At the same time, it is necessary to develop new therapeutic strategies for patients with poor prognosis as diagnosed by TP53 signature.To date, diagnostic systems for reaction . The ProTP53 signature through an analysis of 223 FFPE breast cancer specimens using nCounter and to demonstrate the robust predictive ability of TP53 signature compared to other expression profiles by analyzing RNA-seq data. The second purpose of this study was to clarify the molecular biological background of TP53 signature using RNA-seq data of 153 breast cancer patients and TCGA public data [The first purpose of this study was to develop a diagnostic system for Figure TP53 signature data were derived from microarray data using FF samples. In order to evaluate whether the data acquired through nCounter analysis from FF and FFPE were comparable, we examined correlations between the expression levels of the 31 genes comprising the TP53 signature in FF and FFPE samples. The gene-set used in this study is the same as gene-set used in original TP53 signature. Some reports have confirmed good correlation between the expression values of FFPE and FF samples [TP53 signature with the nCounter system.The previous reports of  samples . Good coTP53 signature status as measured with the nCounter system was determined by analyzing samples from the 30 patients constituting the learning cohort. Fourteen patients had TP53 somatic mutations as detected by Sanger sequence  compared with TP53 signature WT type patients in the nCounter validation cohort  method. Of these 126 filtered genes, 78 were more frequently seen in the TP53 signature MT type than in the WT type , “microtubule-based process”,  or “chromosome organization”  , “regulation of cellular macromolecule biosynthetic process”  or “nucleic acid metabolic process”  . Next, sprocess” , 5. Anal results .Although somatic mutation call using RNA-seq was still challenging, we investigated whether a result similar to that of the TCGA data analysis would be obtained in analysis of our clinical breast cancer samples. We found that, in fact, similar results were obtained (data not shown).PD-L1 and CD8B mRNA expression values, copy number variance (CNV), and somatic mutation number (SMN) were compared between the TP53 signature status groups as defined according to the SVM method using TCGA microarray data. Both PD-L1 and CD8B mRNA expression values were higher in TP53 signature MT type than in TP53 signature WT type . In RNA-seq data of clinical samples, there was no significantly difference in CD8B expression value between TP53 signature status, but PD-L1 mRNA expression value was higher in TP53 signature MT type than in TP53 signature WT type (data not shown).Secondly, e Figure . In addiTP53 signature statuses as determined by nCounter were compared among intrinsic subtypes. The intrinsic subtype of each sample in the nCounter RNA-seq common cohort was determined using RNA-seq count data. All samples in the luminal A subtype were TP53 signature WT type. Half of the samples in the luminal B subtype were TP53 signature MT type. Many samples in the basal and Her2 enriched subtypes were TP53 signature MT type . Furthermore, BRCA1, RB1 mutation, and other gene mutations rarely reported in breast cancer but relating to DNA repair or chromosomal instability were found in samples with TP53 signature MT type along with TP53 gene mutation. These results indicated that the risk score of TP53 signature is an index of chromosomal or genome instability.In order to clarify the reason why MDM2 in tumor cells decreases their ability to activate p53 [MDM2 were diagnosed with TP53 signature MT type, although these samples did not show TP53 structural mutation. This result shows that TP53 signature can evaluate TP53 function comprehensively with or without TP53 structural mutations. Several reports have suggested that not only mutations in the TP53 gene itself but also structural abnormality in other molecules related to the pathway is the mechanism underlying tolerance to DNA-damaging drugs [TP53 signature is a new functional assay system that satisfies this requirement.The presence of high levels of vate p53 . We founng drugs –24. ThesTP53 signature status is a classification indicating genomic and chromosomal instability. Treatment decisions for breast cancer patients are typically based on the oncodriver genes that constitute the treatment targets, and intrinsic subtype is used to classify patients with regard to treatment target. Among the intrinsic subtypes, however, the basal-like subtype is considered to have no clear molecular treatment target. Our data showed that almost all patients with basal-like subtype belonged to the TP53 signature MT type. This result indicates that the basal subtype group is characterized by high genomic and chromosomal instability. Our data also showed that there were some patients with genomic and chromosomal instability in the luminal B and Her2-enriched subgroups. In patients with Luminal B type, about a half of them were TP53 signature MT type. Some Luminal B type patients with TP53 signature MT type did not show TP53 structural mutations. This result showed that there might be other mechanisms except for TP53 structural mutation to obtain chromosomal and genome instability in luminal B type patients. In the TCGA data, 75 patients were diagnosed as Luminal B type, of which 8 were deceased. Seven of these eight patients were diagnosed as TP53 signature MT type. These results showed that breast cancer patients could be classified in more detail using TP53 signature in addition to intrinsic subtype classification, and suggested that the prognosis of patients with TP53 signature MT type is poor with or without molecular target oncodriver genes because of genomic instability. The development of new treatment strategies for patients with genomic instability will improve prognosis of breast cancer patients.As explained above, TP53 signature MT type were consistent with these biomarkers for responsiveness to immune checkpoint inhibitors. These results indicate that the TP53 signature has a potential predictive value for responsiveness to immune checkpoint inhibitors. Indeed, Tolaney et al. reported in a phase 1b/2 study that eribulin mesylate in combination with pembrolizumab led to a high response rate  in patients with metastatic triple-negative breast cancer [TP53 signature MT type. To date, no clinical trials treating breast cancer patients with immune check point inhibitors as adjuvant therapy have been reported. To prove our hypothesis that the TP53 signature has a potential predictive value for responsiveness to immune checkpoint inhibitors, future prospective study or a retrospective sample analysis associated with a clinical trial using immune checkpoint inhibitors should be conducted.Recently, treatments with immune checkpoint inhibitors have led to good outcomes in many type of cancers –28. In st cancer , of whicTP53 signature that is suitable for clinical use. TP53 signature appears to be an index of chromosomal and genomic instability and to have potential predictive value for responsiveness to immune checkpoint inhibitors. The diagnostic system based on TP53 signature developed in this study will help in prognostic assessment, therapeutic decision-making, and treatment optimization in patients with breast cancer.Taken together, we developed a powerful diagnostic system based on TP53 signature status using nCounter. None of this cohort had received chemotherapy or endocrine therapy preoperatively. The same cohort had been used in our previous microarray-based study [TP53 status had been identified in all samples by means of TP53 DNA-direct sequencing.This study was approved by the Ethics Committee at the Tohoku University Hospital. We analyzed 30 patients’ FFPE samples, a set which we called the “nCounter learning cohort,” to determine the cutoff value for diagnosis of ed study , and TP5in situ, those with unknown histology or those with squamous cell carcinoma were excluded from the analysis. Among the validation cohort, we called the samples analyzed by nCounter only the “nCounter cohort” (n = 190) and cases analyzed by RNA-seq the “RNA-seq cohort” (n =153). From within these cohorts, we selected the curatively resected patients with stage I–II breast cancer and called them the “nCounter validation cohort” (n = 174) and the “RNA-seq validation cohort” (n = 132). Samples that were in both the “nCounter validation cohort” and the “RNA-seq validation cohort” were grouped in an “nCounter RNA-seq common cohort” (n = 120).The validation cohort was a prospective breast cancer case series from Hoshi General Hospital and Miyagi Cancer Center from September 2007 to October 2010. Written informed consent for the study was obtained from all patients. None of the patients received had chemotherapy or endocrine therapy preoperatively. A part of each surgical specimen of breast cancer was stored as FF tissue, and the remainder was stored as FFPE tissue. Among the patients enrolled in this study, patients with ductal carcinoma Glass slide specimens with 10-μm thick sections of FF and FFPE tissue blocks were prepared. Tumor cells were collected from FF tissue or FFPE tissue by macrodissection in reference to an HE-stained specimen. Total RNA was extracted from FF tissue or FFPE tissue using an RNeasy mini kit  or an RNeasy FFPE kit (Qiagen), respectively.TP53 signature gene set for nCounter. Primers for each of these 36 genes were designed. In accordance with the manufacturer's instructions, we measured the expression values of the 36 genes using nCounter with 200 ng of total RNA extracted from each FF or FFPE sample.A set of thirty-six genes including five internal control genes was used as the Five patients with both FFPE and FF samples were randomly selected, and expression data of these patients’ samples were measured using the nCounter system. We compared expression data of FFPE with that of FF samples in these five patients by Pearson's product moment correlation coefficient.RNA quality was monitored using the 2200 TapeStation system . Sequencing libraries were generated using the TruSeq RNA Library Prep kit  according to the manufacturer's directions. Sequencing was performed on the Illumina HiSeq2500 platform (Illumina) in rapid mode. Raw image files were processed using the Illumina pipeline for basecalling with default parameters. On average, we obtained 50 million 50-bp-long paired-end reads from the RNA-seq. RNA-seq reads were aligned using STAR2 against the hg19 reference genome . On averTP53 somatic mutations accurately, we checked all samples visually using Integrative Genomics Viewer.Somatic mutation call using RNA-seq data was performed according to the following two steps. First, the SNP call for RNA-seq data was performed using the Genome Analysis Tool kit (GATK version 3.6). Next, we defined the SNP, of which a few were reported in the database as somatic mutations. In brief, each sequenced read was aligned against the human reference genome (hg19) by STAR2, and duplicate-read removals were performed using Picard (version 2.6.0). Splitting reads in splicing site fields were performed using the SplitNCigarReads program, base quality score recalibration using the BaseRecalibrator program, and variant discovery using the Haplotype caller program. All programs were run according to the GATK tool kit. Annotation information was attached to all variants using ANNOVAR (version 20160201), and variants were filtered using the SNP databases 1000g2015aug_eas and esp6500. We identified the base substitutions, the proportion of which was under 1 percent in both SNP databases; the read count of the base substitutions as somatic mutations was over 20 (DP > 20). To determine TP53 signature was calculated using count data of nCounter or RNA-seq according to the following formula.Risk score of TP53 signature = (sum of counts of 22 genes that were upregulated in tumors with TP53 mutation) / (sum of counts of 9 genes that were downregulated in tumors with TP53 mutation)Risk score of TP53 signature status, because TP53 status according to Sanger sequence was known for all patients in this cohort. The cutoff value of TP53 signature score for TP53 signature status was determined to maximize accuracy of TP53 status according to Sanger sequence, and an ROC curve was drawn. TP53 status was determined using only TP53 signature score by the nCounter system, because all samples in the nCounter learning cohort were analyzed only by the nCounter system. In the RNA-seq cohort, on the other hand, only risk score was calculated and cutoff value for TP53 signature status was not determined, because TP53 status according to Sanger sequence was not known in this cohort. TP53 signature status was considered to be mutant type (TP53 signature MT type) when the risk score was higher than the cutoff value, and wild type (TP53 signature WT type) when the risk score was lower than the cutoff value. R package “ROCR” was used to draw the ROC curve and calculate the area under the curve (AUC) [We used the learning cohort to determine the cutoff value for ve (AUC) .TP53 signature status as determined using the nCounter system was evaluated using the chi-square test or the Kruskal–Wallis exact test. RFS rates were calculated according to the Kaplan–Meier method and evaluated by the log-rank test. RFS was defined as the period from the date of operation to the date of recurrence. Univariate and multivariate analysis of various parameters for the prediction of recurrences was conducted using the Cox proportional hazards model. Regardless of the statistical test performed, differences with P < 0.05 were considered statistically significant. In the nCounter RNA-seq common cohort, TP53 structural mutation data was added to clinical factors and TP53 signature status as a predictive factor. All static analysis was conducted using R ver3.25.The association between the various clinicopathological parameters and TP53 signature, Mammaprint, OncotypeDX, and PAM50. Concordance index calculated using the R package survcomp was used to compare predictive performance [Risk scores of Mammaprint, OncotypeDX, and PAM50 were calculated using RNA-seq count data from the nCounter RNA-seq common cohort. R package, genefu version 2.6.0 was used to calculate risk scores . Predictformance . Intrinsformance .http://www.cbioportal.org/study?id=brca_tcga_pub).All TCGA data was retrieved from cbioportal . The differences in CNV and SMN between the TP53 signature groups were compared by the Mann-Whitney test.The differences in CNV and SMN were compared between the different PD-L1 and CD8B obtained from TCGA microarray data were compared between the TP53 signature status groups. Expression values of both PD-L1 and CD8B were compared between TP53 signature status groups by Wilcox test.Expression values of p value under 0.1 was considered indicative of a statistically significant difference.GO enrichment analysis was performed using David ver6.7 , 44. In


Hepatocellular carcinoma is one of the most heterogeneous cancers, as reflected by its multiple grades and difficulty to subtype. In this study, we integrated copy number variation, DNA methylation, mRNA, and miRNA data with the developed “cluster of cluster” method and classified 256 HCC samples from TCGA (The Cancer Genome Atlas) into five major subgroups (S1-S5). We observed that this classification was associated with specific mutations and protein expression, and we detected that each subgroup had distinct molecular signatures. The subclasses were associated not only with survival but also with clinical observations. S1 was characterized by bulk amplification on 8q24, TP53 mutation, low lipid metabolism, highly expressed onco-proteins, attenuated tumor suppressor proteins and a worse survival rate. S2 and S3 were characterized by telomere hypomethylation and a low expression of TERT and DNMT1/3B. Compared to S2, S3 was associated with less copy number variation and some good prognosis biomarkers, including CRP and CYP2E1. In contrast, the mutation rate of CTNNB1 was higher in S3. S4 was associated with bulk amplification and various molecular characteristics at different biological levels. In summary, we classified the HCC samples into five subgroups using multiple “-omics” data. Each subgroup had a distinct survival rate and molecular signature, which may provide information about the pathogenesis of subtypes in HCC. Hepatocellular carcinoma (HCC) is the fifth leading cancer worldwide. It is also the third most common cause of death in all cancers . HCC hasOver the past decade, efforts have been devoted to the molecular classification of HCC. These studies were mainly based on an analysis of genomic alterations, including somatic mutations and copy number variations . Transcrhttp://cancergenome.nih.gov/) provides thousands of samples of various cancers, including data on somatic mutation, DNA methylation, miRNA-seq, copy number variation (CNV), and clinical observations. A lack of methods to integrate these data regarding different biological characteristics has posed a huge problem. In recent years, the method based on the “cluster of cluster” has proven to be a powerful way to detect heterogeneity during carcinogenesis [The alterations of cancer cells can occur on various levels, including somatic mutation, copy number variation (CNV) , methylaogenesis , 15, andIn this vein, we screened the landscape of DNA methylation, copy number variation, gene expression and miRNA levels in over 400 samples of HCC provided by TCGA. We employed and further developed the “cluster of cluster” method to analyze the data. We identified five subgroups according to the improved method, and the subgroups had distinct survival rates, clinical observations and molecular signatures. Subsequently, we combined somatic mutation data for these samples with the subgroups. The mutation landscapes of several important HCC-related genes were significantly different among the subgroups, including TP53, CTNNB1, BAP1, MUC4 and SAGE1. The subgroups were significantly correlated with clinical observations. Distinct molecular signatures identifying each subgroup were summarized, including telomere demethylation, specific gene promoter methylation, PRSS/PRSS2P, 8q24 amplification, UGT2B17 deletion, prognostic miRNA/mRNA expression, and different protein expression levels.The available samples in each platform used in our study are listed in We downloaded DNA methylation data from TCGA and combined 375 samples (level 3) to construct a matrix based on the CpG sites. Loci with NA (not available) in any of these samples were removed. We calculated the standard deviation (SD) for each locus and retained the top 10000 CpG sites with the highest SD values for further analysis.An expression matrix was built with 269 samples from gene scaled estimates (level 3), and only genes that were detected in all samples were retained for further analysis. We then log2 transformed the expression levels. Values less than -26 were replaced with -26 (bottom 0.1%). The standard deviation (SD) of every gene was calculated. The top 6000 genes with the highest SD values were selected for further analysis. After estimating an expression value by RPM, miRNAs (level 3) that were detected in all samples were retained for further analysis after log 2 transformation. Values less than 0 were replaced with 0 (bottom 0.1%). The top 80 miRNAs with the highest SD values were used.Mutations that were called and curated (level 2) by TCGA were downloaded. The mutation matrix with samples/genes as columns/rows were constructed (1 as mutated and 0 as non-mutated). The normalized protein expression levels (level 3) evaluated by microarray were downloaded from TCGA.The COC were performed with the following stepsDivide mRNA into 2 to 15 sub- clusters: 2 to 15 for CNV, 2 to 7 for miRNA, and 2 to 15 for methylation sites;Divide samples into 2 groups according to the features in sub- clusters on platforms ;If the one of sample size of the 2 groups is less than 10, replace the values of the features in sub- clusters with NA (not available) and return back to step 2; if not, divide the next sub- cluster;Rename the values of samples on sub- clusters with 0 or 1;Combine the sub- clusters to form a matrix. The row represents sub- clusters and column as samples;Divide samples with matrix constructed in step 5 into 2 to 7 subgroups;Calculate the survival difference of subgroups. If significant, store the sub- cluster number of platforms; if not, discard the combination;Calculate the recurrence of sub- cluster number of mRNA, miRNA, CNV and DNA methylation, and select the most recurrent for further analysis;Divide the samples into several groups according to “ConsensusClusterPlus”.https://www.r-project.org/). The circos plot was drawn using the R package “RCircos” [http://genome.ucsc.edu/).The analysis was performed by R , which indicated that our developed method performs better than the original COC method and suggests that the method is more powerful.To better interpret our classification results, we correlated the subgroups with clinical information. We found that gender, alcohol consumption, alpha-fetoprotein (AFP) level, and the AJCC (American Joint Committee on Cancer) staging level of the primary tumor were factors associated with these subgroups . There wWe analyzed the molecular signatures of these subgroups. Due to the small sample size of S5, we first analyzed S1-S4. In general, we noticed that mRNA4, mRNA9, CNV8, mRNA11, mRNA13 and CNV9 were enriched in S1. Deletions of UGT2B17 , PRSS2/PSubgroup specific copy number variations were not detected in S2 or S3. Cell cycle, extracellular related genes (mRNA3), and plasma genes (mRNA15) were altered in S2 at the transcriptome level  were common in S4 . PreviouDue to the small sample size of S5, the important characteristics of S5, including the protein levels of TP53/BAK/PTEN/CCND1, were analyzed across S1 to S4 (data not shown). The most important signatures of S5 were clusters mRNA10, mRNA12, mRNA15, and miRNA6 , and theThe multiple types of biological data comprehensively reveal the alterations characteristic of the individual subtypes . HoweverThe integration of multiple biological levels of data facilitates cancer classification, especially for highly heterogeneous cancer. In our work, we integrated the copy number variation, DNA methylation, gene expression and microRNA expression in more than 400 samples. Among them, all data for multiple biological levels were available for 256 samples. We performed “cluster of cluster” analysis of these samples, and five distinct subgroups were identified. We validated the findings with cross-validation and PCA analysis, and the differences between subtypes were also detected at the genetic mutation level. Each subgroup had molecular signatures that were either previously reported or newly found. Consistent with this result, the classification is associated with gender, alcohol intake, AFP level, and the AJCC staging system.Altered features in most samples include the amplification of the 8q24 genes HLA-DQB/DQB and the overexpression of IGF2/H19. Among the samples, 8q24 is a frequently amplified locus containing a set of oncogenes in many cancer types . IncreasWe noted that UGT2B17, an enzyme that catalyzes the transfer of glucuronic acid from uridine diphosphoglucuronic acid to a variety of substrates, was significantly deleted in S1. UGT2B17 is a frequently reported gene in various cancers and is frequently associated with polymorphism deletion. According to previous reports, up to 44% of the patients had a deletion of UGT2B17 in Chinese HBV affected HCC samples . In addiBoth S2 and S3 had hypomethylated chromosome terminal regions and lower TERT and DNMT1/3B expression levels (as observed in Methyl3 and Methyl4). However, the hypomethylation of Methyl5/6 was also identified in S3, which suggests that S3 is less stable. Some transcriptomic characteristic genes were associated with poor prognosis, including increased CYP2E and attenuated CRP and other genes involved in the cell cycle. According to a previous study, CYP2E1 is decreased in HCC, and the overexpression of CYP2E1  can induThe number of distinct molecular signatures in S4 was much lower than those of the other groups. However, we still noticed that in S4, miRNA 203, a tumor suppressor gene that is involved in invasion and migration  and is dTaken together, our integration of multiple biological data levels revealed the landscape of heterogeneity of HCC and successfully classified subtypes that are associated with cancer survival by their molecular signatures.S1 Fig(TIFF)Click here for additional data file.S2 FigDensity of a-d) CNV/mRNA/miRNA/methylation in COC analysis and e) “ConsensusClusterPlus” analysis show that the subgroup is stable when the number reached 5.(TIFF)Click here for additional data file.S3 FigThe subgroups can be divided by the first four main components.(TIF)Click here for additional data file.S4 FigCopy numbers of a) PRSS2/PRSS3P2 and b) GSTT1/GSTTP2 in S1-S4.(EPS)Click here for additional data file.S1 TableAnd for integrated study, samples presented in all these four platforms were used.(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.


The role of minimum β-divergence method in this article is to produce the robust estimators for the location and scale parameters based on the training dataset and outlier detection and modification in test dataset. The performance of the proposed method depends on the tuning parameter β. It reduces to the traditional naïve Bayes classifier when β → 0. We investigated the performance of the proposed beta naïve Bayes classifier (β-NBC) in a comparison with some popular existing classifiers  using both simulated and real gene expression datasets. We observed that the proposed method improved the performance over the others in presence of outliers. Otherwise, it keeps almost equal performance.The naïve Bayes classifier (NBC) is one of the most popular classifiers for class prediction or pattern recognition from microarray gene expression data (MGED). However, it is very much sensitive to outliers with the classical estimates of the location and scale parameters. It is one of the most important drawbacks for gene expression data analysis by the classical NBC. The gene expression dataset is often contaminated by outliers due to several steps involved in the data generating process from hybridization of DNA samples to image analysis. Therefore, in this paper, an attempt is made to robustify the Gaussian NBC by the minimum  The Gaussian naïve Bayes classifier (NBC) overcomes this difficulty of Gaussian LBC by taking the normality and independence assumptions on the variables. If these two assumptions are violated, then the nonparametric version of NBC is suggested in [β-divergence method within two steps. At step-1, the minimum β-divergence method [β-weight function. Then an attempt is made to propose criteria to detect the outlying components in the test data vector and the modification of outlying components by the reasonable values. It will be observed that the performance of the proposed method depends on the tuning parameter β and it reduces to the traditional Gaussian NBC when β → 0. Therefore, we call the proposed classifier as β-NBC.Classification is a supervised learning approach for separation of multivariate data into various sources of populations. It has been playing significant roles in bioinformatics by class prediction or pattern recognition from molecular OMICS datasets. Microarray gene expression data analysis is one of the most important OMICS research wings for bioinformatics . There aested in . In thisested in . There aested in , 15. Howe method –18 attemβ-NBC in a comparison with several versions of robust linear classifiers based on M-estimator [β-NBC outperforms existing robust linear classifiers as mentioned earlier. Then we investigate the performance of the proposed method in a comparison with some popular classifiers including Support Vector Machine (SVM), k-nearest neighbors (KNN), and AdaBoost; those are widely used in gene expression data analysis [An attempt is made to investigate the robustness performance of the proposed stimator , 20, MCDstimator , 22, Ortstimator , and Feastimator –26. We oanalysis –29. We oxjk = T; j = 1, 2,…, Nk} of size Nk for k = 1,2,…, K, where xijk denotes the jth observation of the ith variable in the kth population/class (Ck). Then the NBCs assign a class label  k as follows:fk of kth population/class (Ck) can be written asθk = {μk, Λk}, and here μk = T, is the mean vector and the diagonal covariance matrix isThe naïve Bayes classifiers (NBCs)  are a fap(Ck) are known and the maximum likelihood estimators (MLEs) μk and Λk are obtained based on the training dataset as follows:N = ∑k=1KNk;  i = 1,2,…, p.We assume that the prior probabilities μk) and diagonal covariance matrix (Λk); those are estimated by the maximum likelihood estimators (MLEs) as given in (β-divergence method [It is obvious from -2) that that2) tgiven in –6) base baseμk) e method –18.g(xk) be the true density and f(xk∣θk) be the model density for kth populations; then the β-divergence of two p.d.f can be defined byβ > 0 and Dβ(g(xk), f(xk∣θk)) ≥ 0. Equality holds if and only if g(xk) = f(xk∣θk) for all xk. When β tends to zero, β-divergence reduces to Kullback Leibler (K-L) divergence; that is,β-divergence estimator is defined byθk = {μk, Λk} and the minimum β-divergence estimators μk and the diagonal covariance matrix Λk, respectively, are obtained iteratively as follows:β-weight function, which plays the key role for robust estimation of the parameters. If β tends to 0, then ,,g(xk) beμk is initialized by the median vector, since mean and median are same for normal distribution and the median (Me) is highly robust against outliers with 50% breakdown points to estimate central value of the distribution. The median vector of kth class/population is defined ask is initialized by the identity matrix (I). The iterative procedure will converge to the optimal point of the parameters, since the initial mean vector would belong to the center of the dataset with 50% breakdown points. The proposed estimators can resist the effect of more than 50% breakdown points if we can initialize the mean vector μk by a vector that belongs to the good part of the dataset and the variance-covariance Λk by the identity (I) matrix. More discussion about high breakdown points for the minimum β-divergence estimators can be found in [The mean vector found in .β by CV, we fix the tuning parameter β to β0. The computation steps for selecting appropriate β by T-fold cross validation is given below.To select the appropriate Dk = {xjk; j = 1,2,…, Nk} is split into T subsets; Dk(1), Dk(2),…, Dk(T) where Dk(t) = {xtk; t = 1,2,…, Ntk} and ∑t=1TNtk = Nk.Dataset Dkc(t) = {xsk∣xsk ∉ Dk(t), s = 1,2,…, Ntkc = (Nk − Ntk)} for t = 1,2,…, T.Let Dkc(t).Estimate ively by  based onDk(t), for Compute CV(t) using dataset End.β by𝔇k,β0(β) =  (1/Nk)∑t=1TCVk(t).Computed suitable Nk) is small such that Ntkc = (Nk − Ntk) < p, then T = Nk (leave-one-out CV) can be used to select the appropriate β. More discussion about β selection also can be found in [If the sample size  if x ∉ Ck or contaminated by outlier. Therefore, the β-weight function  + dk(2) + ⋯+dk(r), where r = round (p/2). Then the unlabeled test data vector x can be classified asx  is classified in to class k, then its ith component is said to be outlying if dki > Skr  . Then we update x  by replacing its outlying components with the corresponding mean components from the mean vector  kth population. Let x∗ be the updated vector of x. Then we use x∗ instead of x to confirm the label/class of x  using (When the unlabeled data vector equation . If the β-NBC) classifier in a comparison with four popular classifiers , we generated both training and test datasets from m = 2 multivariate normal distributions with different mean vectors  of length p = 10 but common covariance matrix . In this simulation study, we generated N1 = 40 samples from the first population and N2 = 42 samples from the second population for both training and test datasets. We computed the training error and test error rate for all five classifiers using both original and contaminated datasets with different mean vectors {; t = 0,…, 9}, where the other parameters remain the same for each dataset. For convenience of the presentation, we distinguish the two mean vectors in such a way in which the second mean vector is generated by adding t with each of the components of the first mean vector.To investigate the performance of our proposed (β-NBC) in a comparison of the classical NBC for the classification of object into two groups, let us consider a model for generating gene expression datasets as displayed in N. First we generate a training gene-set using the data generating model . Then we generate a test gene-set using the same model with the same parameters d = 5 and σ2 = 1 as before, where p11 = 30 genes denoted by {A31, A32,…, A60} are generated for group  A and p22 = 30 genes denoted by {B31, B32,…, B60} are generated for group  B with n11 = 25 normal individuals and n22 = 25 patients .To investigate the performance of the proposed classifier (ng model  with parβ-NBC) in a comparison of some other robust linear classifiers based on the robust estimators  as mentioned earlier for the classification of object into different groups, we have generated the training and test datasets from m = 2, 3 multivariate normal distributions with variables p = 10, 5, respectively. We consider n1 = 40 and n2 = 35 (n = n1 + n2) samples from m = 2 different multivariate normal populations Np and Np. Here µ2 = µ1 + Ω with Ω = 0,1,…, 10 such that µ1 = µ2 for Ω = 0; otherwise µ1 ≠ µ2, where the scalar number Ω is the common difference between two corresponding mean components of μ1 and μ2, respectively. Similarly, for generating the training and test datasets, we consider the n1 = 30, n2 = 30, and n3 = 30 (n = n1 + n2 + n3) samples from m = 3. It is carried out with different means and common variance-covariance matrix of multivariate normal populations Np, Np, and Np. In this case we consider μk = μk + Ω with Ω = 0,1,…, 10 and k = 1,2, 3 such that μ1 = μ2 = μ3 for Ω = 0; otherwise μ1 ≠ μ2 ≠ μ3, where the scalar number Ω is the common difference among the corresponding mean components of μ1, μ2, and μ3, respectively.To demonstrate the performance of the proposed classifier (β-NBC) in a comparison with four popular classifiers  with the real gene expression dataset, we considered the head and neck cancer (HNC) gene expression dataset from the previous work [To demonstrate the performance of the proposed classifier  is also statistically significant at 5% level of significance. So we may conclude from simulated dataset 1 that our proposed method performed better than the other classical methods for the contaminated dataset. It keeps equal performance in absence of outliers for the original dataset.From β-NBC) in a comparison of the classical NBC for the classification of objects into two groups, we considered the simulated dataset 2. Figures To investigate the performance of the proposed classifier , false positive rate (FPR), area under the ROC curve (AUC), and partial AUC (pAUC) based on 50 replications of the dataset to measure the performance of all classifiers. A method is said to be better than others, if it produces larger values of TPR, AUC, and pAUC and smaller values of FPR and MER.p = 15 for the two- (2-) class classification. The performance measures have been estimated by the classical, FSA, MCD, MVE, MCD-A, MCD-B, MCD-C, OGK, and proposed methods. They show the average estimates of AUC and pAUC for seven classifiers using simulated dataset 3 in absence and presence of outliers. We observed that in absence of outliers all the classifiers produce almost similar results. The proposed classifiers produced better result than the classical NBC and other robust estimators in presence of different levels  of outliers. Also MCD, MCD-A, MCD-B, and MCD-C show the constant performance result at the same level of outlier rate and varied for the different level of outlier rates. The ROC analysis also supported these results which are shown in Figures p = 5 the number of variables. The performance measures were estimated for each of these methods. To investigate the performance of the proposed method in a comparison with other methods  for multiclass (3) classification problem. We generated simulated datasets 3 based on 50 replicated with We also investigated the performance of the proposed method in real microarray gene expression dataset. The normalized Head and Neck cancer (HNC) dataset is considered here . The RNAβ-NBC) in this dataset to classify cancer genes  performs better for identifying the gene group in the HNC dataset. For classification problem, we have considered half of the differentially expressed genes (594/2 = 297) as training gene-set and we identified their group using hierarchical clustering (HC). p values <0.01 for the different performance results excluding MCC and MER. Then we may say that they are highly statistically significant. The MCC and MER are statistically significant at 5% level of significance because of the p values < 0.05. Hence, the performances of the proposed methods in real HNC data analysis are better than classical and other methods. Also this data set is contaminated by outliers reported in [We also computed different performance measures , negative predicted value (NPV), prevalence, detection rate, detection, prevalence, Matthews correlation coefficient (MCC), and misclassification error rate) by the five classification methods  using HNC dataset . From Taorted in . So we cβ-divergence method within two steps. For both simulated and real data analysis, at first, the mean vectors and the diagonal covariance matrices were computed by the minimum β-divergence estimators for the Gaussian NBC based on the training dataset. Then outlying test data vectors were detected from the test dataset using the β-weight function and outlying components in each test data vector were replaced by the corresponding values of their estimated mean vectors. Then the modified test data vectors were used as the input data vectors in the proposed β-NBC for their class prediction or pattern recognition. The rest of the data vectors from the test dataset were directly used as the input data vectors in the proposed β-NBC for their class prediction or pattern recognition. We observed that the performance of the proposed method depends on the tuning parameter β and the initialization of the Gaussian parameters. Therefore, in this paper, we also discussed the initialization procedure for the Gaussian parameters and the β-selection procedure using cross validation in Sections β → 0. Therefore, we call the proposed classifier β-NBC. We investigated the robustness performance of the proposed β-NBC in a comparison of several robust versions of linear classifiers based on MCD, MVE, and OGK estimators taking the smaller number of variables/genes (p) with larger number of patients/samples (n) in the training dataset, since these types of robust classifiers also suffer from the inverse problem of its covariance matrix in presence of large number of variables/genes (p) with small number of patients/samples (n) in the training dataset. We observed that the proposed β-NBC outperforms the existing robust linear classifiers as early mentioned in presence of outliers. Otherwise, it keeps almost equal performance. Then we investigated the performance of the proposed method in a comparison of some popular classifiers including Support Vector Machine (SVM), K-Nearest Neighbors (KNN), and AdaBoost which are widely used for gene expression data analysis [p < n and (ii) p > n, and it can resist the effect of 50% breakdown points. If the dataset does not satisfy the normality assumptions, then the proposed method may show weaker performance than others in absence of outliers. However, the nonnormal dataset can transform to the normal dataset by some suitable transformation like Box-Cox transformation [β-NBC) in a comparison of some popular existing classifiers  including some robust linear classifiers  using both simulated and real gene expression datasets, where simulated datasets satisfied the normality and independent assumptions. We observed that the proposed method improved the performance over the others in presence of outliers. Otherwise, it keeps almost equal performance. Usually gene expression datasets are often contaminated by outliers due to several steps involved in the data generating process from hybridization to image analysis. Therefore the proposed method would be more suitable for gene expression data analysis.In this paper, we discussed the robustification of Gaussian NBC using the minimum analysis –29. In tormation . Then thβ-NBC for estimating the robust location and scale parameters. In the simulation studies 1 and 2, we showed that, in presence of outliers, the proposed β-NBC outperforms other popular classifiers while datasets were generated from the multivariate and univariate normal distribution, respectively, and it keeps equal performance with the other classifiers, in absence of outliers. We also investigated the robustness performance of the proposed β-NBC in a comparison of linear classifier using some popular robust estimators in the simulation study 3. From this simulation study we observed that the proposed β-NBC outperforms existing robust linear classifiers. Finally we applied in the real HNC dataset; our proposed β-NBC showed better performance than the other traditional classifiers. Therefore, we may conclude that, in presence of outliers, our proposed β-NBC outperforms other methods using both simulated and real datasets.The accurate sample class prediction or pattern recognition is one of the most significant issues for MGED analysis. The naïve Bayes classifier is an important and widely used method for the class prediction in bioinformatics. However, this method suffers from outlying problems to estimate the location parameters in the MGED analysis. To overcome this we proposed The R source code for the robust naive Bayes classifier (β-NBC). The robust classification of microarray gene expression data.


Identifying molecular signatures of disease phenotypes is studied using two mainstream approaches: (i) Predictive modeling methods such as linear classification and regression algorithms are used to find signatures predictive of phenotypes from genomic data, which may not be robust due to limited sample size or highly correlated nature of genomic data. (ii) Gene set analysis methods are used to find gene sets on which phenotypes are linearly dependent by bringing prior biological knowledge into the analysis, which may not capture more complex nonlinear dependencies. Thus, formulating an integrated model of gene set analysis and nonlinear predictive modeling is of great practical importance.In this study, we propose a Bayesian binary classification framework to integrate gene set analysis and nonlinear predictive modeling. We then generalize this formulation to multitask learning setting to model multiple related datasets conjointly. Our main novelty is the probabilistic nonlinear formulation that enables us to robustly capture nonlinear dependencies between genomic data and phenotype even with small sample sizes. We demonstrate the performance of our algorithms using repeated random subsampling validation experiments on two cancer and two tuberculosis datasets by predicting important disease phenotypes from genome-wide gene expression data.We are able to obtain comparable or even better predictive performance than a baseline Bayesian nonlinear algorithm and to identify sparse sets of relevant genes and gene sets on all datasets. We also show that our multitask learning formulation enables us to further improve the generalization performance and to better understand biological processes behind disease phenotypes. Predictive modeling is frequently used to find molecular signatures of disease phenotypes from genomic data, which helps us better understand underlying biological processes behind phenotypes and reduce data acquisition cost for future clinical samples by doing targeted profiling instead of genome-wide screens. To this aim, supervised machine learning methods such as linear classification and regression algorithms are trained to predict disease phenotypes, and features with relatively higher importance values (e.g. features with larger magnitude weights) in these parametric models are included into the signature. However, as illustrated by existing studies , 2, moleGene set analysis methods try to identify gene sets on which disease phenotypes are dependent by calculating an enrichment score for each gene and transforming these scores into gene set scores using a summarization procedure . The maiTo benefit from the best of both worlds, integrating gene set analysis and predictive modeling is already considered in many existing studies –7, whichWe suggest to integrate these two components using a nonlinear framework by extending our earlier Bayesian formulation . Here, wWe perform repeated random subsampling validation experiments on two cancer and two tuberculosis datasets to demonstrate the better predictive performance of our two algorithms over a baseline Bayesian nonlinear algorithm and to show the biological relevance of the genes and gene sets selected to disease phenotypes modeled.In this study, we use two cancer and two tuberculosis datasets, where we solve binary classification problems to predict phenotype values from genomic data and to extract molecular signatures of disease phenotypes.Micro-satellite instability is a hypermutable phenotype caused by the loss of DNA mismatch repair activity. It is frequently observed in several tumor types such as colorectal, endometrial, gastric, ovarian and sebaceous carcinomas . Tumors https://tcga-data.nci.nih.gov), which groups the patients into three categories: (i) ‘micro-satellite instability high’ (MSI-H), (ii) ‘micro-satellite instability low’ (MSI-L) and (iii) ‘micro-satellite stable’ (MSS). The preprocessed genomic characterizations of primary tumors from the patients (i.e. mRNA gene expression) are downloaded from https://www.synapse.org/%23%21Synapse:syn300013, where 20,530 normalized gene expression intensities are provided for each profiled primary tumor. We remove the patients with missing phenotype value or genomic data from further analysis. At the end, there are 261 and 330 patients with available phenotype value and genomic data for COADREAD and UCEC datasets, respectively. Table The phenotype values of cancer patients for both datasets are downloaded from the TCGA website  ‘active tuberculosis’ (ATB), (ii) ‘latent tuberculosis infection’ (LTBI) and (iii) ‘other disease’ (OD). These repositories contain background subtracted and quantile normalized intensities of 47 323 probes for each individual. There are 537 and 334 individuals with available phenotype and genomic data for ADULT and PEDIATRIC datasets, respectively. Table We consider the problem of predicting phenotype values from genomic data using classification algorithms. Instead of training classifiers that use all available features, we want to develop classifiers that use very few but biologically relevant input features to identify a molecular signature of the phenotype and to reduce the data acquisition cost for test samples. However, the molecular signatures identified from, for example, gene expression data are not robust when we have limited training data , 2. In sN is the number of data points, and m, which may be a set of genes from a biological pathway or a set of genes with similar biological functions, and P is the number of gene sets.We formulate the prediction task as a binary classification problem defined on the genomic data, denoted as domain p, small n). (ii) We can learn better classifiers using nonlinear kernels such as the Gaussian kernel (i.e. kernel trick). (iii) We can use domain-specific kernels (e.g. graph and tree kernels for structured objects) to better capture the underlying biological processes .We define the factors for the first part of our probabilistic model as ζ(·),η(·) and π(·) denote the shape parameters and the success probability parameter of their arguments. We can update the approximate posterior distributions as rm is defined as μ,Σ,ρ(·)) denotes the truncated normal distribution with the mean vector μ, the covariance matrix Σ and the truncation rule ρ(·) such that TruncatedNormal)∝Normal if ρ(·) is true, and TruncatedNormal)=0 otherwise. The approximate posterior distributions can be updated as The factors for the second part of our probabilistic model are defined as q(a) and obtain the posterior predictive mean of the latent variables g⋆ for a new data point x⋆ as We can replace f⋆ can also be found by replacing q(b)q(e|s)q(s): f⋆〉 to predict the class label by looking at its sign.The posterior predictive mean of the predicted output T datasets, and, for each dataset, we have an independent and identically distributed sample Nt is the number of data points in the dataset t. We also have a list of gene sets We formulate the joint modeling of prediction tasks on multiple datasets using a multitask learning approach, which models distinct but related tasks conjointly to improve overall generalization performance. We are given Our single-task learning model SBMKL is extended towards multitask learning to obtain ‘sparse Bayesian multitask multiple kernel learning’ (SBMTMKL).The distributional assumptions of the first part can be modified as The distributional assumptions of the second part are written as The distributional assumptions of the third part can be modified as q(Θ) as a factorized approximation: We approximate the posterior distribution over the model parameters and the latent variables by a variational distribution: rm is defined as The update equations of the approximate posterior distributions for all model parameters and latent variables are very similar to those of SBMKL except for the binary indicator variables. We can update the approximate posterior distribution of them as q(at) instead of gt,⋆ for a new data point xt,⋆ in the task t as We can use the approximate posterior distribution ft,⋆ can also be found by replacing q(bt)q(et|s)q(s): ft,⋆〉 to predict the class label by looking at its sign.The posterior predictive mean of the predicted output a⊤ki+b). We again learn the posterior distribution over the model parameters and the latent variables using a deterministic variational approximation as we do for our methods. We call this algorithm ‘Bayesian relevance vector machine’ (BRVM). We have three main reasons for choosing this particular baseline algorithm: (i) BRVM can make use of kernel functions to obtain nonlinear models like our methods. (ii) We can see the effect of using gene set information by comparing our methods to BRVM. (iii) BRVM uses the same type of inference mechanism with our methods.We use a kernelized Bayesian classification algorithm, which is known as relevance vector machine , as the To illustrate the effectiveness of our proposed methods SBMKL and SBMTMKL, we report their results on four datasets (i.e. two cancer and two tuberculosis datasets) and compare them to the baseline algorithm BRVM, which does not make use of gene set information, using repeated random subsampling validation experiments.For each dataset, we create 100 random train/test splits to obtain robust results. For each replication, the training set is defined by randomly selecting 75 % of the data points with stratification on the phenotype, and the remaining 25 % of the samples are used as the test set. The training set is normalized to have zero mean and unit standard deviation, and the test set is then normalized using the mean and the standard deviation of the original training set.We extract gene sets from ‘the Molecular Signatures Database’ (MSigDB) , which c2 denotes the ℓ2-norm, and we set the kernel width s to the mean of pairwise Euclidean distances between the data points: To calculate similarity between data points for all methods, we use the Gaussian kernel: For BRVM, we calculate a single kernel over all input features. For SBMKL and SBMTMKL, we calculate a separate kernel function for each gene set over the corresponding features. Note that the Gaussian kernels calculated on the gene sets take values between 0 and 1 by definition, and there is no need for eliminating small/large gene sets or performing additional normalization steps to remove the effect of gene set size.αλ,βλ)=, = and ν=1. The hyper-parameter values of SBMKL and SBMTMKL are selected as =,σg=0.1,=,=,= and ν=1. Note that  are set to these particular values to produce very sparse binary indicator variables, leading to classifiers with very few gene sets used for prediction. For BRVM, we perform 200 iterations during variational inference, whereas we perform 50 iterations for SBMKL and SBMTMKL.The hyper-parameter values of BRVM are selected as (We use ‘area under the receiver operating characteristic curve’ (AUROC) to compare classification results. AUROC is used to summarize the receiver operating characteristic curve, which is a curve of true positives as a function of false positives while the threshold to predict labels changes. Larger AUROC values correspond to better performance.On the cancer datasets, we run binary classification experiments to separate MSI-H patients from others (i.e. MSI-L and MSS), which is in agreement with the earlier studies that combine MSI-L and MSS tumors into the same group . For BRVOn the tuberculosis datasets, we perform binary classification experiments to separate individuals with ATB from others , which is critical in clinical settings because we should correctly identify individuals who need tuberculosis treatment . Figure To illustrate the biological relevance of our methods, we analyze their abilities to identify relevant gene sets based on the binary indicator variables inferred during training. For each gene set, we count the number of replications in which the corresponding binary indicator variable is nonzero. Table We also count the number of replications for each gene in which it is included in the final classifier. Figure We also evaluate the gene set selection results of our methods on the tuberculosis datasets. Table Figure Integrating gene set analysis and predictive modeling is already considered by many existing studies, which fail either to capture nonlinear dependencies between genomic data and phenotype or to model multiple related datasets conjointly.In this study, we integrate gene set analysis and nonlinear predictive modeling of disease phenotypes by casting this problem into a binary classification framework defined on the gene sets with a sparsity-inducing prior on their weights. To this aim, we propose a Bayesian multiple kernel learning algorithm, which produces a classifier with sparse gene set weights, by extending our earlier Bayesian formulation . We thenTo demonstrate the performance of our algorithms SBMKL and SBMTMKL, we perform repeated random subsampling validation experiments on four datasets of two major human diseases, namely, cancer and tuberculosis. On the two cancer datasets , 13, we In the experiments reported, we use real-valued gene expression measurements as genomic data. Our methods can also be applied to discrete data such as mutation profiles of tumors, which are hard to use in classical gene set analysis methods due to their very sparse nature. As a possible extension, we plan to use our kernel-based formulations on cancer datasets to identify driver mutations using kernels for discrete data such as the Jaccard similarity coefficient.


DPP4, SCG5 and CA12) has demonstrated promise in thyroid carcinoma assessment. However, more reliable prediction methods combining clinical features with genomic signatures with high accuracy, good stability and low cost are needed.A key challenge in thyroid carcinoma is preoperatively diagnosing malignant thyroid nodules. A novel diagnostic test that measures the expression of a 3-gene signature  were compared. Seven clinical characteristics were selected based on a training set (539 patients) and tested in three test sets, yielding predictive accuracies of 82.3% (n = 232), 81.4% (n = 70), and 81.9% (n = 72). The predictive sensitivity, specificity, and accuracy were 72.3%, 80.5% and 76.8% for the model based on the gene expression signature, 66.2%, 81.8% and 74.6% for the model based on the clinical data, and 83.1%, 84.4% and 83.8% for the combined model in a 10-fold cross-validation (n = 142).These findings reveal that the integrated model, which combines clinical data with the 3-gene signature, is superior to models based on gene expression or clinical data alone. The integrated model appears to be a reliable tool for the preoperative diagnosis of thyroid tumors. The incidence of thyroid carcinoma has substantially increased in the United States in recent years. In 2008, the estimated number of new cases of thyroid cancer was 37,340, in contrast to the estimated 60,220 new cases in 2013, which indicates that the incidence nearly doubled in five years [A key challenge in thyroid cancer research lies in distinguishing benign thyroid nodules from malignant tumors –7. The pWe hypothesis that the integration of small gene signatures and clinical data would substantially impact the predictive accuracy of thyroid tumor models and have promise or application in routine clinical practice. First, clinical data, including patient history, medical examination results and ultrasound imaging analysis, are typically available and form the foundation of day-to-day clinical decisions. Furthermore, data on clinically important variables have the distinct advantage of a relatively low noise level, which is important for cancer prediction accuracy.Second, gene expression profiles have demonstrated the power to help determine the heterogeneity of various tumors , 9, 10. DPP4, SCG5 and CA12—that is measured via qPCR and performed well in distinguishing benign and malignant thyroid nodules[In our previous study, we identified a three-gene signature—To select and validate clinical variables that are significantly correlated with thyroid tumor malignancy, we collected data from 771 patients with clinically significant thyroid nodules who had undergone thyroid ultrasonography and were ultimately diagnosed with a thyroid tumor after partial or total thyroidectomy operations. The patients had received treatment in 2011–2012 at the Otolaryngology Department in Shanghai Renji Hospital, China. The mean age ± standard deviation of the 771 patients, including 202 males (26.2%) and 569 females (73.8%), was 47.4 ± 12.5 years (range: 13–77 years). Thyroid ultrasonography examinations were performed and recorded by two radiologists who were professionals in thyroid sonography using a L12-5 transducer  on an S2000 scanner . Two additional independent cohorts, which include 70 (Cohort 2) [DPP4, SCG5 and CA12 (which were selected by a Bayesian model averaging (BMA) algorithm in our previous research and predict thyroid tumors with good accuracy), reverse transcription real-time qPCR was performed using the SYBR Green method and the previously reported primer sets [-ΔCt×100 (ΔCt = Ct target gene−Ct GAPDH) [Extraction and analysis of RNA were performed as previously described (our paper). To validate the expression levels of the three genes—t GAPDH) .Five hundred and thirty-nine patients , which included 241 benign and 298 malignant samples, were randomly stratified as the training set to construct the prediction model. Two hundred and thirty-two patients , which included 104 benign and 128 malignant nodules, comprised the test data.≥ 3 cm = 4), (5) Nodule number in ultrasound , (6) Nodule echo type in ultrasound with respect to normal thyroid parenchyma , (7) Ultrasound lymph node number , (8) Ultrasound lymph node morphology , (9) Ultrasound lymph node boundary , (10) Ultrasound lymph node veins , and (11) Calcification . The ultrasound images in our study were reviewed by two experienced sonographers (J.D. and L.W) with more than 5 years’ experience. As for the inconsistent results, the two examiners with another expert examiner (J.X.) who has more than 15 years’ experience would review and reach a consensus by discussion.The original RF model contains 23 variables , includiThe random forest algorithm  has commThe most commonly used classification methods can be divided into two groups: one category comprises the strong classification algorithms, such as support vector machine (SVM) and Naïve Bayes (NB); the other category comprises the combination classification algorithms, which are also referred to as weak classification algorithms, such as random forest (RF). SVM and RF are the most widely used classifiers in bioscience; thus, comparisons between the performances of these two methods have been performed many times –18. RF iThe arrangement of the training and test sets to construct and validate the model based on clinical information is summarized in DPP4, SCG5 and CA12) measured by real-time qPCR, the clinical predictive factors previously described, and the combined gene signature and clinical variables were applied to the random forest classification with default parameters. The information obtained from Cohorts 2 and 3 was from two centers; thus, one cohort was used as the training set, and the other cohort was used as the test set. In addition, 10-fold cross-validation of the 142 samples (together with Cohorts 2 and 3) was conducted to assess the integrated model. The work flow for the comparison of the classifier models based on the three-gene signature, the clinical information, and the integration of gene expression with clinical data is summarized in One hundred and forty-two thyroid tissue samples, including 70 samples from Cohort 2 and 72 samples from Cohort 3, had both clinical and gene expression information. The relative mRNA expression levels of the three genes , a delay in undergoing surgery , data input errors (n = 7), and disagreements in the histopathologic diagnosis (n = 2). Thus, 771 patients (90.9%) were included and were randomly divided into the training set  and the test set . Furthermore, the clinical data from two independent data sets, which included Cohort 2 [To evaluate the potential risk factors involved in diagnosing malignant thyroid tumor, univariate analyses of the demographic data, physical examination and ultrasound-based variables in the training set were performed; the abbreviations for the clinical variables are listed in mtry, which represents the number of different descriptors tried at each split; and ntree, which represents the number of trees in the forest. For the ntree parameter, we employed default values (ntree = 500); for mtry, we utilized a 10-fold cross-validation to test the cross-validated prediction performance of the models with a sequentially reduced number of predictors. As shown in mtry = 7, the model attained the optimum mtry with the lowest MSE at each step. Because the %IncMSE is consistent with the importance of the descriptors, we determined the most important parameters based on the %IncMSE values , and 84 of the 104 benign nodules, a specificity of 80.7% . The predictive accuracy was 82.3% . For the test set Cohort 2, which comprised 70 samples, the model correctly identified 23 of the 31 malignant samples, a sensitivity of 74.2% , and 34 of the 39 benign samples, a specificity of 87.1% . The predictive accuracy was 81.4% . For the test set Cohort 3, which comprised 72 samples from Xinhua Hospital, the classifier discriminated 29 of the 34 malignant nodules, a sensitivity of 85.3% , and 30 of the 38 benign samples, a specificity of 78.9% . The predictive accuracy was 81.9% . The predictive performances on the three data sets are summarized in Although the predictive performance based on the 7 clinical variables was good in the random forest algorithm, a subset of patients with malignant tumors would still be misclassified into the benign group because of similar clinical symptoms. This finding suggests that gene expression level variables should be integrated to further improve the predictive accuracy and to analyze the mechanism of thyroid tumor at the gene level. In the combined model, the expression levels of the three genes selected by an iterative BMA method in our previous study  was combDPP4, SCG5 and CA12, which were measured by qPCR in thyroid tissue samples, combined with the 7 selected significant clinical variables were detected and recorded for 142 patients, including 70 patients in Cohort 2 and 72 patients in Cohort 3. The relative gene expression levels of all the 142 patients are summarized in Table B in DPP4 and SCG5 were significantly different, whereas CA12 exhibited little expression difference between benign and malignant thyroid nodules; these findings are consistent with our previous research [The gene expression levels of The two data sets originated from different centers. Thus, Cohorts 2 and 3 were utilized as training and test sets, respectively, to compare the predictive performances of the random Forest model based on the three-gene signature, the 7 clinical variables, and the combination of gene expression and clinical data . To furtThe diagnosis of thyroid cancer remains a common problem in routine physical examination. It is important to preoperatively identify malignant thyroid nodules. With the development of genomic technology and advances in analyzing complex biomedical information, many investigators have focused on the molecular classification of thyroid nodules based on oligonucleotide microarray gene expression patterns using tissues or FNA samples , 20, 21.To some extent, clinical data can address the deficiencies of genomic data. The routine clinical data used to aid in the diagnosis of thyroid tumors include the demographic data, physical examination data and ultrasound characteristics of patients with thyroid nodules. Recent studies have been conducted to distinguish malignant thyroid nodules according to characteristics evaluated by high-resolution thyroid ultrasonography –29. CurrIn our study, 23 clinical variables that were considered to have correlations with malignant thyroid tumors were selected by the consensus of senior otolaryngologists and sonologists. A RF method was utilized to simplify the variables in the prediction model, and 7 variables were selected to distinguish between the benign and malignant groups in the training set, which included 1 demographic, 1 clinical and 5 ultrasound variables. Several features, including (1) irregular nodule morphologies, (2) nodules with hypoechogenicity, (3) nodules with calcification or micro-calcifications, (4) a lack of cyst formation, (5) patients at a young age, (6) palpate hard nodules upon physical examination, and (7) unclear boundaries of a nodule, were vital characteristics of malignant thyroid tumors and were included in our prediction model based on the clinical data. The distributions of the 23 descriptors were compared between the benign and malignant thyroid nodules. There were no significant differences in the number or position of the nodules between the benign and malignant thyroid tumors. Apart from these two characteristics, the remaining variables comprised risk factors for malignant tumors.The model based on the 7 clinical variables performed well and was stable. In three independent data sets from two centers, the predictive accuracies were all greater than 80% using a random forest model, a value superior to those reported in previous studies that only used ultrasound parameters to predict thyroid nodule characteristics , 28–31. DPP4, SCG5 and CA12).Our study further confirms previous evidence that predictive accuracy can be enhanced by integrating clinical variables with genomic data –35. HoweTo our knowledge, there are no publicly available databases that contain both gene expression data and relatively complete clinical information for thyroid tumors. In the current study, we measured the expression of the three previously identified genes via qPCR in 142 patients from two centers and then combined these data with 7 clinical factors selected in the current research to construct an integrated model to predict malignant thyroid nodules. To further reduce the impact of the unbalanced distribution from the two centers, we utilized a 10-fold cross-validation in addition to a 2-fold cross-validation (one data set as the training set and the other data set as the test set). It is clear that regardless of the validation set that was used, the best predictive performances were achieved by the random forest model based on the integrated clinical and molecular variables, which outperformed models that used clinical or genomic data alone. The gene expression model had a higher sensitivity than the clinical information model but a relatively low specificity in our study, and the clinical information model showed the reverse performance. Thus, in combination, these methods complement each other to produce an increased predictive accuracy.However, we should note that this study comprised a pilot study. With advances in molecular medicine and improvements in personalized medical databases, more complex clinical factors and other clinical factors (such as the characteristics of ultrasound elastography or the levels of other serum biomarkers of thyroid tumors) and omics data  may be further studied to improve the model and facilitate its day-to-day clinical application in thyroid cancer management.S1 Fig(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S1 FileTable A. Histopathological subtype distribution in three cohorts. Cohort 1 comprised 711 patients from Renji Hospital with clinical information. Cohort 2 comprised 70 patients from Renji Hospital with clinical and gene expression information. Cohort 3 comprised 72 patients from Xinhua Hospital with clinical and gene expression information. Table B. Summary of the qPCR results for the expression of DPP4, SCG5 and CA12 in Cohort 2 and Cohort 3.(DOCX)Click here for additional data file.S2 File(XLSX)Click here for additional data file.


This paper introduces an approach to classification of RNA-seq read counts using grey relational analysis (GRA) and Bayesian Gaussian process (GP) models. Read counts are transformed to microarray-like data to facilitate normal-based statistical methods. GRA is designed to select differentially expressed genes by integrating outcomes of five individual feature selection methods including two-sample t-test, entropy test, Bhattacharyya distance, Wilcoxon test and receiver operating characteristic curve. GRA performs as an aggregate filter method through combining advantages of the individual methods to produce significant feature subsets that are then fed into a nonparametric GP model for classification. The proposed approach is verified by using two benchmark real datasets and the five-fold cross-validation method. Experimental results show the performance dominance of the GRA-based feature selection method as well as GP classifier against their competing methods. Moreover, the results demonstrate that GRA-GP considerably dominates the sparse Poisson linear discriminant analysis classifiers, which were introduced specifically for read counts, on different number of features. The proposed approach therefore can be implemented effectively in real practice for read count data analysis, which is useful in many applications including understanding disease pathogenesis, diagnosis and treatment monitoring at the molecular level. Discovery of genes that are differentially expressed is helpful in gaining insights into disease pathogenesis, and discovering biomarkers for diagnosing and predicting the clinical status of patients. Identifying gene biomarkers is often performed using DNA microarray, which measures gene expression of the entire human genome. DNA microarray technology however suffers from the cross-hybridization procedure that yields noisy gene expression profiles. RNA sequencing (RNA-seq) has been emerging as a favorite method against the microarray technology . RNA-seqAs the RNA-seq technology provides count data, much interest has focused on statistical methods designed specifically for discrete counts, for example approaches using Poisson and negative binomial (NB) distributions. Witten et al.  introducDue to the overdispersion issue, i.e. the variances are likely to exceed the means for a considerable number of genes , the PoiRobinson and Smyth  presenteModelling sequencing data using count distributions is mathematically intractable and complicated because of the presence of extreme values, high skewness and the mean-variance dependency. Therefore, an alternative approach has emerged by using transformation procedures for the count RNA-seq data and applying normal-based microarray-like statistical methods. This reduces the disadvantages relating to the mathematical intractability of count distributions compared to the normal distribution and opens access to a wide range of known algorithms developed for microarray data. Several prevalent methods include logarithm transformation , variancUsing the voom transformation, we introduce an aggregate feature selection method based on the grey relational analysis (GRA) technique  to deal The proposed methodology for analysis of RNA-seq read counts is graphically presented in Once discriminant feature subsets have been selected, they serve as inputs into the GP models for classification. GP is fast and computationally tractable based on analytic formulae. A GP is completely characterized by its mean and covariance functions but it is not limited by a parametric form. Being a nonparametric method, the number and nature of GP parameters are flexible and not fixed in advance but are determined from data. Therefore, uncertainty and complexity of RNA-seq data can be addressed effectively by GP models. Under the GP viewpoint, the models are transparent and hence amenable to interpretation compared to black-box methods such as neural networks . GeneralRaw RNA-seq data are assembled in integer read counts. Specific characteristics of RNA-seq data that concern analysts are the presence of extreme values, high skewness, and the mean-variance dependency (i.e. heteroscedasticity). Logarithm transformation is a prevalent method to eliminate RNA-seq extreme values . The varm alternatives and n criteria (attributes) where the ith alternative can be expressed as Yi =  where yij is the performance value of the criterion j of the alternative i. To formulate gene selection as an MCDM problem, we treat genes (features) as alternatives and individual methods as criteria. Therefore, there are m features corresponding to m alternatives. In this paper, n is equal to 5 as there are 5 individual methods corresponding to 5 criteria. Outcomes of individual methods are scores of every feature. For each individual method, we represent its scores as the performance values of corresponding features. The following presents steps of the GRA algorithm.GRA was introduced by Deng  and has (1) Grey relational generating: This step is to translate the performance values of all alternatives into a comparability sequence. It normalizes data sequence for the experimental results within 0 and 1. If the larger target value of the original sequence is the better, then the normalization is performed by:xij is the generating value of the grey relational analysis, yij among all alternatives i = 1,2,…,m and yij.Alternatively, if the smaller target value is the better then the original sequence is normalized by:X0 as  =  and then find the alternative whose comparability sequence is the closest to the reference sequence X0.(2) Define the reference sequence: Once the grey relational generating procedure is complete, all performance values are scaled into . An alternative will be the best choice if all of its performance values are equal to or close to 1. Therefore, we define the reference sequence xij to xj0. The larger the coefficient is the closer between xij and xj0. This coefficient can be computed by:ij = |xj0 − xij|, α is the distinguishing coefficient, α ∈ . The distinguishing coefficient may expand or compress the range of the grey relational coefficient. In this paper, we set α = 0.5 for all experiments.(3) Calculate the grey relational coefficient: This coefficient is used to determine how close Xi and X0 using:wj is the weight of attribute j and m alternatives i = 1,2,…,m. The grey relational grade represents the degree of similarity between the comparability sequence and the reference sequence. Therefore, if a comparability sequence for an alternative achieves the greatest grey relational grade with the reference sequence, that alternative is the best choice.(4) Calculate the grey relational grade between For the purpose of feature selection for classification, we rank alternatives (features) based on their corresponding grey relational grades. Features have the top grey relational grades are selected to form a feature set.μ1 and μ2, whereas σ1 and σ2 are the sample standard deviations, and n1 and n2 are the sample sizes [The next subsections scrutinize background of individual feature selection filter methods whose outcomes are used for the proposed GRA approach. These methods are accomplished by ranking features via scoring metrics. They are statistic tests based on two sets of data samples in the binary classification problem. The sample means are denoted as le sizes .The two-sample t-test is a parametric hypothesis test that is applied to compare whether the average difference between two independent sets of data samples is really significant. The test statistic is calculated by:t is used to evaluate the significance among genes. The higher the absolute value, the more important is the gene.In the application of t-test for gene selection, the test is performed on each gene by separating the expression levels based on the class variable. The absolute value of Relative entropy, also known as Kullback-Liebler distance or divergence is a test assuming classes are normally distributed. The entropy score for each gene is computed using the following expression:After the computation is complete for every gene, genes with the greatest entropy scores are selected to serve as inputs to the classification techniques.The Bhattacharyya distance can be calculated from the standard deviation and mean of each class as follows:The Wilcoxon rank sum test  is a tesAssemble all observations of the two populations and rank them in the ascending order.The Wilcoxon statistic is calculated by the sum of all the ranks associated with the observations from the smaller group.The hypothesis decision is made based on the p-value, which is found from the Wilcoxon rank sum distribution table.In the applications of the Wilcoxon test for gene selection, the absolute values of the standardized Wilcoxon statistics are utilized to rank genes.X in the two populations as F1(x) and F2(x). The tail functions are specified respectively Ti(x) = 1 − Fi(x), i = 1, 2. The ROC is given as follows:Denote the distribution functions of The larger the AUC, the less is the overlap of the classes. Genes with the greatest AUC therefore are chosen to form a gene set.A nonparametric GP is a generalization of the Gaussian probability distribution based on a Bayesian methodology. GP is defined as a collection of random variables, any finite number of which have a joint Gaussian distribution. GP can be used for function approximation problems including both classification and regression. In the regression problems, likelihood function is often assumed to be Gaussian, which combines with a GP prior to yield a posterior GP over functions. This exact Bayesian inference manipulation is analytically tractable. In classification problems, as the targets are discrete class labels, the Gaussian likelihood is therefore inappropriate. Therefore, an approximate inference is needed for classification problems. Several methods have been proposed that include Laplace’s method, Expectation Propagation (EP), variational approximations and Markov chain Monte Carlo (MCMC) modelling, e.g. see , 38.The GP method for binary classification in this study is implemented by customizing the Gaussian processes for machine learning toolbox developed by Rasmussen and Nickisch . DetailsTwo benchmark real datasets are utilized in this study for comparisons. We name the first dataset as “Mont-Pick” as it is obtained from a combination of two studies Montgomery et al.  and PickThe second data set “cervical cancer” is available from Gene Expression Omnibus  under acIn the Mont-Pick dataset, the CEU and YRI samples were sequenced by different groups using potentially different facilities. Therefore, the batch effect would be a factor that affects the performance comparisons of RNA-seq data analysis approaches. To deal with this issue, we have included the design option that addresses the batch effect in the voom transformation method, which is implemented in the limma package . Figs 3 Before voom transform, the white region locates at the bottom of color bars in both datasets see Figs  and 4a. To highlight the advantages of GRA-based feature selection method, we implement a number of competing methods for comparisons including ReliefF , iteratiThe following methods are also applied for comparisons with the designed GP classifier: k-nearest neighbors (kNN) , multilaPr) and “Recall” (Re) of the classification procedure to compute the score expressed by:Four different performance metrics including accuracy rate, F1 score statistics (F-measure), AUC and mutual information (MI) are used to evaluate performance of classification methods. F-measure considers both the “Precision”  are the marginal probability distribution functions of C respectively.The MI between estimated and true label is calculated by:The five-fold cross validation method is employed for experiments. Data samples are divided at random into five distinct subsets and four subsets are used for training classifiers whilst the last subset is for testing. For unbiased comparisons, each classifier is repeated 30 times and the average performance is reported along with the standard error.To draw convincing conclusions in evaluating performance of feature selection methods and classifiers, we implement the Mann-Whitney U-test  for compNote that the test is performed to compare between the set of 30 outcomes generated by GRA method and that obtained by each of the competing feature selection methods using the same classifier. Similar procedure is performed to compare the GP classifier with its competing methods, i.e. kNN, MLP, SVM and AdaBoost using the same feature selection method.After voom transformation, GRA-based gene selection is employed for RNA-seq data to select genes that are differentially expressed for classification. GRA-based method performs as a filter method that ranks genes by combining outcomes of individual methods t-test, entropy, Bhattacharyya distance, Wilcoxon, and ROC. It therefore obtains the quintessence of these individual methods and provides stable and most discriminant subsets of genes. Feature subsets of top ten genes selected by GRA-based method serve as inputs into classifiers for demonstration although different number of genes can be used. For comparison, the same number of genes is selected by other methods in order to form feature subsets. Tables p-value of the statistical Mann-Whitney U-test between each of the competing methods and the GRA method. For example, the value of 0.003 in the cell Accuracy-ReliefF in p-value of the Mann-Whitney U-test between two sets of accuracy outcomes: one set is generated by using ReliefF and the other is obtained by GRA. The p-value smaller than 0.05 (the 5% significance level) indicates that the difference between two sets are statistically significant. In other words, the GRA method is significantly better than the ReliefF method. Values in italic in Tables p-values that are greater than 0.05.Each cell in these tables represents the mean and standard error of 30 classification outcomes. The value in brackets shows the In the Mont-Pick dataset, GRA shows a great performance compared with its competing methods. Specifically, GRA’s accuracy is of 96.77%, which is higher than ReliefF, Simba, SNR and IG of 93.78%, 84.81%, 96.05% and 90.80% respectively. Similar finding is seen in the cervical cancer dataset where GRA method outperforms other feature selection methods with regard to the accuracy metric. GRA obtains 93.43% of accuracy whilst those of ReliefF, Simba, SNR and IG are 88.33%, 87.35%, 88.23% and 90.05% respectively. Via other performance metrics, i.e. F-measure, AUC and MI, GRA feature selection method also demonstrates a considerable superiority to its competing methods. For example, in the Mont-Pick dataset, MI of GRA is of 88.56%, which is much greater than that of ReliefF at 75.89%, Simba at 42.99%, SNR at 78.88% and IG at 72.68%. Likewise, in the cervical cancer dataset, GRA’s MI is of 73.96%, which is the highest performance among the examined feature selection methods.The GRA method obtains not only greater performance but also more stable results compared with its competing methods. This is demonstrated via standard errors of the results. In the Mont-Pick dataset, GRA results’ standard errors are mostly smaller than those of ReliefF, Simba, SNR and IG. In the cervical cancer dataset, GRA also obtains smaller standard errors than those of its competing methods except only one case MI-ReliefF.p-values of the Mann-Whitney U-test are smaller than 0.05 except only one case Accuracy-SNR. Therefore, the Mann-Whitney U-test rejects the null hypothesis that results of two methods (GRA and each of the competing feature selection methods) come from the same distribution at the 5% significance level. This means that GRA is significantly better than its competing methods in terms of all performance metrics. In the cervical cancer dataset, most p-values of the Mann-Whitney U-test are smaller than 0.05, except the comparisons of GRA with the IG method  and the SNR method (for MI metric).Results of the Mann-Whitney U-test for evaluating feature selection methods demonstrate the statistical significance of GRA against its competing methods. In the Mont-Pick dataset, We use the GRA-based feature selection method to obtain subsets of top ten features that are fed into every classifier for comparisons. Results of all classifiers are presented in Tables Clearly, the GP classifier achieves greater performance compared with its competing methods in both datasets. The difference between GP with kNN, MLP, SVM and AdaBoost in the cervical cancer dataset is more considerable than that in the Mont-Pick dataset. The gap between GP and its competing methods is more than 5% in the cervical cancer dataset. More considerably, GP’s MI is greater than those of kNN, MLP, SVM and AdaBoost by more than 13%. MI of kNN, MLP, SVM and AdaBoost are respectively of 57.49%, 51.53%, 60.29% and 57.47%, which are much lower than 73.96% of the GP classifier.p-values are almost smaller than 0.05, except three cases, AUC-kNN, Accuracy-SVM and MI-SVM, in the Mont-Pick dataset and two cases, AUC-SVM and MI-SVM, in the cervical cancer dataset.With regard to the Mann-Whitney U-test results, x* to the class for which the following expression is largest:c and c′ are constants that are not dependent on the class label, whilst k. We set k. A Poisson model for RNA sequencing data states that s* = s1, …, sn are the size factors for the training data, which can be estimated using the total count, median ratio and quantile as follows:In this subsection, we compare our approach, GP classifier using GRA-based feature subsets, with sparse Poisson linear discriminant analysis (sPLDA) classifiers, which were proposed by Witten . The claX.. is the total number of counts of the training data.Total count: Median ratio: q* is the 75th percentile of counts for the test observation, and qi is the 75th percentile of counts for the ith training observation.Quantile: gi is given by dkj for sparse features is provided by:ρ is a nonnegative tuning parameter that is chosen by cross-validation. The number of features involved in classification is different when ρ is different. For unbiased comparisons, the number of features selected by our approach GRA-GP is the same with those determined by sPLDA. There are three approaches of sPLDA based on three corresponding methods of estimating the size factors for the training data, i.e. total count, median ratio and quantile. The comparisons are graphically depicted in Figs The estimate of Results presented in these figures are obtained using the five-fold cross validation for each of the competing methods. We limit the number of features to approximately 300 and the performance is measured by accuracy in percentage. For each of the specified number of features, each classifier is repeated 30 times and the average result is reported. It is clear that GRA-GP method significantly dominates all three methods of sPLDA in both datasets based on different number of features. In the Mont-Pick dataset, the gaps between GRA-GP method with its competing methods are very large when the number of features are smaller than 100. GRA-GP is still constantly superior to sPLDA classifiers when the number of feature increases. In the cervical cancer dataset, there are small gaps between GRA-GP and its competing methods when the number of features are smaller than 25. These gaps are larger when the number of features increases. sPLDA median ratio relatively ranks as the second best method after the GRA-GP. This highlights the effectiveness of our approach against the sPLDA classifiers.This paper proposes a new approach to RNA-seq count data classification using GRA-based feature selection method and the nonparametric GP models. RNA-seq data are assembled in integer read counts that present extreme values, high skewness, and heteroscedasticity. The voom transformation applied to RNA-seq data has turned them into microarray-like data by which a range of normal-based statistical methods can be utilized. On one hand, GRA systematically combines outcomes of individual methods, i.e. two-sample t-test, entropy test, Bhattacharyya distance, Wilcoxon test and ROC, and provides stable and robust feature subsets. By incorporating advantages and quintessence of the individual methods, GRA has shown a clear superiority to its competing methods that include ReliefF, Simba, signal to noise ratio, and information gain.On the other hand, the nonparametric GP models based on the Bayesian inference methodology have addressed effectively the complexity of RNA-seq data. GP has demonstrated a considerable dominance in RNA-seq data classification against its competing methods including kNN, MLP, SVM and ensemble learning AdaBoost. Through analytic formulae, GP models are computationally tractable and easier to handle and interpret than their conventional counterparts such as neural networks. Via the characterization of mean and covariance functions, GP model fitting requires only the first- and second-order moments of the process to be specified. GP therefore has the generalization capability that has increased the classification performance. More considerably, the proposed GRA-GP approach has produced greater classification performance on different numbers of features against the sPLDA classifiers, which were proposed particularly for read counts modelling.The use of benchmark real datasets along with the employment of various evaluation metrics, i.e. accuracy rate, F-measure, AUC and MI, ensure the findings of this research are well-justified. Application of the Mann-Whitney U-test has confirmed the statistical significance of the comparisons. This implies that the proposed approach can be implemented for many applications including finding potential markers of diseases, virus and bacteria type classification, and cancer prediction. Further work would be devoted to exploring different feature selection methods that may provide great performance specifically for count data classification. With the effectiveness in classifying RNA-seq data, GP models have demonstrated as a promising Bayesian approach in analysis of genomic data. Investigating Bayesian GP models to deal with challenges of other types of biological data is worth another future study.S1 FileThis file contains the description of the voom transformation method.(PDF)Click here for additional data file.S2 FileThis file contains the details of the Gaussian process method.(PDF)Click here for additional data file.S3 FileThis file contains the graphical comparisons by box plots of feature selection methods and classifiers.(PDF)Click here for additional data file.