The closely regulated process of mRNA translation is crucial for precise control of protein abundance and quality. Ribosome profiling, a combination of ribosome foot-printing and RNA deep sequencing, has been used in a large variety of studies to quantify genome-wide mRNA translation. Here, we developed Xtail, an analysis pipeline tailored for ribosome profiling data that comprehensively and accurately identifies differentially translated genes in pairwise comparisons. Applied on simulated and real datasets, Xtail exhibits high sensitivity with minimal false-positive rates, outperforming existing methods in the accuracy of quantifying differential translations. With published ribosome profiling datasets, Xtail does not only reveal differentially translated genes that make biological sense, but also uncovers new events of differential translation in human cancer cells on mTOR signalling perturbation and in human primary macrophages on interferon gamma (IFN-γ) treatment. This demonstrates the value of Xtail in providing novel insights into the molecular mechanisms that involve translational dysregulations. The global measurement of ribosome occupancy on mRNAs is commonly used as a proxy in estimating rates of protein synthesis. Here the authors describe Xtail, a computational approach that facilitates the extraction of accurate quantitative insight from ribosome profiling data (Ribo-Seq). The expression of a protein coding gene involves multiple tightly regulated steps, including DNA transcription, post-transcriptional RNA processing, messenger RNA (mRNA) translation and post-translational processing. Previous research on gene expression regulation has been largely focused on the regulatory levels above translation, such as epigenetic regulations at the DNA and chromatin levels, transcription, RNA processing and decay and so on. However from a global perspective, the abundance of protein—the final product of gene expression—is only partly controlled by transcription or mRNA abundance, and mRNA translation has been increasingly recognized as another major element of gene expression regulation2345The global quantitative assessment of mRNA translation has lagged behind the genomic and transcriptomic analyses until recent advances in ribosome profiling, which bring the quantification of translation to the genome-wide level and single-codon resolution513Similar to other high-throughput profiling techniques, ribosome profiling generates genome-wide read-outs, and therefore requires sophisticated statistical tools to screen for true-positive hits from background noise. For a given mRNA species, the abundance of RPF measured by ribosome profiling depends on the translation rate and the mRNA expression level as well. Therefore, a method that integrates both data of RPF and mRNA abundances is needed for isolation and precise quantification of differential translations on top of the transcriptional changes. Last, many of the previous studies using ribosome profiling were performed with very few replicates, therefore necessitating specially designed statistical models that estimate the technical variations and statistical significance properly. Previously in literature, a few analysis strategies have been proposed to search for differential translations with ribosome profiling data, including the quantification of translational efficiency (TE)1519Due in part to the lack of a well-performing analysis method, many of the previous studies with ribosome profiling were focused on individual or a small set of genes undergoing strong differential translation. The advantage of ribosome profiling as a genome-wide assessment of gene translation has not been fully exploited to derive a comprehensive understanding of translational regulations.Here, we developed a new analysis pipeline, Xtail, to quantify the magnitudes and statistical significances of differential translations at the genome-wide scale with ribosome profiling data. Compared with existing methods, Xtail results in significant improvements in the sensitivity to differential translations and the accuracy of differentiating translational changes from false discoveries, as shown by multiple tests with simulation data and real data from two published studies on mammalian target of rapamycin (mTOR) signalling perturbation in human cancer cellsAs discussed above, for a given mRNA transcript, the abundance of RPF indicates ribosome occupancy on all copies of this mRNA species. The count of RPF reads mapped on the coding region of a given gene depends on both the mRNA abundance and its rate of translation. Therefore, in a comparison between two conditions, differential translation can be characterized by the dissimilarity between the changes in mRNA and RPF expressions across the two conditions. In other words, for a gene undergoing differential translation across two conditions, the fold changes of its RPF and mRNA expression levels would be significantly different. The extent of such difference indicates the magnitude of differential translation. Otherwise, if the changes in RPF and mRNA levels are well coordinated, then the rate of mRNA translation is unaltered. Based on the reasoning above, we designed a method pipeline, Xtail, to quantify the magnitude and statistical significance of the translational change for each gene.A detailed description of Xtail is given in the method section, and the general outline is illustrated in 20212223For each gene, on the basis of the negative binomial distributions of RPF and mRNA read counts, we calculated the posterior probabilities for a range of log2 fold changes (log2FC), and eventually established probability distributions for log2FC of mRNA and RPF. Similarly, in a parallel process, we also derived a probability distribution for log2 ratio of RPF to mRNA (log2R), in each of the two conditions. Next, we generated a joint probability matrix by multiplying the two discrete probability distributions of log2FC (or log2R). Finally, a discrete probability distribution for the differential translation of this particular gene was calculated from this joint probability matrix. The statistical significance and credible interval of this differential translation were then inferred on the basis of this distribution. With this strategy, Xtail quantifies differential translations at the genome-wide level. Please refer to the section of methods for more details.To compare the performance of Xtail with other existing methods  in correctly identifying differential translations with ribosome profiling data, we generated a series of simulation datasets with different numbers of samples in each condition . DiffereXtail and other existing methods were applied on the simulated datasets with 1, 2 or 3 samples in each condition. Note that RiboDiff and anota require at least two and three samples per condition, respectively. Receiver operating characteristic (ROC) and precision recall curves were prepared with the results of these methods . ConsideIn practice, many biological processes involve gene expression regulations at both levels of transcription and translation. It is well expected to see some genes undergoing transcriptional regulation only and some other transcriptional regulations being reinforced or counteracted by translational regulations. Therefore, it is important to have a method that can precisely extract the effect of translation from a mixture of transcriptional and translational regulations. To specifically test this, we generated another ribosome profiling dataset with the same strategy as above, but granted the same fold changes to the mRNA and RPF of some genes  and different levels of fold changes to the mRNA and RPF of some other genes . As shown by the ROC and precision recall curves , Xtail aTo evaluate the performance of Xtail in accurately assessing real differential translations in practice, we used two published ribosome profiling datasets, one from human PC3 cells in response to mTOR signalling perturbationP value distributions  from Xtail have the longest tails . We selected the top 100 translationally down-regulated genes , and performed Gene Ontology (GO) and the KEGG pathway enrichment analyses to identify the biological functions and processes that were perturbed due to the gene translation repression by PP242  genes with FDR<0.1. We chose the top 100 translationally up- and down-regulated genes separately, and performed GO and the KEGG pathway enrichment analyses to assess potential functions or biological processes enriched in these up- and down-regulation gene sets . SimilarIn general, the biological processes and pathways enriched in the translationally up-regulated genes include immune response, inflammatory response, responses to virus and other stimulus, Toll-like receptor signalling pathway, chemotaxis and so on . This isRNA processing and nucleotide metabolism are enriched in the list of down-regulated genes from Xtail . The oriP value of the mRNA differential expression obtained with DEseq2  were not well supported by methods other than Xtail. We therefore focused on these four genes in the following discussion.In the original study that produced the ribosome profiling data, PP242 was used as an mTOR inhibitor, which suppressed PC3 cell migration and prostate cancer metastasisGNB2L1, also called RACK1, is a well-studied scaffold protein that regulates multiple signalling pathways involved in critical cellular processes, such as mRNA translation, cell motility and survivalIPO7, also called RANBP7, is one of the importin β-like transport receptors, whose major function is in nuclear protein importS-adenosylhomocysteine in methylation reactionsin vivoAHCY, also called SAHH, belongs to the adenosylhomocysteinase family, which catalyses the hydrolysis of In summary, a quick survey of the top 20 results of Xtail provided valuable insights into the molecular responses of PC3 cells to mTOR inhibition, and generated novel but plausible hypotheses about the molecular mechanism of PP242-supressed tumour growth and metastasis. These results reaffirm the outstanding performance of Xtail in precisely, and comprehensively identifying events of translational dysregulation. This example also showed the potential of Xtail in reanalyzing published ribosome profiling datasets for more comprehensive and novel understandings of translational regulations in various contexts.mRNA translation is being increasingly recognized as a crucial step in the extensively regulated process of gene expression. Ribosome profiling has become a standard method to quantify the rates of mRNA translations and to identify irregular translational processes on a genome-wide scale. Until now, a large number of datasets have been generated by ribosome profiling, shaping the landscapes of translational regulation in a variety of experimental and physiological conditions. These studies have greatly improved our understanding of translational controls in cellular physiology and various diseases. However, many of the previous works focused on small sets of genes that showed the strongest signal of translational dysregulations or were of particular interest to the investigators. This is due partly to the lack of a well-performing method that can comprehensively and precisely extract differential translations from ribosome profiling data.Z-scores by first grouping genes according to their expression levels and then fitting a normal distribution within each group1915Previously, several methods have been proposed for the differential translation analysis with ribosome profiling data. Among them, Babel uses an errors-in-variables regression model to compare ribosome associations within and between conditionsIn the present study, we developed Xtail, an integrative analysis pipeline, to systematically assess differential translations with ribosome profiling data. Xtail applies two parallel pipelines to quantify the discoordination between the mRNA and RPF changes or between the RPF-to-mRNA ratios in two conditions, as a measurement of differential translation. As shown by the tests performed on both simulated and real data, Xtail achieved very high sensitivity while keeping the type I error minimal, demonstrating a substantial improvement over the existing methods. When applied on published datasets from mTOR signalling perturbation in cancer cells and IFN-γ treatment in primary macrophages, Xtail revealed translationally responsive genes that make biological sense and more importantly, provide novel insights into the molecular machineries of these biological processes. This nicely illustrates the value of Xtail, not only in processing future ribosome profiling data, but also in revisiting previously published studies. We propose that reanalyzing the large collections of previously published ribosome profiling data with Xtail would generate more complete and accurate surveys of translational dysregulations in various experimental and physiological contexts. These surveys would provide unique mechanistic information, at the level of genome-wide translational regulation, for better understanding of important biological processes, such as stress responses, key pathway perturbations and disease onset.http://hannonlab.cshl.edu/fastx_toolkit/). Next, sequencing reads originating from rRNAs were identified and discarded by aligning the reads to rRNA sequences of the particular species using Bowtie (version 1.1.2) with no mismatch allowed. The remaining reads were then mapped to the genome and spliced transcripts using Tophat2 v2.1.0 with default parameters except for the following: –bowtie1, –no-novel-juncs, –read-realign-edit-dist=0. Two mismatches were allowed for this step of alignment.The initial processing , mapping and counting of raw sequencing reads are not in the scope of Xtail. Different strategies of data pre-processing for ribosome profiling have been used in literature38195051For each gene, mRNA expression was estimated by mRNA-seq reads, which were counted using HTSeq-count5173After the pre-processing procedure described above, Xtail takes in raw read counts of RPF and mRNA, and performs median-of-ratios normalizationXtail is based on a simple assumption that under certain experimental or physiological condition, if a gene was not subjected to any translational dysregulation, the abundance of RPF from its coding region, as revealed by ribosome profiling, would either remain undisturbed if the mRNA expression remains stable or change coordinately with the mRNA expression. In other words, if the response of RPF abundance to the experimental condition was not coordinated with that of mRNA expression, then it is highly suspected that this gene undergoes translational dysregulation. Therefore, Xtail first estimates the fold changes of RPF and mRNA across two conditions separately, and then uses the ratio of these twofold changes (ratio of fold changes) to quantify the magnitude of differential translation. Mathematically, this is equivalent to first estimating the ratios of RPF to mRNA in two conditions, and then taking the fold change of these two ratios (fold change of ratios) across two conditions.As illustrated in α and means μ of these NB distributions has been well addressed by a number of data-processing tools sophisticatedly designed for RNA sequencing, including DSSα and means μ.Ribosome profiling is based on small RNA sequencing technique. For RNA sequencing with very limited sample numbers, the Negative Binomial (NB) model has been widely used to estimate the distributions of read counts across samples. Compared to Poisson distribution, NB is more flexible, and it allows technical or biological variability that may lead to a variance higher than the mean. NB models have been widely used and shown to work well in multiple analysis methods for RNA sequencing data, such as DESeqα and means μ. mRNA or RPF read count K for gene g in sample i is described as:Specifically, for each gene, normalized read counts of RPF or mRNA in all samples were used to fit NB distributions with dispersions si) using the median-of-ratios normalization method as described and used in multiple algorithms including DESeqAs mentioned earlier, the raw read counts were then scaled by a normalization factor  in the two conditions. Therefore, to establish a probability distribution for the translational changes, which would be used to infer statistical significance of differential translations, we need to estimate the distributions for log2FC of RPF and mRNA or for log2R in two conditions.μgi, can be written with the following generalized linear model:First, the mean of mRNA or RPF expression in each sample, ϕg is the expression base level, X is a 0/1 vector of covariates indicating whether sample i belongs to condition one or two, and coefficient βg represents the log fold change of expression compared to the base level ϕg. For the RPF or mRNA of each gene, on the basis of the NB distribution of its read count, the posterior probability for a given value of βg can be calculated bywhere intercept fNB is the probability mass function of the NB distribution, which is given bywhere βg (log2FC), for either mRNA or RPF, by calculating the probabilities Pr(βg) for 10,000 values of βg, which are uniformly distributed in the range of . βg,L and βg,U, the lower and upper limits of the sampling range, were located where Pr(βg) reaches 1e−50 or below. Using the same strategy, Xtail also derives a discrete probability distribution of log2R in each of the two conditions. Here ϕg was defined as mRNA expression, and βg represents the log2 RPF-to-mRNA ratio.On the basis of the definition above, Xtail derives a discrete probability distribution of Finally, Xtail tests for each gene whether there is a significant difference between log2FC of RPF and log2FC of mRNA .P value for a positive (up-regulation) differential translation. Otherwise, if the translational fold change tended to be smaller than 1 (probability larger than 0.5), the posterior probability of the fold change being 1 or even larger was used to estimate the P value for a negative (down-regulation) differential translation. This is technically not the definition of P value, but as suggested in literatureP value. Therefore, for a two-tailed test, the P value of differential translation is estimated to be twice the summation of the elements in the upper or lower triangle, whichever is smaller, of the matrix –log2FC(mRNA)) is generated by taking the summation of the elements in each diagonal that is parallel to the main diagonal.Last, the Benjamini–Hochberg multiple testing adjustment for βg1, Δβg2], is then derived so that the probability of being above the upper bound is the same as the probability of being below the lower bound . The credible level (γ) is set to be 0.95 by default and is adjustable as an optional input of Xtail.On the basis of this distribution, the credible interval of the translational fold change, [ΔP values are reliably estimated. However, for differential translation analysis with ribosome profiling data, we need to quantitatively compare two log2FC values, of mRNA and RPF. Deviations of the two log2FC values due to technical noise of the small read counts would generate large bias towards false discoveries of uncoordinated RPF and mRNA changes, that is, falsely discovered differential translations. To address this problem, we introduced a simple but effective procedure. In addition to the comparison of log2FC distributions of mRNA and RPF, a second analysis pipeline was implemented in Xtail to compare the log2 ratios of RPF to mRNA (log2R) between the two conditions. As discussed above, theoretically this equally assesses the coordination of mRNA and RPF changes across two conditions. Specifically, following the same procedure as described above for the comparison of log2FC, Xtail generates another joint probability matrix by multiplying the two probability distributions of log2R in the two conditions (βg=log2R(C2)–log2R(C1)), was derived from this joint probability matrix.This strategy generally works very well, except for the genes that are subjected to strong transcriptional dysregulation, that is, from an extremely low-expression level in one condition to a relatively high expression in the other condition. In such cases, comparison of the mRNA or RPF between the two conditions would yield large log2FC values, which are highly sensitive to the lower expression level of mRNA or RPF in one of the two conditions. In practice, as smaller read counts generally bear more technical noise, the precision of the estimated log2FC values for such genes is usually sacrificed. This is not a critical issue for differential expression analysis with RNA sequencing data, as the absolute values of log2FC, when they are relatively large, are not critically important as long as the nditions . AnotherP value for differential translation is calculated by taking the summation of the upper or lower triangle of the joint probability matrix, multiplied by two.The The point estimate and credible interval of the translational fold change are derived from the probability distribution of the difference of log2R between two conditions.P value, point estimate and credible interval of the differential translation. For most genes with a fairly good number of read counts and thus reliable estimates of mRNA and RPF abundances, these two pipelines yielded similar assessments of differential translation. This supports the rationality of Xtail's parallel-pipeline design. In other cases, the two sets of results can be largely different, and the more conserved one  was selected as the final assessment of differential translation.As introduced above, the differential translation of each gene is evaluated by these two parallel pipelines, generating two sets of results, each of which includes the Z-scores after fitting the data of these 300 genes into a normal distributionP values were also inferred from these distributions.To evaluate the performances of Xtail and the other existing methods, we selected two published ribosome profiling datasets. One of them is from human prostate cancer cell PC3 after mTOR signalling inhibition with PP242 (GSE35469 in GEO)Simulation data was generated from a published ribosome profiling dataset with four biological replicates (GSE62134) in a study of the translational responses of mouse B-cells to HuR knock-out and LPS treatmentA dataset without biological replication was simulated by randomly assigning one of the four control samples to condition 1 and another one for condition 2. Next, the same procedure as described above was followed to define true positives and negatives of differential translations in this single-sample data .2n biological replicates for a simulated dataset with n samples in each condition. Therefore, to generate datasets with more than two samples in each condition, we took the original data of four biological replicates, and derived a normal distribution from the four read-outs of mRNA or RPF, for each gene. Next, two additional values of mRNA or RPF expression were generated by sampling from the normal distribution above. This adds two pseudo replicates to the original four-replicate data. A three-sample dataset was then generated by assigning three replicates as condition 1 and the other three as condition 2, followed by assignment of fold changes to mRNA or RPF data in one of these two conditions.As described above, this strategy of data simulation requires data from Xtail and other existing methods were applied on these simulated datasets. The overall performances of the tested methods were assessed by ROC and precision analysis using the ROCR package.P values of differential translation, as reported by each method. The same number of top-ranked genes were selected and divided into two sets according to the direction of translational regulation, up or down. GO and KEGG enrichment analysis were conducted with these gene sets using the Database for Annotation, Visualization and Integrated DiscoveryFrom the results of different methods including Xtail, Babel, RiboDiff, baySeq and TE, genes were ranked by their https://github.com/xryanglab/xtail. All the datasets used in this paper, including simulated data, normalized PC3 and macrophage datasets are presented in The ready-to-use Xtail pipeline is freely available as an R package at How to cite this article: Xiao, Z. et al. Genome-wide assessment of differential translations with ribosome profiling data. Nat. Commun. 7:11194 doi: 10.1038/ncomms11194 (2016).Supplementary Figures 1-7A custom script used to count RPF reads.Simulation dataset and results.PC3 dataset and results.Macrophage dataset and results.Sample shuffled PC3 dataset and results.Sample shuffled macrophage dataset and results.Top 20 genes identified by Xtail with the PC3 dataset.


Classifiers based on molecular criteria such as gene expression signatures have been developed to distinguish Burkitt lymphoma and diffuse large B cell lymphoma, which help to explore the intermediate cases where traditional diagnosis is difficult. Transfer of these research classifiers into a clinical setting is challenging because there are competing classifiers in the literature based on different methodology and gene sets with no clear best choice; classifiers based on one expression measurement platform may not transfer effectively to another; and, classifiers developed using fresh frozen samples may not work effectively with the commonly used and more convenient formalin fixed paraffin-embedded samples used in routine diagnosis.Here we thoroughly compared two published high profile classifiers developed on data from different Affymetrix array platforms and fresh-frozen tissue, examining their transferability and concordance. Based on this analysis, a new Burkitt and diffuse large B cell lymphoma classifier (BDC) was developed and employed on Illumina DASL data from our own paraffin-embedded samples, allowing comparison with the diagnosis made in a central haematopathology laboratory and evaluation of clinical relevance.We show that both previous classifiers can be recapitulated using very much smaller gene sets than originally employed, and that the classification result is closely dependent on the Burkitt lymphoma criteria applied in the training set. The BDC classification on our data exhibits high agreement (~95 %) with the original diagnosis. A simple outcome comparison in the patients presenting intermediate features on conventional criteria suggests that the cases classified as Burkitt lymphoma by BDC have worse response to standard diffuse large B cell lymphoma treatment than those classified as diffuse large B cell lymphoma.http://www.bioinformatics.leeds.ac.uk/labpages/softwares/ or on github https://github.com/Sharlene/BDC.In this study, we comprehensively investigate two previous Burkitt lymphoma molecular classifiers, and implement a new gene expression classifier, BDC, that works effectively on paraffin-embedded samples and provides useful information for treatment decisions. The classifier is available as a free software package under the GNU public licence within the R statistical software environment through the link The online version of this article (doi:10.1186/s13073-015-0187-6) contains supplementary material, which is available to authorized users. Gene expression patterns represent an attractive molecular phenotype for the classification of cancer –4: they MYC oncogene and immunoglobulin gene [We have adopted the example of Burkitt lymphoma (BL). This is a highly proliferative neoplasm that occurs sporadically in North America and European countries, but also has a variant associated with HIV infection and an endemic form common in Africa which is associated with Epstein–Barr virus (EBV) . The crilin gene , normalllin gene , 18, andlin gene –21. Thislin gene , while ilin gene . Howeverlin gene  has recelin gene , 26. Thilin gene –29, and Two seminal studies , 31 intrHere, starting from the above work, we investigate optimal classification algorithms and gene lists to recapitulate the original classifiers, and by examining the transferability of the optimal classifiers between data sets we effectively compare the definitions of BL applied in each data set and classifier. Our own clinical data are based on RNA extraction from FFPE samples using the Illumina DASL  technology, while the above classifiers were based on RNA extracted from fresh-frozen samples and different Affymetrix arrays. RNA in FFPE samples is more degraded, and although experimental protocols are improving, the data from this source remain significantly more noisy, and the change of measurement platform could have an equally significant effect. Nevertheless, FFPE data are likely to be the clinical reality for the foreseeable future, particularly in diagnostic laboratories responsible for large geographical areas with many hospitals. We investigate the production of a classifier based on a reduced gene set that can be effectively transferred between different gene expression measurement platforms in publicly available data sets and our own clinical data, and make a preliminary assessment of its likely clinical utility.The data sets used in this study are summarized in Table We also included 249 FFPE samples GSE32918) from a previous study , togethe8 from a This study is covered by standard NRES  ethics approval for Haematological Malignancy Diagnostic Service  local cases and treatment was not modified as a consequence of the study. The re-analyses of data from the LY10 and RCHOP14/21 clinical trials are separately covered by each trial’s ethical approval. This research is fully compatible with the Helsinki declaration.Preparation was done in R. All Affymetrix data sets except GSE4732_p1 were processed with the affy package  from rawPerformance of classifiers was assessed using standard measures . Unless otherwise stated, performance was assessed by tenfold cross-validation when considering performance within a particular data set. We also assessed transferability of classifiers by training on one data set and testing on another. Further detail of these processes is provided in the "We tested a total of ten algorithms, Bayes Net, Naïve Bayes, libSVM, SMO, Neural Network, Random Forest, Function Tree, LMT (logistic model tree), REP Tree and J48 pruned tree within GSE4732_p1 and GSE4472, respectively, using the Weka  machine c. We used the automatic script easy.py provided in the libSVM for a parameter grid search to select the model parameters: the search range of c value was 2−5 to 215 with a step of 22, the range of γ values was 23 to 2−15 with a step of 2−2 and the cross-validation fold was 5 [We optimized parameters for one classification method, the support vector machine (SVM) implemented in libSVM . Four cold was 5 . Note thIn the case of the SVM classifier applied to our Illumina data set, the BL probability is a posterior class probability obtained from libSVM, employing an improved implementation of Platt’s posterior probability function for binary classification .Subsequent development of classifiers involved a number of gene lists derived from those used in the authors’ classifiers for GSE4732_p1 and GSE4475 by consideration of issues such as availability of a gene expression measure for the gene on all platforms, robustness to over-fitting, and transferability to unknown data derived from different measurement platforms, as detailed in "Z-score, rank and two more sophisticated methods, XPN and DWD , 48 implThe developed classifier was implemented in the BDC package using the R package mechanism , and is The two existing classifiers were developed within GSE4732_p1 and GSE4475, respectively. Table We developed classifiers using feature sets corresponding to the 214 gene list from the original classifier in GSE4732_p1, and the 58 gene list from the original classifier in GSE4475. Figure Motivated by the fact that no platform has gene expression measurements for all the genes used in either original classifier, and aiming to reduce gene lists where possible because classifiers based on fewer features are less complex and less susceptible to over-fitting, we next sought to optimize the gene list for our classifier. At the same time we investigated the effect of optimizing SVM parameters. We considered further gene lists based on the existing classifiers: the 21 genes common to both original classifiers; the 28 genes for which measurements are available in GSE4732_p1 and are part of the classifier used in GSE4475; and the 172 genes that are part of the classifier genes used in GSE4732_p1 and available in GSE4475. A further list of 60 genes was newly identified by comparing the differentially expressed genes of the high confidence cases in each data set against 129 non-mBL in GSE4475; further details are given in Additional file The results presented in Fig. Normalization of data to produce an expression measure that is comparable between platforms is an essential first step in producing transferable classifiers. We compared four cross-platform normalization methods, Z-score, Rank, XPN and DWD. The Z-score and Rank methods are the least sophisticated, but could be applied to data for small numbers of genes measured by most technologies. The other methods are more sophisticated and there is evidence that they perform better in some applications , 49, butFirst of all we considered the simple comparison of classifiers trained on one data set (GSE4732_p1 or GSE4475) and tested on the other. Table The performance of the above classifiers on other available data sets is also reported in Table GSE10172 is a smaller data set generated by the group  who produced GSE4475. Classifiers trained on either GSE4475 (strict) or GSE4732_p1 produce zero error rate for DLBCL cases but higher errors for BL: however, this is a relatively small data set and these findings may not be significant. Nevertheless, it is again the case that the classifier trained on the wide definition of BL in GSE4475 does produce a more accurate classification in GSE10172  and HIV-related BL cases in contrast to the sporadic cases from the other data sets. Table To conclude, these studies show that despite using substantially different methods and genes, classifications within GSE4732_p1 or GSE4475 represent a largely consistent definition of BL that can be used as a basis for a classifier that uses fewer genes and transfers well between the two data sets. While this classifier does not apparently perform as well on other smaller and more diverse data sets, inconsistencies are largely related to intermediate cases and depend on where the boundary between classes is placed in a spectrum of cases in the training data. A similar test of the training set effect on GSE4475_p1 is shown in Additional file p = 0.95) because of its stronger consistency within and between the two larger data sets that were used in training studies. Of 592 samples in the version 3 and version 4 data together, 556 (93.9 %) have the same classification independent of normalization methods. For some cases the data sets contain replicates; 124 cases have a replicate on version 3 and version 4 together (including cases replicated within each version and some cases that are not replicated within a version but that have data from both versions). The variance of the BL probability of the total 124 replicates is given in Fig. Following the above investigations, we trained a 28 gene-based SVM, the BL and DLBCL classifier BDC, on the GSE4475 data set with a BL probability threshold of 0.95, and applied it to our Illumina data sets Table  using seThe detailed results for all replicated cases are shown in Fig. MYC gene are considered separately.Our final BDC classification was based on reducing the Illumina data set to a single replicate for each case, choosing version 4 data in preference to version 3, micro-dissected tissue in preference to usual sampling, and otherwise choosing the newest array data. This gave a classification for 403 samples. The current clinical diagnosis of these samples is based on a range of immunophenotypic and molecular  data as previously reported  and the MYC rearrangement and/or discrepancies in immunophenotype. Of the ten diagnosed DLBCL cases predicted as BL, three showed a BL phenotype without MYC rearrangement. We also looked further at the small group diagnosed as DLBCL but with MYC rearrangement detected. This is a group of particular interest, many of which are now classified as “lymphoma with features intermediate between BL and DLBCL”, and though many studies have reported a poor prognosis, currently there is no specific treatment for this group [p = 0.4 compared with the R-CHOP-treated DLBCLs without MYC rearrangement. Full information is provided in the Gene Expression Omnibus data set).Generally there is a high level of agreement between the two diagnoses . Of the 11 clinical BL cases classified as DLBCL by BDC, three had classic BL characteristics, indistinguishable on conventional criteria from BL, but the remainder of the group included a high level of aberrant cases, with non-classic is group –53. In oThe work presented here provides an important step in establishing an optimized, parsimonious and open access gene expression-based classifier for BL. By using the results of one classifier and its associated data set for training, and the other as test data, we have shown that two substantially different classifiers in the research literature have a high degree of concordance and that their results can be recapitulated, at least within the level of uncertainty associated with intermediate cases. We have also shown that this unified classifier can be successfully applied to other public data sets and to data from routine clinical samples. In the context of our own clinical data, the classifier shows a high degree of concordance with the original diagnosis.At a technical level, the reduction of the gene set compared with the original classifiers is a substantial advantage, making the classifier simpler and opening the possibility of using other measurement technologies such as quantitative PCR or NanoString in clinical applications. In addition, our detailed exploration of different training sets is noteworthy, since classifiers developed so far have largely been trained and tested within single data sets. Clearly the output of a classifier for borderline cases is critically dependent on the labelling of similar cases in the training data: our study maps the effect of changing training classification criteria in detail, and highlights differences in the classification of borderline cases between different data sets when examined in the context of gene expression criteria. Our final decision was to train the classifier on a two-way definition of BL based on the original class of GSE4475, but this nevertheless assigns fewer cases as BL than indicated in some other public data sets.Other recent work in the field has also highlighted the possibility of using reduced gene sets , 54 for Dependence on training data highlights the underlying difficulty in this and many similar studies, which is the lack of a ‘gold standard’ against which to evaluate new classifiers. Even though disease categories like BL and DLBCL have developed over many years with a variety of phenotypic and molecular diagnostic criteria, there are still a significant number of cases which are complex and neither expert pathological assessors nor recent molecular classifiers can effectively distinguish them. An alternative evaluation is to examine survival separation or treatment response, which is the primary clinical concern, and we used our own clinical data to examine outcome on the same treatment for cases where gene expression classification disagreed with the original diagnosis. Such discordant cases are relatively few even in a large data set, and the next step will be to make this evaluation in more cases as they become available. However, it is important to note that the treatment options in the setting of B-cell malignancies are likely to evolve at a high rate in the near future, and thus the use of clinical outcome with currently conventional therapy is likely to be an unstable parameter against which to assess the value of classification.Our decision to develop a binary classifier for BL versus DLBCL, instead of introducing a third intermediate class, is related to the issues described above. Since there are only two main treatment regimes, a third class is not clinically useful. We prefer a classifier that makes a decision one way or the other on intermediate cases, bearing in mind that uncertainty is reflected in the associated class probabilities. It would be naïve to suggest that such a classifier could be the sole basis for treatment decisions, but it can effectively add to the weight of evidence a clinician might consider.More recent findings have indicated new genetic distinctions between BL and DLBCL , 21, 55.We have previously developed an applied gene expression-based classifier for the separation of DLBCL cases into so-called “cell of origin” classes in samples derived from FFPE material . This toThe identification of cases of BL is clinically critical. Classic cases of this disease are treated effectively with intense regimens but not with the standard treatment for DLBCL. However, an intense regimen is more costly, less convenient and unsuitable for weaker patients who may not withstand the toxic challenge. Intermediate cases therefore represent a significant difficulty. Our data show that it would be naïve to suggest that gene expression-based classification can solve this problem, but that it does have a potential role to play. We suggest that in cases with a standard diagnosis of DLBCL, gene expression could be used alongside other evidence and phenotypic features in deciding whether to treat with more intensive therapy. Future work should evaluate this suggestion, alongside the incorporation of genetic data in classification.


It has been implemented in the www.stemformatics.org resource, to assist researchers wishing to benchmark their own MSC datasets or data from the public domain. The code is available from the CRAN repository and all data used to generate the MSC test is available to download via the Gene Expression Omnibus or the Stemformatics resource.Mesenchymal stromal cells (MSC) are widely used for the study of mesenchymal tissue repair, and increasingly adopted for cell therapy, despite the lack of consensus on the identity of these cells. In part this is due to the lack of specificity of MSC markers. Distinguishing MSC from other stromal cells such as fibroblasts is particularly difficult using standard analysis of surface proteins, and there is an urgent need for improved classification approaches. Transcriptome profiling is commonly used to describe and compare different cell types; however, efforts to identify specific markers of rare cellular subsets may be confounded by the small sample sizes of most studies. Consequently, it is difficult to derive reproducible, and therefore useful markers. We addressed the question of MSC classification with a large integrative analysis of many public MSC datasets. We derived a sparse classifier (The Rohart MSC test) that accurately distinguished MSC from non-MSC samples with >97% accuracy on an internal training set of 635 samples from 41 studies derived on 10 different microarray platforms. The classifier was validated on an external test set of 1,291 samples from 65 studies derived on 15 different platforms, with >95% accuracy. The genes that contribute to the MSC classifier formed a protein-interaction network that included known MSC markers. Further evidence of the relevance of this new MSC panel came from the high number of Mendelian disorders associated with mutations in more than 65% of the network. These result in mesenchymal defects, particularly impacting on skeletal growth and function. The Rohart MSC test is a simple  These minimal common criteria were hard-coded into the Stemformatics annotation pipeline, we had a dedicated annotator responsible for the quality of these annotations and these were reviewed independently by two additional annotators. Sixteen MSC datasets met our ‘gold standard’ training set criteria for accompanying phenotype of MSCs, together with 27 datasets containing cells from non-mesenchymal or non-stromal sources, which we refer to as non-MSCs. In total, 41 datasets were included in the training set, with two datasets containing both MSCs and non-MSCs, with a total of 125 MSC samples and 510 non-MSC samples from 10 different microarray platforms   ## Extract GC-RMA bg-corrected expression values without re-running additional bg-correction  data.bgexpr <- rmawhere:data” is loaded raw CEL data“affinity_data” is precomputed probe affinity produced by “compute.affinities”“Affymetrix Power Tools v1.14.4.1 (“apt_probeset_summarize” tool). Exon probe expressions were summarised to the transcript level.Affymetrix Gene ST arrays were RMA background corrected using Illumina chips were background corrected using code: lumiB)where:data” is non-normalized BeadStudio / GenomeStudio expression data returned by “lumiR”“Agilent chips were background corrected using code: dat <- backgroundCorrect  datbg <- dat  bgave <- averepswhere:datraw” is non-normalised Agilent data returned by “read.maimages”“All data was subsequently log2 transformed and a YuGene transformation was applied . YuGene In order to combine all the datasets described in The combined training data set included the gene expression measurement of 41,185 genes mapped by at least one probe in one dataset. When a dataset had no probes mapping to a particular gene, the expression values of the gene were arbitrarily set to zero for all samples from that dataset. A pre-screening step was then performed to discard genes that were not present in at least half of the samples.sparse variant of Partial Least Square Discriminant Analysis (sPLS-DA) (http://biojs.io/d/biojs-vis-rohart-msc-test.The MSC signature was identified using a novel implementation of the sPLS-DA)  implemensPLS-DA) . Full deTwenty-six genes selected on component 1 equated to 20 proteins with a curated interaction in the NetworkAnalyst protein interaction database  consortium, accessed July 2015 ). These t-test, with a significance threshold of 10−6. For exploration of MSC subsets, a linear mixed model with dataset as random effect was fitted for each gene for which both the mean of bone marrow samples and other sites were higher than the median of all gene expression values. This retained 16,903 genes. P-values were obtained by ANOVA and corrected for multiple testing with the Benjamini–Hochberg procedure , and these included CD73 (NTE5), CD105 (Endoglin), PDGFRB and VCAM1. The average expression of the remaining markers is provided in in silico marker set that reproducibly identified bona fide MSC samples regardless of platform or laboratory differences, and provide a molecular test that was simpler, and more accurate than current methods.The International Society for Cellular Therapy  has collat least the minimal common set of CD73+, CD105+, CD45− and bilineage differentiation. The training set consisted of 125 MSC samples from 16 independently derived datasets derived predominantly from bone marrow, but also included studies from other adult, neonatal and fetal stromal sources. MSC were compared to 510 definitively non-MSC samples from primary human tissues and cell lines, including cultured fibroblasts, haematopoietic cells and pluripotent stem cell lines . From these efforts, a gold standard ‘training set’ was identified as meeting high confidence MSC phenotype including ll lines  and S3.To fully integrate and interrogate these data, we derived a novel cross-study analysis framework. Our approach, described in We reasoned that if the majority of genes discriminating between MSC and non-MSC are describing a common biology and are highly correlated, then a subset of these genes could be identified that would represent the entire network. Therefore, we iteratively assessed how the inclusion of each gene contributed to the overall accuracy of the signature. This found the subset of variables that were most stable and least redundant at a statistical level, and that would represent the greater network of MSC-related measurements . SixteenCells derived from bone marrow were reliably grouped together with this method , and MSCwww.stemformatics.org assessed the MSC score across 200 iterative predictions, where a sample must have a 95% pass rate to be classed as an MSC. The distribution of the training sample scores was used to determine high confidence scores (The implementation in e scores . By usinPRRX1), a transcription factor important for early embryonic skeletal and facial development, and with a de novo mutation spectrum in the embryonic dysmorphology syndrome Agnathia-otocephaly (BMP14/GDF5) lead to developmental abnormalities in chondrogenesis and skeletal bone  with demonstrated roles in the modification of extracellular matrix proteins including proteoglycans, as well as regulators of growth factor and cytokine signalling. This included the cell migration inducing protein (KIAA1199/CEMIP), which is secreted in its mature form. It regulates Wnt and TGFr milieu . DDR2 isr milieu . CCDC80 r milieu . SRPX2 ir milieu . The chapresumptive MSC (213 samples) or presumptive non-MSC (499 samples) based on their origin and use in the source publication  prior to testing these with the signature. Implementation of the Rohart Test in the www.stemformatics.org resource allowed us to evaluate a wide range of different experimental paradigms. Despite the lack of phenotypic information associated with these datasets, the agreement between publication status and our classification was high. Five percent of the presumptive non-MSC (27/499) were misclassified by the signature as MSC, and around half of these (>13) were neonatal or fetal dermal fibroblasts  or to adipose-like cells (https://www.stemformatics.org/workbench/rohart_msc_graph?ds_id=6208#) or when undergoing reprogramming of an adipose-tissue derived iPSC (https://www.stemformatics.org/workbench/rohart_msc_graph?ds_id=5018).The majority of public microarray datasets available to us had limited phenotypic data available, so these were not used to derive our MSC signature. Nevertheless we annotated each of these samples as lication . Where Mroblasts . Others roblasts  and cert+ CD146+ CD31/Epcam− CD56/Ncam− with demonstrated skeletal muscle differentiation, were classified as MSC . Datasets in the training set; accompanies Figure 2 and methods.Click here for additional data file.10.7717/peerj.1845/supp-3Supplemental Information 3Table S5 - (auxiliary spreadsheet). Datasets that contributed to the testing set and result of the Rohart test. Accompanies Figure 3. MSC status is unknown in the absence of phenotype data provided in the manuscript.Click here for additional data file.10.7717/peerj.1845/supp-4Supplemental Information 4P < 0.01. Top Differentially expressed genes between MSC from different sites. Linear mixed model, FDR adjusted P < 0.01.Table S6. (auxiliary spreadsheet). Top Differentially expressed genes between MSC from bone marrow compared to other sites. Linear mixed model, FDR adjusted Click here for additional data file.


L1-type regularization approaches have been widely used for uncovering cancer driver genes based on genome-scale data. Although the existing methods have been widely applied in the field of bioinformatics, they possess several drawbacks: subset size limitations, erroneous estimation results, multicollinearity, and heavy time consumption. We introduce a novel statistical strategy, called a Recursive Random Lasso (RRLasso), for high dimensional genomic data analysis and investigation of driver genes. For time-effective analysis, we consider a recursive bootstrap procedure in line with the random lasso. Furthermore, we introduce a parametric statistical test for driver gene selection based on bootstrap regression modeling results. The proposed RRLasso is not only rapid but performs well for high dimensional genomic data analysis. Monte Carlo simulations and analysis of the “Sanger Genomics of Drug Sensitivity in Cancer dataset from the Cancer Genome Project” show that the proposed RRLasso is an effective tool for high dimensional genomic data analysis. The proposed methods provide reliable and biologically relevant results for cancer driver gene selection.Uncovering driver genes is crucial for understanding heterogeneity in cancer.  L1-type regularization approaches, e.g., lasso [n). The elastic net, which has been widely used in bioinformatics research, may provide erroneous estimation results for coefficients of highly correlated variables with different magnitudes, especially those that differ in sign, because of its “grouping effect”. However, coefficients of highly correlated variables with different magnitudes are frequently observed in bioinformatics research, since genes in common biological pathways are usually correlated, and their regression coefficients can have different magnitudes or different signs. Furthermore, adaptive L1-type regularization methods suffer from multicollinearity, since their adaptive data driven weights are based on Ordinary Least squares (OLS) estimators.Much research is currently underway to understand the complexity of the heterogeneous genetic networks underlying cancer. To identify the heterogeneous genetic networks that underlie cancer, various large scale-omics projects , Sanger Genomics of Drug Sensitivity in Cancer dataset from the Cancer Genome Project, and others) have been initiated and have provided large amounts of data, such as genomic and epigenomic data for cancer patients or cell lines. A crucial issue in cancer research is to identify cancer driver genes based on various genomic data analysis , since efficient identification of cancer drug targets facilitates development of successful anti-cancer therapies. Although various ., lasso , have be., lasso . The las., lasso  suffer fL1-type regularization approaches by using a random forest strategy, the method is computationally intensive because it employs two step bootstrap procedures. Furthermore, Wang et al. [To resolve these issues, Wang et al.  proposedg et al.  performeWe propose a novel statistical strategy to identify driver genes of anti-cancer drug sensitivity in line with the random lasso. We introduce recursive bootstrap approaches to simultaneously measure the significance of each gene and perform driver gene selection. We also propose a novel threshold based on a parametric statistical test to effectively identify driver genes based on bootstrap regression modeling. By using a recursive bootstrap procedure, we perform time-efficient bootstrap regression modeling for high dimensional genomic data analysis without loss of modeling accuracy. Furthermore, the proposed feature selection method using parametric statistical test can be a useful tool for variable selection based on the bootstrap regression modeling.http://www.cancerrxgene.org/), and identify potential driver genes of anti-cancer drug sensitivity. Numerical analyses show that the proposed recursive random lasso and elastic net are time-efficient procedures, and outperform high dimensional genomic data analysis .Using Monte Carlo simulations of various scenarios, we demonstrate the effectiveness of the proposed recursive random lasso and elastic net with a parametric statistical test for high dimensional regression modeling. We also apply the proposed statistical strategy to the publicly available “Sanger Genomics of Drug Sensitivity in Cancer dataset from the Cancer Genome Project” ;i = 1, …, n}, where yi are random response variables and xi are p-dimensional vectors of the predictor variables. Consider the linear regression model,β is an unknown p-dimensional vector of regression coefficients and εi are the random errors which are assumed to be independently and identically distributed with mean 0 and variance σ2. We assume that the yi are centered and xij are standardized by their mean and standard deviation: Suppose we have λ is a tuning parameter controlling model complexity. By imposing a penalty term, the sum of the absolute values of the regression coefficients, the lasso can simultaneously perform parameter estimation and variable selection.Tibshirani  proposedp > n case, the lasso selects at most n variables, because of the convex optimization problem. This implies that the lasso is not suitable for driver gene selection, since genomic alteration data is typically high dimensional data.In the The lasso cannot account for grouping effect of predictor variables, and thus tends to select only one variable from among highly correlated variables, even if all are related to response variable. However, genomic alterations of genes  that share a common biological pathway are usually highly correlated, and the genes may be associated with a complex cancer mechanism considered to be the response variable. This also implies that the lasso is not suitable for genomic data analysis.However, a recent work suggested that the lasso may suffer from the following limitations :In the L1-type regularization methods have been proposed. The elastic net [L2-penalty on the lasso, the elastic net performs effectively feature selection in high dimensional data analysis, i.e., there is no limitation on subset size. Furthermore, the elastic net can enjoy the following grouping effect:To overcome these drawbacks, various stic net  in partihe ridge  and lassThe property of “grouping effect” leads to erroneous estimation results when coefficients of highly correlated variables with different magnitudes, especially those with different signs. However, coefficients of highly correlated variables with different magnitudes are frequently observed in bioinformatics research, since genes in the common biological pathway are usually highly correlated, and their regression coefficients can have different magnitudes or a different sign.Although the elastic net performs well for high dimensional data analysis, Wang et al.  demonstrL1-type penalties have also been proposed and are widely used in various fields of research:The adaptive adaptive lasso:adaptive elastic net:γ > 0. By using the weight, we can discriminately impose a penalty on each feature depending on their significance, and thus effectively perform feature selection. Zou and Hastie [L1-type regularization methods suffer from the same drawbacks as the common methods, i.e., when using the adaptive lasso, the number of selected variables cannot exceed n, and the adaptive elastic net may also provide erroneous estimation results when coefficients of highly correlated variables with different magnitudes are present.where d Hastie  and Zou d Hastie  establisL1-type approaches, and proposed the random lasso based on a bootstrap strategy that employs the random forest method. In the random lasso procedure, randomly selected q variables are considered as candidate variables in regression modeling for each bootstrap sample. Thus, the results do not suffer from the highly correlated variables drawbacks, since each bootstrap sample may include only a subset of the highly correlated variables. Furthermore, the random lasso can overcome the subset size limitation, since variable selection is based on the results of bootstrap regression modeling with randomly selected q1 or q2 variables in each bootstrap sample.Wang et al.  detailedWang et al.  proposedAlgorithm 1Random lassoB bootstrap samples with size n by sampling with replacement from the original dataset.∘ Draw b1 ∈ {1, 2, …, B}, q1 candidate variables are randomly selected, and the lasso is applied for regression modeling and we obtain estimators j = 1, …, p.∘ For the xj is calculated as ∘ The importance measure of Step 1: Generating importance measures of predictor variables.B bootstrap samples with size n by sampling with replacement from the original dataset.∘ Draw b2 ∈ {1, 2, …, B}, q2 candidate variables are randomly selected with a selection probability of xj proportional to Ij, and the adaptive lasso is applied for regression modeling, and we obtain the estimator j = 1, …, p.∘ For the j = 1, …, p.∘ Compute the final estimator, Step 2: Variable selectionIj) will be small or close to zero. On the other hand, the coefficients of crucial predictor variables may be consistently large in different bootstrap samples, and thus a crucial gene has a large value of Ij. This implies that the selection probability Ij provides effective feature selection. Wang et al. [q1 and q2 as tuning parameters, and the importance measure Ij can also be used to weight for the adaptive lasso.For noise predictor variables, the coefficients in the respective bootstrap samples are estimated to be small or to have different signs, and thus the absolute value of the average coefficients . The proposed recursive random lasso (elastic net) is implemented by the following algorithm.We propose an effective modeling strategy in line with the random lasso, called a recursive random lasso (or elastic net). To efficiently perform high dimensional genomic data analysis, we propose a recursive bootstrap procedure for generating the importance measure and regression modeling. We also propose a novel threshold to effectively select predictor variables in bootstrap regression modeling using a parametric statistical test. Furthermore, a number of candidate predictors, Algorithm 2Recursive random lasso (or elastic net)B bootstrap samples with size n by sampling with replacement from the original dataset.Draw b = 1), q candidate variables are randomly selected and the lasso (or elastic net) is applied for regression modeling. We then obtain estimators j = 1, …, p.For the first bootstrap sample  with wj = 1/Ij is applied for regression modeling. We obtain the estimators j = 1, …, p.For Final estimators are computed as t* via the parametric statistical test.Finally, we perform variable selection based on the threshold B × p binary matrix D obtained from the above recursive bootstrap procedures. We set an element of the binary matrix as Dbj = 1 for a non-zero bth bootstrap sample; otherwise Dbj = 0. In other words, we consider that the binary matrix is obtained from Bernoulli experiments, and let Dj be a random variable associated with Bernoulli trials as follows:In order to effectively perform feature selection, we propose a parametric statistical test based on the bootstrap regression modeling results. We first consider a π can be estimated as follows,B bootstrap samples. For reasonable variable selection, we then consider the following statistic:B Bernoulli trials (i.e. B bootstrap samples). The statistic Cj follows the Binomial distribution p-value for each predictor variable as follows,p-value with a threshold t* = 0.05 as follows,I(⋅) is an indicator function. We can expect that the parametric statistical test can overcome false positive feature selection results of bootstrap regression modeling. Although we have described the proposed variable selection strategy focused on the random lasso procedure, the parametric statistical test will be a useful tool for bootstrap regression modeling.The Bernoulli random variable has the following probability density function,εi are N, and the correlation between xl and xm is 0.5l−m||.Monte Carlo simulations were conducted to investigate the effectiveness of the proposed modeling strategy. We simulated 100 datasets from the following linear regression model,n = 100 and p = 1000 as βj = 3 for 50 randomly selected variables, otherwise βj = 0,Type1: n = 100 and p = 1000 as βj = 3 for 25 randomly selected variables, βj = −3 for 25 randomly selected variables, otherwise βj = 0,Type2: n = 100 and p = 1000 as βj = 3 for 150 randomly selected variables, otherwise βj = 0.Type3: n = 100 and p = 1000 as βj = 3 for 75 randomly selected variables, βj = −3 for 75 randomly selected variables, otherwise βj = 0,Type4: n = 50 and p = 2000 as βj = 3 for 40 randomly selected variables, otherwise βj = 0,Type5: n = 50 and p = 2000 as βj = 3 for 20 randomly selected variables, βj = −3 for 20 randomly selected variables, otherwise βj = 0,Type6: n = 50 and p = 2000 as βj = 3 for 200 randomly selected variables, otherwise βj = 0.Type7: n = 50 and p = 2000 as βj = 3 for 100 randomly selected variables, βj = −3 for 100 randomly selected variables, otherwise βj = 0,Type8: We considered the following simulation situations:s/n, and selected s based on the root mean squared error in the validation dataset. We considered the number of bootstrap samples to B = 1000 and a dataset constructed with training, validation, and test datasets with sample size n, respectively. The tuning parameters were selected by 5-fold cross validation based on the training dataset.To evaluate the proposed recursive random lasso and elastic net procedures, we compared the performance of our methods, recursive random elastic net (RCS.RD.EL), recursive random lasso (RCS.RD.LA), with the lasso (LASSO), adaptive lasso (AD.LA), elastic net (ELA), and existing random lasso (RD.LA). In numerical studies, we used a ridge estimator for weight in the existing adaptive lasso, and we considered the threshold of the existing random lasso to be We first evaluated the computational efficiency of our methods. Ij for predictor variables with truly non-zero coefficients and truly zero coefficients in the recursive random elastic net (RCS.RD.EL), recursive random lasso (RCS.RD.LA) and random lasso (RD.LA), where the numbers in parentheses are the average of the importance measures for small number of bootstrap samples B = 20.To show the effectiveness of recursive bootstrap strategy, we compared the importance measures for the random lasso procedures. Ij is recursively calculated during regression modeling. Furthermore, the Ij of our method is based on a randomly selected number of candidate predictor variables q, whereas in the existing random lasso method, Ij is based on the tuning parameters q1 and q2 selected by minimizing prediction error in the validation dataset. In short, our method provides time-effective procedures compared with the existing random lasso.In the existing random lasso, the importance measure is calculated independently with regression modeling . However, in our method, the B = 20 given in parentheses of From We then compared the results of regression modeling based on prediction accuracy in the test dataset and the variable selection results shown in Figs We also compared variable selection results given as the average of true positive rate  and true negative rate  in In short, the proposed recursive random lasso and elastic net methods are not only computationally effective but produce outstanding regression modeling results . This results imply that our methods can be useful tools for high dimensional genomic alteration data analysis.http://www.cancerrxgene.org/). The dataset contains the gene expression levels, copy number and mutation status for 654 cell lines and the half-maximal inhibitory drug concentrations  of 138 anti-cancer drugs as an indicator of drug sensitivity. We considered the expression levels of 13321 genes and the IC50 values of anti-cancer drugs to reveal driver genes, which are available from the resources: “Cell line genetic (mutation and copy number) and gene expression data used for EN analysis” and “Cell line drug sensitivity, mutations and tissue type”, respectively, in “http://www.cancerrxgene.org/”. Many IC50 values are missing from the Sanger dataset, and we therefore considered only 99 anti-cancer drugs, which have non-missing observations for at least 600 cancer cell lines, as response variables. The expression levels of 10% of the genes  having the highest variance in all samples were considered as predictor variables. We employed B = 1000 bootstrap replications and the tuning parameters were selected by 5-fold cross validation.We applied the proposed strategies to identify potential driver genes of anti-cancer drug sensitivity in the publicly available “Sanger Genomics of Drug Sensitivity in Cancer dataset from the Cancer Genome Project” : a platinum-compound chemotherapy drug that stops cancer cells from growing. Target: DNA crosslinker. Used to treat: testicular, ovarian, bladder, head and neck, breast, cervical and prostate cancers. Side effects: nausea and vomiting, kidney toxicity, low white blood cell counts, and low red blood cell counts.Docetaxel (trade name: Taxotere): belongs to a class of chemotherapy drugs that works by preventing division of cancer cells. Targets: Microtubules. Used to treat: breast, non-small cell lung, advanced stomach, and head and neck cancers. Side effects: nausea, diarrhea, hair loss, nail change, low white blood cell counts, and low red blood cell counts.Doxorubicin (trade name: Adriamycin): an anti-cancer chemotherapy drug that is classified as an “anthracycline antibiotic”. It slows or stops the growth of cancer cells, and binds to DNA by intercalation between specific base pairs, thus blocking DNA synthesis [Target: DNA intercalation. Used to treat leukemia, bladder, breast, stomach, lung, ovarian and thyroid cancers, and soft tissue sarcoma. Side effects: hair loss, myelosuppression, oral mucositis, and diarrhea.ynthesis . Target:Gemcitabine (trade name: Gemzar): an anti-cancer chemotherapy drug that is classified as an antimetabolite. Gemcitabine prevents the growth of cancer cells, eventually resulting in their destruction. It inhibits thymidylate synthetase, which leads to inhibition of DNA synthesis and cell death [Targets: DNA replication.Used to treat pancreatic, non-small cell lung, bladder, metastatic breast, and ovarian cancers, and soft-tissue sarcoma. Side effects: flu-like symptoms , fatigue, and poor appetite.ll death . TargetsVinorelbine (trade name: Navelbine): an anti-cancer chemotherapy drug that is classified as a “plant alkaloid”. Vinorelbine kills cancer cells by interfering with their DNA, which is necessary for their growth and reproduction. The antitumor activity of vinorelbine is thought to be due primarily to inhibition of mitosis at metaphase through its interaction with tubulin [Target: Microtubules. Used to treat non-small cell lung, breast, and ovarian cancers, and Hodgkin’s disease. Side effects: temporary decrease in white and red blood cells, muscle weakness, and constipation. tubulin . Target:We then identified potential driver genes using the proposed recursive random elastic net. We focused on five popular anti-cancer drugs: Cisplatin, Docetaxel, Doxorubicin, Gemcitabine and Vinorelbine, which have attracted considerable for cancer research , 7. We wIj among the selected genes for each anti-cancer drug . There are, however, differences between selected driver genes of our study and given in the project website, since we consider only 10% of genes  having the highest variance as candidate genes in regression modeling. Although the identified driver genes by our method are difference from the driver genes identified by the project, we can see through Drug sensitive-specific driver genes were identified by the “Cancer Genome Project”. In the project, they considered regression modeling and applied the elastic net to identify driver genes. The results are given in the project website . Solid lines indicate potential driver genes identified for each anti-cancer drug and dashed lines indicate PPIs between genes. The anti-cancer drug cisplatin has the largest sub-network constructed by PPIs with a path length of 1. In NEDD9, TCP1, CCT5, ACTC1, CS, CLIC4, and NCAM1, these genes are connected with a large number of genes (n ≥ 9) by PPIs. We also focused on driver genes with large sub-network, i.e., Ij) than average of all selected genes  for identifying driver genes. To effectively perform high dimensional genomic data analysis, we used recursive bootstrap strategies in line with the random lasso method. Furthermore, we have proposed a parametric statistical test for gene selection based on the results of bootstrap regression modeling.Numerical studies showed that the proposed methods show outstanding performance for variable selection and prediction accuracy. Furthermore, our methods showed time-effective performance compared with existing random lasso. We expect that our methods based on recursive bootstrap regression modeling and parametric statistical test will be useful tools for high dimensional genomic data analysis, especially driver gene selection. Furthermore, we expected that the proposed parametric test can be used effectively for variable selection in bootstrap regression modeling.L1-type regularization method against initial selection.Although the proposed parametric statistical test performs well for feature selection, our method is sensitive to the initial selection of predictor variables, because the initial selection result directly affects the selection probability in the random forest procedure. Thus, further work is required for robust recursive random Furthermore, we have focused on the proposed recursive random lasso in not theoretical but practical viewpoint. We considered constructing theoretical properties of our method  as one of further work of this study.Variation in gene expression levels in cancer is known to be caused by copy number variation, and thus the two features should be considered concurrently when searching for driver genes. We also considered cancer driver gene selection via analysis of copy number driven expression levels via extension of the recursive random lasso strategies.