We here show that the frequency of human and mouse βJβV combinations deviates from the one expected based on each gene usage frequency. This bias is observed mainly in functional (F) rearrangements, but also slightly in non-functional (NF) rearrangements. Preferred βJβV combinations in F clones are shared between donors and samples, suggesting a common structural mechanism for these biases in addition to any host-specific antigen-induced peripheral selection. The sharing holds even in clones with Jβ1 that share the same βD1 gene. βJβV usage is correlated with the Molecular Weight and Isoelectric Point in F clones. The pairing is also observed in the Double Positive cells in mice thymocytes, suggesting that the selection leading to such a pairing occurs before thymic selection. These results suggest an additional structural checkpoint in the beta chain development prior to thymic selection during the T cell receptor expression. Understanding this structural selection is important for the distinction between normal and aberrant T cell development, and crucial for the design of engineered TCRs.The  The TCR repertoire diversity is generated by two main mechanisms: the rearrangement of V (D) and J gene segments and by the nucleotide addition and removal at the junction between those segments (T cells recognize self and foreign peptides through the interaction of their T-cell receptors (TCRs) with MHC bound peptides , 2. The segments , 5.The TCR repertoire is then shaped through the T cell development. T cells arise from hematopoietic stem cells that migrate to the thymus where they require signals from nonhematopoietic stromal cells, such as thymic epithelial cells (TECs) and mesenchymal fibroblasts for survival, leading to positive selection based on ligand specificity , 7. A thα chain is composed of two segments (Vα (variable) and αJ (joining)). The β chain contains a third intermediate gene - βD (diversity). During the β chain rearrangement, there is first a recombination of one βD and one βJ, followed by a recombination of βJβD with βV, to form a rearranged βDβ JβV gene segment.The TCR α chain rearrangement, all the genes between the rearranged αV and Jα are removed. However, αV genes that are 5’ and Jα genes that are 3’ to the rearranged αV - Jα are still present allowing for multiple rounds of rearrangement . This process and the parallel process in the B cell Light Chain (LC) have been shown to induce a correlation between αV and Jα gene usage  were shown to differ between diseases (V20 - 01 and J02 - 02 was increased in the βV - βJ repertoire (p < 0.001) of the healthy volunteers compared to patients  = P(βV) P(βJ).Multiple models were developed for the generation probability of TCRs and BCRs . Those iβV - βJ usage is not only highly variable, but also differs from what is expected from their separate frequencies. We propose multiple measure that suggest that this pairing is the result of a structural selection step preceding thymic selection.To summarise, specific V and J genes as well as V-J combinations have been shown to be more frequent than others in many contexts. We here show that the We used the notation presented in We used four datasets in this analysis:The RH dataset. T cell receptor sequence data of alopecia patients before and during sensitisation with diphenylcyclopropenone and healthy volunteers at equivalent time points. The data contains 98 samples of β chains from 34 different patients. Participants were recruited from patients who had been diagnosed with alopecia, were aged between 18 and 70, identified as suitable for DPC treatment by a consultant dermatologist, and were now attending their first visit to the Alopecia Clinic at Salford Royal Hospital for DPC therapy. Twenty-nine of the individuals who participated in the study provided blood samples for TCR sequencing (TCRseq), for between one and four of the study time points . Flow cytometry data was obtained for peripheral blood mononuclear cells (PBMCs) from 10 treated patients, and patch test data for 24 patients , lymph nodes (LN), spleen (Spl)), and lungs. Donors were free of cancer and negative for hepatitis B, C, and HIV. The dataset contains four CD4+ and CD8+ T cell types: TCM (CD45RA- CCR7+), TEM (CD45RA- CCR7-CD69-), TRM (CD45RA- CCR7- CD69+), and TEMRA (CD45RA+ CCR7-) cells.  thymocytes were sorted based on CD4+, CD8α+, and CD69- gates from B6 or MHC-Knock Out animals (For more details on each of the datasets see β JβV) pairs P(β JβV) and the expected frequency, defined as the product of the relative frequencies of βV and βJ, P (βV) P(βJ), and computed:We compared for each sample the observed relative frequency of all (M (β JβV) distribution, we multiplied all the values by 100 to obtain values in percentages. Only βV and βJ in the sample were considered.The probabilities are defined per sample (i.e. using only clones in this sample), and each clone was counted once, irrespective of the clone size. When we analyzed the M (β JβV) values for all sample pairs.To quantify the similarity of deviation from a random pairing between samples, we computed the Spearman correlation between the i and j. Each sample contains only a subset of the βV and βJ genes βikV, βikJ, βjkV, βjkJ. For each pair of samples, the common  pairs were taken s.t.Given a pair of samples iM and jM for each pair in S, and computed the Spearman correlation for these pairs.We computed βV, βJ) pairs that deviate from the null model of random pairing, we computed for each pair in our dataset over all samples P  and P(βV) P(βJ). Then, we performed a paired T-test on P and P(βV) P(βJ) for each pair separately. We applied a Benjamini-Hochberg correction . The clone size or frequency was not used in the analysis. In addition, for the functional F clones, we also used the non-functional data (NF) clones as a comparison.We used two null models to compare our results. The first null model was generated by scrambling the βV and βJ was calculated. In addition, for each file and pair, we took its CDR3 and computed the sum of the Kyte Doolittle (KD), the Molecular Weight (MW) and the Isoelectric Point (IP) for all of its amino acids and averaged the values for each pair. Then, we calculated the M  values for each βV, βJ pair in a given file, and averaged over all the pairs in the same dataset. We then computed the Spearman correlation between the sum of the gene lengths, the KD, the MW or the IP and the mean M  values.For each dataset, we used only the F clones. We took all possible pairs of a given file, and for each pair, the total lengths of βV, βJ) the M  and M1 , where M1 is the measure for the mixed data both for the real data and for the first null model. Next, we calculated the Spearman correlation coefficient on these two samples.To test the correlation between different samples, only the common pairs of the two samples were taken. We calculated for each pair  on the real data is different from the distribution of M  on the null model, we performed the two-sided Kolmogorov-Smirnov statistic on two samples  on the real data is different from the standard deviation of M  on the null model, we used a two-sided T-test on two related samples of scores. We also used this test to identify which pairs have a signal. For each pair , we calculated over all samples P  and P (βV) P (βJ), and performed the above test for P  and P (βV) P (βJ) for each pair separately. We applied the Benjamini-Hochberg correction , and ignored allelic differences (V01-02:01 → V01-02).We used 4 datasets for the analysis, RH, MM, Emerson and the LV datasets (see Methods). Each dataset contains several patients (see Methods). Some contain samples from different compartments (CD4 vs CD8), as well as different conditions . We analyzed only DNA sequencing based repertoire, and each sample contains both functional and non-functional clones. We removed all samples with less than 1000 clones. In the Emerson dataset, we used a random sample of 100 patients. We ignored the frequency of each clone in each donor to avoid biases induced by differential amplification. We grouped βV and βJ usage frequencies are paired, we compared the βV, βJ frequency distribution of functional (F) clones in each sample with the one expected under the null hypothesis of independent pairing. To compute that, the marginal probability of each βJ  P (βJ) value  in P  is larger  than expected by P (V4) P (J2) .To test whether βV, βJ) pair in a given sample:To systematically quantify this deviation, we computed for each  is expected to be zero for random pairing, finite size effect can induce deviations from zero. We thus compared the distribution of M  to the null model results, where the βV and βJ of the clones were scrambled. Specifically, we used the clones in the sample and randomly reassigned the βV genes of the different clones (see Methods). The distribution of M  for the F clone is wider than for the null model, as further shown.While, in principle, the value of M  distributions and performed a paired T-test on the standard deviations in the real and null models over all samples for each dataset. The standard deviation of the real clones is larger than the null model for all files .To quantify the difference, we computed the standard deviation in the real and null model of M Vβ, Jβ disll files  on the dβJβV usage also exists in the NF clones, we computed M  in the non-functional data , and found a deviation from the βV and βJ null model also in NF rearrangements. The standard deviation of the NF clones is slightly larger than the standard deviation of the null model   samples and samples of patients who had been diagnosed with alopecia by using a two-way ANOVA test. We obtained a p-value of 3.74e-4 for healthy vs unhealthy, 1.62e-125 for observed vs random and 0.244 for the interaction effect, suggesting that the difference between the real data and the null model is not induced by the condition of the host .βJβV usage was found in both F and NF clones, with more significant differences for the F clones, and limited differences between CD4 and CD8 T cells. Antigen-driven selection may be a simple explanation for the differences we found between F and NF clones. An alternative model may be preferential pairing of βV and βJ during rearrangement, or a structural selection preceding selection in the thymus. We here provide multiple lines of evidence for the last possibility, with a major contribution of structural selection.To summarize, a bias βV prefer some βD 1 or βD 2, which in turn prefer some βJ, leading to indirect pairing, between βV and βJ. T-cells have only two βD genes and two cassettes of βJ, where βj genes in the βJ 1 cassette bind to βD 1 and βj genes in the βJ 2 cassette can bind both DbD_\β genes. Thus, if the preferential βJβV binding would be induced by the choice of a specific βD gene, it should disappear, when only clones with βJ genes in the βJ 1 cassette are analyzed. We thus separated all clones according to their βJ gene groups, and analyzed the pairing in each group separately (βJ 1 and βJ 2). Formally, we separated each repertoire into two sub-repertoires according to the family of the βJ gene. Then, we calculated M  for each sub-repertoire, and repeated the tests above  vs 0.07 (βJ 2) for RH, 0.156 (βJ 1) vs 0.153 (βJ 2) for MM and 0.099 (βJ 1) vs 0.069 (βJ 2) for the Emerson data. We performed a T-test for the F clones between βJ 1 and βJ 2 and found that for the RH and Emerson datasets there are significant differences between βJ 1 and βJ 2 (p < 7.04e - 57 and p < 1.92e - 44) compared to MM where we found no significant difference (0.25). In addition, for all datasets, the difference between the real data and the null model is significant for both βJ 1 and βJ 2 genes , except for the NF clones in the βJ 2 MM dataset (p > 0.05). Thus, selection for βD cannot explain the observed bias.For all datasets, the standard deviation of the real data is larger than the standard deviation of the null model  values for all sample pairs from different hosts in the RH dataset, and computed the distribution of the correlation  pairs of these two samples were taken. One can clearly see that the correlation of the null model is centered around zero, while the correlation of the real data is centered around 0.6 for the F clones and 0.2 for the NF clones. The same holds for the other datasets (data not shown). The similarity between samples is consistent in the different βJ gene families (βJ 1 - βJ 2 - p < 1e - 100 for both βJ 1 and βJ 2). T-tests between the F and NF correlation distribution and the random distribution p < 1e - 100 for both βJ 1 and βJ 2).If pairing is induced by structural selection, it should be similar between hosts and samples. Alternatively, if the pairing is antigen-driven, we would expect it to differ between hosts and especially between CD4 and CD8 T cells. To test for that, we computed the Spearman correlation between the M Vβ, Jβ valβV and βJ loci compositions. If the βV, βJ pairing is affected by a genetic bias, we expect samples from the same host to have more similar biases than between hosts. Indeed, a slightly higher correlation was observed in samples within-host than between hosts for both F and NF samples (T-test between the correlations within-host and the correlations between hosts for both βJ 1 and βJ 2 genes: F clones – p < 6.68e - 39 (βJ 1) and p < 3.52e - 75 (βJ 2), NF clones – p < 3.37e - 8 (βJ 1) and p < 3.39e - 50 (βJ 2), null model – p = 0.91 (βJ 1) and p = 0.22 (βJ 2) . If antigen-driven selection also contributes to the paring mechanisms, we would expect CD4 T cells clones to have more similar pairing to other CD4 T cells than to CD8 T cells and vice versa.M  among patients and compartments and compared the effect of compartment vs the effect of hosts. We analyzed the F clones of the MM dataset. In order to check whether samples of the same patient or the same compartment are more similar, we computed the correlation within hosts (H+), within compartments (C+) and between hosts (H-) and between compartments (C-). For βJ 1 family, the correlations within compartment (H-C+) were only slightly higher than the one between compartments (H-C-) . However, the correlations within hosts (H+C-) were much higher . The correlations within-host and compartment (H+C+) were the highest   and within hosts (H+C-) were slightly higher than the one between compartments (H-C-) . The correlations within-host and compartment (H+C+) were the highest  .To test for that, we explored the correlations between the values of M Vβ, Jβ amop < 2.39e - 124). Compartments were not grouped more than expected randomly. The stronger similarity within donors further suggests a stronger effect of the genetically induced bias in the rearrangement mechanism than the antigen-driven one, and the correlation in all samples that is higher in the F than NF clones suggest an important component of structural selection.We further tested if samples in the same host or same compartment were clustered together, we clustered the correlations using hierarchical clustering based on the Euclidean distance and complete linkage [βV, βJ) pairs with the most significant deviation from random pairing (p < 0.01), and found that there is a large overlap in these specific pairs between the different datasets . In addition, most of the significant pairs that overlap between the three datasets have the same deviation sign .If the selection is indeed genetic/structural and it happens before any antigen-induced selection, we expect the pairs selected for and against to be consistent among datasets, and between CD4 and CD8 T cells. To test that, we analyzed all the  between any two datasets, and compared M  values among datasets, or among compartments in the same dataset (CD8 vs CD4 cells). Indeed, M  is highly consistent among the datasets for both βJ 1 and βJ 2, with a higher average correlation for βJ 1 (0.81 vs 0.72) .We further analyzed the common significant pairs $ i.e. M distributions and performed a paired T-test on the standard deviations in the real and null models  pairing exists even in the βJ 1 family genes that only use βD 1 in NF clones. However, there is no direct rearrangement of βV and βJ, so it is unclear how can such a pairing occur. We hypothesized that the pairing between βV and βJ is through the length of the junction between βV and βD and the length of βJ and βD. In other words, different βJ genes favor different junction lengths and so do different βV genes. This length preference combined with a preference for intermediate length CDR3 genes  is the difference between the end of germline βV and the beginning of germline βD for the first junction and similarly with βD and βJ for the second junction. For the βJ gene, we performed this analysis on βJ 1 and βJ 2 separately (βJ 1 (βJ 2 (data not shown). Indeed, consistently, J01 - 03 has the highest average junction length and J01 - 06 has the lowest for the βJ 1 family gene. For the βJ 2 family, J02 - 06 has the highest, and J02 - 01 has the lowest junction length. Similarly, different βV have different junction lengths. Thus, βV and βJ may match to ensure the proper CDR3 length.To test that, we calculated the average number of insertions minus the number of deletions for each βV, βJ) pair in each F sample, the average length (the sum of βV and βJ genes length in AA), molecular weight (MW), hydrophobicity (as measured by the kyte doolittle -KD score), and charge (as measured by the iso-electric point - IP).To test that pairings that produce intermediate receptor sizes are preferred, we computed for the receptor with each  values for intermediate to low isoelectric points, molecular weights and length, and a more complex picture for the KD. In other words, V and J genes pair to favor intermediate polarity and weight, but also some specific polarity of the resulting receptor.We computed a two-dimensional histogram on the RH dataset for both the βV - βJ pairing.The peripheral T cell receptor repertoire is known to be shaped by three main selection mechanisms - thymic positive and negative selection and antigen-driven peripheral selection –32. We hVβ - Jβ pairing, associated with a preference for intermediate length, molecular weight and polarity of the CDR3. However, other biases may have to be incorporated when developing artificial TCRs.The genetic engineering of T cells for immunotherapy is one of the best hopes for novel cancer treatments . Such reβV - βJ pairing is ubiquitous and shared in all datasets studied in F clones, with some preferential pairing occurring in NF clones too. We proposed multiple evidences for structural selection events. Specifically, we showed that the frequency of human βJβV combinations deviates from the one expected based on random pairing and each gene usage frequency. Preferred βV - βJ pairs are shared between samples and between datasets. This sharing (as measured by the correlation coefficient) is maximal in samples within a donor. The correlations within each host are much higher than the correlations between different hosts, and the correlation between CD4 and CD8 T cell samples is higher than between samples from different compartments. Beyond the general distribution, the βV, βJ pairs most deviating from random pairing are similar in different datasets and conditions. We have analyzed bulk sequencing, and not single-cell data. Our results are robust in different sets sampled with different methods and different primers. We thus believe they should hold in single-cell data.We have shown that preferred βJ 1 and βJ 2 J genes in mice. The simplest molecular explanation for such a preferential pairing would be that βV - βJ pairs affect the biochemical properties of the receptor, and that receptors on the extremities of the distribution are selected against, as we have shown here for multiple biochemical properties, such as the length in nucleotides, the molecular weight, the charge and the polarity of the receptor. This is consistent with the relation between the V-J combination used and the CDR3 length distribution, especially for pathogen-specific TCRs  βJ recombination is the main diversity generation mechanism in receptor repertoires. This diversity derives in large part from the multiple combinations of possible joining events and through an inherent imprecision in the joining reaction . Thus, a different analysis is required, since we cannot neutralize the effect of HD. We now explore this as a follow-up work.As for the bias in https://elifesciences.org/articles/54747https://link.springer.com/article/10.1186/s13073-021-00918-7https://www.nature.com/articles/ng.3822?report=readerhttps://www.nature.com/articles/s41467-019-08906-7.Publicly available datasets were analyzed in this study. This data can be found here: RL performed the analysis, produced the figures and wrote a part of the manuscript. YL supervised and conceptualized the analysis and wrote a part of the manuscript. All authors contributed to the article and approved the submitted version.The work of RL was funded by ISF grant 870/20 and by an internal BIU DSI grant.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. t:All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Breast cancer (BC) is the most common malignancy worldwide and neoadjuvant therapy (NAT) plays an important role in the treatment of patients with early BC. However, only a subset of BC patients can achieve pathological complete response (pCR) and benefit from NAT. It is therefore necessary to predict the responses to NAT. Although many models to predict the response to NAT based on gene expression determined by the microarray platform have been proposed, their applications in clinical practice are limited due to the data normalization methods during model building and the disadvantages of the microarray platform compared with the RNA-seq platform. In this study, we first reconfirmed the correlation between immune profiles and pCR in an RNA-seq dataset. Then, we employed multiple machine learning algorithms and a model stacking strategy to build an immunological gene based model (Ipredictor model) and an immunological gene and receptor status based model (ICpredictor model) in the RNA-seq dataset. The areas under the receiver operator characteristic curves for the Ipredictor model and ICpredictor models were 0.745 and 0.769 in an independent external test set based on the RNA-seq platform, and were 0.716 and 0.752 in another independent external test set based on the microarray platform. Furthermore, we found that the predictive score of the Ipredictor model was correlated with immune microenvironment and genomic aberration markers. These results demonstrated that the models can accurately predict the response to NAT for BC patients and will contribute to individualized therapy. At present, NAT for BC patients with aggressive phenotypes has been recommended by several clinical practice guidelines. To achieve higher pCR rates and better prognosis, anthracycline and/or taxane-based therapy is currently the preferred treatment regimen. However, only 14.7%~52.9% (Breast cancer (BC) is the most common malignant tumor and the fifth leading cause of cancer-related death worldwide. In 2020, about 2,261,419 females were diagnosed with BC, and 684,996 died from BC globally . Therefoin vitro cell line or a pan-cancer dataset. This may lead to their prediction failure in vivo or in patients with specific cancer types and specific treatments due to the complex and variable biological environments in vivo. Moreover, a few machine learning models to predict the response to NAT in BC patients have also been proposed. Some models integrated clinicopathological features . Transcripts per million (TPM) data and clinicopathological information of GSE163882 and GSE123845 datasets were obtained from Gene Expression Omnibus  and the literature . Raw data and clinicopathological information of GSE20271 profiled on a DNA microarray platform (Affymetrix Human Genome U133A 2.0 Array), were obtained from GEO. Samples in the datasets with incomplete pCR information were removed. Another RNA-seq dataset of BC patients was downloaded from The Cancer Genome Atlas , and the relevant mutation and immune microenvironment data were obtained from the literature (https://www.gsea-msigdb.org/).Immune gene list and category information were obtained from IMMPORT  to identify DEGs between patients who achieved pCR and those who did not , Sequence Read Archive , and The Cancer Genome Atlas .Publicly available datasets were analyzed in this study. This data can be found here: Gene Expression Omnibus  and the National Natural Science Foundation of China .We thank the contributors and providers of GSE123845, GSE163882, GSE20271, and TCGA-BRCA for sharing the datasets in public databases.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


RNA sequencing and other high-throughput technologies are essential in understanding complex diseases, such as cancers, but are susceptible to technical factors manifesting as patterns in the measurements. These batch patterns hinder the discovery of biologically relevant patterns. Unbiased batch effect correction in heterogeneous populations currently requires special experimental designs or phenotypic labels, which are not readily available for patient samples in existing datasets.We present POIBM, an RNA-seq batch correction method, which learns virtual reference samples directly from the data. We use a breast cancer cell line dataset to show that POIBM exceeds or matches the performance of previous methods, while being blind to the phenotypes. Further, we analyze The Cancer Genome Atlas RNA-seq data to show that batch effects plague many cancer types; POIBM effectively discovers the true replicates in stomach adenocarcinoma; and integrating the corrected data in endometrial carcinoma improves cancer subtyping.https://bitbucket.org/anthakki/poibm/ (archived at https://doi.org/10.5281/zenodo.6122436).Bioinformatics online. High-throughput molecular technologies are central to understanding complex diseases, such as cancers. However, datasets are often aggregated from several hospitals, treated with different protocols, and analyzed with different measurement technologies, which leads to unwanted factors creeping into the data, manifesting in experiment specific (‘batch’) patterns , 2017, tet al., 2014), can adjust the analysis for the presence of such factors. However, these models might be arduous to integrate into more complex analysis algorithms, such as network inference, and as a result, modular batch correction algorithms have been developed to preprocess the data for other analyses , which is based on an idea of inferring virtual reference samples from the data. Consequently, special experimental designs or design factors are not required since POIBM automatically learns these from the data. This enables unbiased correction on complex patient data where the phenotypes are not known and exact replicates are not available. POIBM is designed to be optimal for RNA-seq count data, similar to ComBat-seq  or a low-rank known linear combination is used ; iju are the expression profiles of the matching pairs; and Y, respectively; as in above. Further, Let xρ and yρ on the datasets X and Y, respectively. If xρ and yρ are chosen to be a lower bound of the fractions of shared phenotypes, the scheme remains unbiased.When the data feature samples for which a matching sample cannot be interpolated, such as when the datasets are known to contain major unique phenotypes each, a trimming procedure is necessary: the model is imposed only on a fraction of samples kjw are updated such that:kjw are set to zero. The updates of The model of X, the source read count matrix Y, and some parameters: maximum number of EM iterations, number of restarts, and fraction of target xρ and source samples yρ to be used. The restarts are used to combat local solutions, which occur particularly when trimming is used. The restarts use uniform random initial assignment of the trimmed samples. The other values are initialized as ic = 1, The algorithm inputs the target read count matrix ic, and the total RNA factors kjw hold information on to which target sample each source sample is being mapped. The batch correction from the source to the target space is finally applied by multiplying in the batch coefficients:ic are explicitly estimated, out-of-sample mapping of future data is also possible.The model directly provides the batch coefficients HER2 with 12 controls; batch 2 (GEO: GSE59765) has 6 samples overexpressing EGFR with 6 controls; and batch 3 (GEO: GSE83083) has 9 samples overexpressing KRAS (G12V mutant) with 9 controls. Genes with zero expression in all samples of any batch were removed. The final matrix contained 47 samples and 18 013 genes. The samples can be divided into either three technical batches or four phenotypes, i.e. HER2, EGFR, KRAS or control.A specially constructed RNA-seq experiment, as proposed in After applying each method, the batch corrected data were scaled into counts per million (CPM) and log-transformed for comparison using principal component (PCA) and variance analysis (ANOVA) as in https://gdac.broadinstitute.org/) on March 3, 2021. Genes not present in all datasets were removed. In total, the data consisted of 59 datasets, 37 cancer types, 17 959 samples (some of which occurred in multiple datasets) and 21 184 genes. The data was split into 6 batches by the processing institute, pipeline and sequencing platform.The Cancer Genome Atlas (TCGA) level 3 RNA-seq data for each cancer type was downloaded from the Broad GDAC Firehose portal  RNA space. The methods differ in either the unmodeled variation (error model) or in the retained modeled variation (payload model). ComBat and RUVSeq use Gaussian error models in log-RNA space, while ComBat-seq uses a negative binomial error model and PRISM and POIBM use scaled Poisson models in raw RNA space. Specifically, the last three methods model explicitly discrete and heteroscedastic RNA-seq data. ComBat, ComBat-seq and RUVSeq allow a known linear payload (e.g. linear group factors), while more general methods like PRISM can further learn these factors (i.e. bilinear model), and POIBM uses probabilistic sample matching.k was set to 1. PRISM rank-1 factorization inputs one batch at a time and outputs the marginal gene and sample coefficients as in As for the input, ComBat requires the batch labels, the groups and a log-transformed count matrix. The output is a corrected matrix in the log-space. ComBat-seq uses the batch labels, groups and the count data matrix, while the parameter ‘shrink’ was set to false (default). The output is a corrected matrix in the raw count space. RUVSeq uses the groups and the count matrix, and the number of factors of unwanted variation POIBM is a novel method for correcting batch effects in RNA-seq data between heterogeneous populations. The novelty of the method is that two types of heterogeneity are tolerated: (i) distinct phenotypes in the samples composing the dataset—it is only necessary that a sufficient number of virtual target samples can be interpolated from a dataset; and (ii) stochasticity (noise) due to natural gene expression variability and RNA-seq sampling. Moreover, the underlying phenotypes need not to be known a priori, but are learned in the process, which means that special experimental design or replicate samples are not necessary.https://bitbucket.org/anthakki/poibm/ under the simplified BSD license.POIBM utilizes only two expression matrices of read counts, a target matrix and a source matrix. Each sample in the source matrix is compared with all samples in the target matrix, from which a virtual target sample is constructed , as detailed in Section 2. The methods used in the comparison were ComBat , and infer the batch coefficients from these. This is unlike to the other methods, which require known batch labels, which were provided for the analysis. While running POIBM without trimming produced unsatisfactory results as the similar  results . Similar results .EGFR cases remain mixed with the control samples. However, the latter is exhibited by all of the methods, with and without both the batch and phenotypic information, suggesting that the phenotypes are in fact partly overlapping.Our results indicate that POIBM is effective in removing the unwanted batch variance, while the biological variance is left intact . The priQuantitatively, POIBM retains a similar level of phenotypic (condition) variance as ComBat-seq  and ComBThe results suggest that POIBM can significantly outperform both RUVSeq and the PRISM rank-1 on these data, and match the performance of the newest state-of-the-art methods such as ComBat-seq, with respect to both removing batch specific variation and retaining phenotypic variance. However, the main difference here is that ComBat-seq, ComBat, RUVSeq and linear PRISM are informed of which samples are controls and which are not , while POIBM discovers the phenotypic labeling automatically . Despite this lack of information, POIBM still performs no worse. Compared to rank-1 PRISM, which uses the same RNA-seq model than POIBM but lacks the phenotypic modeling, we conclude that the novel sample matching approach is the key to the superior performance.The methods were also compared using Monte Carlo simulations as detailed in the The Cancer Genome Atlas (TCGA) is a vast collection of molecular data from various cancer types. Despite the data being collected from various sources and analyzed at various institutions, studies of its batch effects are scarce. In most studies, the analysis is limited into a particular subset of samples to mitigate batch effects , 2017, oOn the TCGA level 3 expression data, one obvious source of batch effects is that the data are sequenced using either Illumina GA (‘illuminaga’) or HISEQ (‘illuminahiseq’) sequencing system, were processed using an older  or a newer pipeline , and were processed either at University of North Carolina (‘unc.edu’) or at Canada’s Michael Smith Genome Sciences Centre (‘bcgsc.ca’). These combinations yielded a total of six batches, a shown in We performed a pairwise estimation of the batch effects in each batch-pair using POIBM, which quantifies the extent of batch effects between the different batches. Correction coefficient of unity is indicative of a lack of batch effect, while large deviations suggest more drastic batch effects. The deviation of the logarithmic batch coefficients from unity over all genes were consequently used as distances between the batches in a hierarchical clustering. The differences between the clusters  indicaterage cf. , suggestBy cancer type  the implWe inspected the POIBM established sample matchings in stomach adenocarcinoma (STAD) . This caBetween the clusters, we found that tion cf. , as expeSimilar findings were made regarding the TCGA acute myeloid leukemia (LAML) data, as detailed in the Next, we analyzed the data for uterine corpus endometrial carcinoma (UCEC)  nor with four clusters , but had suitable overlap with five clusters . We performed the clustering for both uncorrected data , which iP-values P-value of P-values P-values P-value of 0.45), further evidencing that the addition of the new samples changes the overall population distribution.We found that the clusterings of the uncorrected data exhibit strong batch specificity . The corrected data exhibits association between the serous histology and the mitotic cluster  and the uncorrected  the mitotic and the hormonal clusters, respectively, significantly differ from the other two which are not significant. This further supports the finding that adding the new, batch corrected data does not only yield more statistical power but also a clinically more refined picture of the two minor clusters.We tested the association with between the clusters and patient overall survival . The surWe note that the uterine serous tumors share genomic features with serous ovarian and basal-like breast cancers (We designed POIBM, an effective method for batch correction of RNA-seq data that is designed to perform well on heterogeneous populations and on discrete, noisy RNA-seq data. The uniqueness of the method is that for each source sample a virtual target sample is formed from the target dataset, from which the batch coefficients are inferred. This implies that the matching samples need not to be known, and replicates need not to exist, but these are learned from the data. POIBM also models the discrete and heteroscedastic nature of RNA-sequencing or other count data, which makes it suitable for low-coverage sequencing data.We used engineered breast cancer cell line overexpression experiments to show that POIBM can automatically learn the underlying phenotypic structure and matching replicate samples. Furthermore, our results indicate that even in the absence of the phenotypic labels it performs at least as well as the existing methods, which require such labeling. This is essential for complex datasets like cancer patient samples where the phenotypes are not known a priori, but are under investigation from the datasets in question and/or feature variation even within the samples of the same tumor.By examining the publicly available TCGA RNA-seq data, we discovered that many of the cancer types contain their data distributed over two or more technical batches, and we showed that these technical factors can disturb the downstream analyses of the data if used without correction. We harmonized all the 17 959 RNA-seq samples with the six batches across all the cancer types, which facilitates the use of TCGA expression data for more accurate analyses and for unbiased comparisons across cancers. Specifically, we showed that in stomach adenocarcinoma POIBM can accurately identify the technical replicates, which allows identification of the implications of the batch effects, while in endometrial carcinoma we showed that batch harmonization using POIBM is necessary to extract full clinical power from the expression dataset.We expect our methodology is indispensable for analyses integrating data from various collections, and even for long-running data collections, as the sequencing platforms and analysis pipelines cannot necessary be kept fixed. Our approach generalizes directly to any count data such as proteomics, and can be influential in advancing batch correction efforts for other molecular data domains.btac124_Supplementary_DataClick here for additional data file.


Studies have shown that classifying cancer subtypes can provide valuable information for a range of cancer research, from aetiology and tumour biology to prognosis and personalized treatment. Current methods usually adopt gene expression data to perform cancer subtype classification. However, cancer samples are scarce, and the high-dimensional features of their gene expression data are too sparse to allow most methods to achieve desirable classification results.In this paper, we propose a deep learning approach by combining a convolutional neural network (CNN) and bidirectional gated recurrent unit (BiGRU): our approach, DCGN, aims to achieve nonlinear dimensionality reduction and learn features to eliminate irrelevant factors in gene expression data. Specifically, DCGN first uses the synthetic minority oversampling technique algorithm to equalize data. The CNN can handle high-dimensional data without stress and extract important local features, and the BiGRU can analyse deep features and retain their important information; the DCGN captures key features by combining both neural networks to overcome the challenges of small sample sizes and sparse, high-dimensional features. In the experiments, we compared the DCGN to seven other cancer subtype classification methods using breast and bladder cancer gene expression datasets. The experimental results show that the DCGN performs better than the other seven methods and can provide more satisfactory classification results.The online version contains supplementary material available at 10.1186/s12859-022-04980-9. Human cancer is a heterogeneous disease triggered by random somatic mutations and driven by multiple genomic alterations due to uncontrolled abnormal cell proliferation and spreading to other cells and tissues , 2; cancGene expression data reflect the direct or indirect measurement of the abundance of gene transcript mRNA in cells. These data can be used to analyse which gene expression characteristics have changed, the correlations among genes, and how the activities of genes are affected under varying conditions. These data thus have important applications in medical clinical diagnoses, drug efficacy judgements, and in revealing disease mechanisms. Hence, gene expression data can be used in cancer subtype classification research, and many methods based on gene expression data have been presented.The cancer subtype classification task can be formulated as a supervised learning problem in which established tumour subtypes are used as category labels to ensure that the features learned by the model are relevant to prior biological knowledge . Early rIn 2017, Soh et al.  developeIn 2019, Yang et al.  used a sIn past studies applying the above methods, different measures have been taken to address the characteristics of cancer gene expression data through either linear dimensionality reductions or data equalizations. However, linear dimensionality reduction methods are easily affected by irrelevant information, some methods cannot handle high-dimensional gene table data well, and the classification results are thus not ideal . To addrThe main contributions can be summarized as follows. (1) By combining CNN and BiGRU, we proposed a deep learning method named DCGN that can obtain more credible features from high-dimensional sparse gene expression data. The experimental results prove that the DCGN method can obtain ideal classification results. (2) The Gaussian error linear unit (gelu) activation function is applied to the cancer classification task, and we prove through experiments that its performance is superior to those of the rectified linear unit (relu), exponential linear unit (elu), etc. (3). The DCGN performs well when applied to five high-dimensional datasets and has a good generalization ability.DCGN adopts gene expression data to perform cancer subtype classification. It consists of three modules see Fig. . 1. The First, classes for which the sample size is less than 15% of the total sample size are specified as minority sample sets , a convolution layer, a BiGRU layer, and another convolution layer. The input layer first goes through the FC layer, and the FC layer computation process is essentially matrix multiplication. Then, the computational result is output by the activation function. The calculation formula is expressed as follows, where x represents the input matrix, W is the weight parameter, b represents the bias, GELU is the activation function of this layer, and Y represents the nonlinear output through the activation function.The activation function is the "switch" that determines whether a neural network transmits information or not; this function is crucial in neural networks. Different activation functions greatly impact the training effect of neural networks. At present, the most commonly used activation functions are the relu(Recitified Linear Unit) function, sigmoid function, elu function, etc. In this paper, an activation function called gelu(Gaussian Error Linear Unit) is selected. Some experiments have shown that gelu is superior to other activation functions, such as relu and elu, for tasks ranging from computer vision to natural language processing . We condGelu can be seen as a combination of relu and dropout ideas. For high-dimensional gene expression data, excessive features may affect the feature-learning procedure. Sometimes we want to regularize unimportant information to zero, and the nonlinear variation feature of the gelu activation function can perform stochastic canonical transformation. It can be understood that a given input value should be multiplied by 1 or 0 according to its specific situation. For a more mathematical description, each input value x that obeys the standard normal distribution N is multiplied by a Bernoulli distribution. In Fig. The gelu function has the following form:al paper  as folloThe outputs of the FC layer are next subjected to convolution operations. Because CNN are mostly used for image processing, the calculation process typically involves a number of image channels ); however, the data used in this article are characterized by numerical matrices of gene expression data, which differ from image data, so it is necessary to describe the calculation process. The CNN calculation is different from that of the FC layer. The input matrix format includes four dimensions: the number of samples, height, width, and number of channels. The output matrix format has the same dimensional order and meaning as the input matrix, but the sizes of the last three dimensions are changed by the convolution operation. The meaning of the weight matrix (convolution kernel) dimensions is different from those of the above two matrices. These are the height of the convolution kernel, the width of the convolution kernel, the number of input channels (the number of channels in the input matrix), and the number of output channels (the number of convolution kernels).Taking the first convolutional layer as an example, the FC layer output as N,1024) becomes  after a Reshape operation is applied, where N represents the number of samples in the batch, the height and width are both 32, and the number of channels is only one. The first convolutional layer is the conv2D layer with 128 convolutional kernels of size , padding = same, strides = 2. The term "padding = same" indicates that the output size is equal to the input size divided by the strides and rounded up. The calculation process is shown in Fig. 024 becomThe convolution layer also contains a maximum pooling layer. This layer can reduce the size of the model, improve the calculation speed, and improve the robustness of the extracted features. However, the maximum pooling layer has no parameters to learn and can only takes the maximum value from the target area; thus, the numbers of input and output channels do not change..The gated recurrent unit (GRU) uses an update gate and a reset gate. The update gate determines how much information from the past should be allowed to pass through the gate, while the reset gate decides how much information from the past should be discarded. First, we obtain the two gating states from the last transmission down state When the gating signal is obtained, we first use reset gating to obtain the reset data Finally, the most critical step in GRU is the “update memory” step, in which we perform both forgetting and remembering tasks. The update gate The above process represents forward delivery, and the BiGRU layer contains both forward and reverse gated recurrent units, as shown in Fig. The DCGN takes the output of the feature-learning module into the classification module composed of four fully connected layers after a straightening operation is performed. We use a dropout layer after each fully connected layer to improve the generality of the network and to mitigate the interactions between neurons. The last layer directly outputs the tensor computed by the network, which may be optimally numerically stable.The loss function of the neural network is the SparseCategoricalCrossentropy function; this function can convert digital coding into a one-hot coding format and then apply the cross entropy loss function to the data  and the predicted label value. The multicategorical cross-entropy loss function is actually an extension of the bicategorical cross-entropy loss function, as expressed in Eq. , where MTo demonstrate the validity of the proposed method, we conducted experiments on breast and bladder cancers. The breast cancer dataset used herein was obtained from a previous Molecular Taxonomy of Breast cancer International Consortium (METABRIC)  study. CThe number of nodes in the feature learning module was set to 1024, 128, 64, and 64, while the number of nodes in the classification module was set to 128, 64, 32, and 10. For the model construction and performance evaluation steps, we randomly divided the data into a training set, a validation set, and a test set containing 80%, 10% and 10% of the samples, respectively. To improve the memory utilization and parallelization efficiency in the large matrix multiplication process, we set the batch size to 256. Then, we used the Adam method [To prove the robustness of the method proposed in this paper, we selected seven methods based on machine learning or deep learning approaches to conduct experiments. The following text briefly introduces the compared methods, among which gcForest , SAE, BiThe basic SVM model is a linear classifier with the largest interval defined on the feature space; in the gradient boost decision tree (GBDT) , the decEvaluation metrics are critical criteria used to measure whether a method performs well when facing a given problem. For classification problems, metrics such as the accuracy, precision, recall, F1-score, and confusion matrix  are normTo prove the influence of the gelu activation function selected in this paper on the model, we selected three other activation functions, relu, elu, and tanh, as the activation functions of the model and conducted comparative experiments on the bladder urothelial carcinoma (BLCA)-TCGA dataset. The experimental results are shown in Fig. There are many robust network structures in deep learning, and different combinations of networks may perform differently. To demonstrate that the DCGN proposed in this paper can provide better results than other network structures, we used different neural networks to obtain free combinations and verified the networks on the BRCA 20,000-dimension dataset. The experimental results are shown in Fig. From Fig. To further validate the effectiveness of the proposed approach, we compared DCGN with the seven methods mentioned in “Comparative methods: section on the BRCA 20,000-dimension dataset. The dimensionality of the data matrix after data enhancement was , and the specific results are shown in Table From Table A confusion matrix is a situation analysis table that summarizes the prediction results of a machine learning classification model. In the form of a matrix, the situation in the dataset can be summarized according to two standards: the real category and the category predicted by the classification model. A confusion matrix thus gives a more intuitive picture of how well a model performs, because all correct predictions are shown on the diagonal and all wrong predictions are shown off the diagonal; thus, it is very straightforward to identify incorrect predictions. Figure In addition, two multiclassification metrics, the Kappa coefficient  and HammAs is widely known, the generalization ability of a model is an important criterion for judging its quality. Our proposed model performed well on the BRCA 20,000-dimension dataset. To demonstrate the generalization ability of the proposed model, we next conducted experiments on four high-dimensional BLCA datasets. The BLCA datasets were processed separately according to the four molecular typing systems as described in “Experimental data” section. After data enhancement, we loaded the data matrix and labels into each model to perform the experiments.The experimental results of the BLCA datasets are shown in Tables The method proposed herein still has some limitations. In this study, our method exhibits decent classification performances when applied to breast cancer and bladder cancer datasets. The subtype classifications of these cancers have been established; however, there are many cancers for which subtypes have not been accurately identified. Therefore, supervised learning of these other cancers is not yet possible. In addition, our approach to cancer classification is based solely on gene expression data. However, several recent studies have shown  that comIn this paper, we proposed the DCGN, a deep learning method for cancer multiclassification tasks; this proposed model can better handle high-dimensional cancer data than other available models. In terms of classification evaluation indicators, such as the accuracy and precision, the DCGN performs well on all five analysed datasets, especially on the BLCA-TCGA and BLCA-CIT datasets, with values exceeding 99%. These results show that the method proposed in this paper can obtain ideal classification results and has a superior generalization ability. However, this paper considers only gene expression data, and we will integrate multiomics data to further study cancer subtype classification in future work.Additional file 1: Deep learning approach for cancer subtype classification using high-dimensional gene expression data.


HR) is the most frequently used measure of association between gene expression and patient survival, but it is prone to an overestimation bias. If rare diseases are investigated in the absence of an external cohort, it is difficult to control this lack of accuracy. We propose a simple, test-based method to obtain the HR, adjusted for the overestimation bias. Validation using both simulated data and gene expression profiles from two publicly available data sets is provided. Furthermore, we show that the proposed method is able to identify a new gene with potential oncogenic activity in the reanalysis of a data set including 134 patients affected by Stage 4S neuroblastoma.Studies aimed at assessing the potential prognostic role of gene expression profiles in cancer patients often employ running procedures to select optimal cut-offs for the identification of groups with a poorer outcome. The corresponding hazard ratio (HR) is usually estimated, representing a measure of the relative risk between patients with marker values above and below the cut-off. A posteriori methods identifying an optimal cut-off are appropriate when the functional form of the relation between the marker distribution and patient survival is unknown, but they are prone to an overestimation bias. In the presence of a small sample size, which is typical of rare diseases, the external validation sets are hardly available and internal cross-validation could be unfeasible. We describe a new method to obtain an unbiased estimate of the HR at an optimal cut-off, exploiting the simple relation between the HR and the associated p-value estimated by a random permutation analysis. We validate the method on both simulated data and set of gene expression profiles from two large, publicly available data sets. Furthermore, a reanalysis of a previously published study, which included 134 Stage 4S neuroblastoma patients, allowed for the identification of E2F1 as a new gene with potential oncogenic activity. This finding was confirmed by an immunofluorescence analysis on an independent cohort.The early evaluation of prognostic tumour markers is commonly performed by comparing the survival of two groups of patients identified on the basis of a cut-off value. The corresponding hazard ratio ( HR) obtained by the corresponding Cox regression model [p-value, adjusted for the overestimation bias, can be obtained to test the null hypothesis of no association between the marker levels and the patients’ survival by a random permutation analysis. The distribution of the corresponding test statistic is obtained under the null hypothesis by recursively swapping the follow-up times and the corresponding outcome indicators in couples of patients randomly selected in the data set [p-value but does not remove the overestimation bias from the HR. The purpose of this study is to illustrate a simple, test-based method to obtain HR estimates that are adjusted for the overestimation bias. An example of its application will be provided by a reanalysis of data from a previously published study involving 134 patients with Stage 4S neuroblastoma (NB) [The early evaluation of potential tumour markers for prognostic applications is usually carried out by comparing the survival of two groups of patients identified on the basis of a threshold value. A cut-off selected a priori can be used for such a purpose, based on the percentiles of the observed marker distribution as median, tertile, or quartile values . In moston model . In any on model ,3,4. In data set . The prooma (NB) .HR estimates. T be the (likely biased) test statistic calculated for the comparison of two groups identified by an optimal cut-off and let T*k), obtained from the proportion of T*k)( ≥ T [Let *(k) ≥ T ,7:(1)p*=T is usually a test statistic for the comparison of two survival curves or for the inference on the corresponding coefficient from a Cox regression model. For instance, a Cox model is usually employed to assess the association between a tumour marker evaluated at a specific cut-off and patient survival. The corresponding regression coefficient represents an estimate of the natural logarithm of the HR (ln(HR)) between the group of patients with marker values above the selected threshold and those with values below the threshold [HR) is prone to an overestimation bias when the threshold is identified by a running procedure. Here, we propose a simple method to obtain an unbiased estimate of ln(HR) from the corresponding adjusted p-value (p*), which is estimated according to Equation (1).In the analysis of patient survival, hreshold . The estHR) = 0), a normal asymptotic distribution for ln(HR) can be assumed [V is the variance of ln(HR) and Under the null hypothesis  is easily obtained by replacing HR:Let n = 393). Their characteristics are summarized in MYCN amplification was observed in 153 (20%), and 373 (48%) were diagnosed in localised stages: namely, 143 in Stage 1, 125 in Stage 2, and 105 in Stage 3. There were 412 (53%) patients diagnosed with metastatic disease, including 320 at Stage 4 and 92 at Stage 4S. The number of observed deaths was 229. Random splitting allowed for a quite balanced distribution of the variables in the training and in the test sets, except for a slightly higher proportion of patients with disseminated disease in the former (55.5% vs. 49.4%). This was due to a higher proportion of Stage 4 patients (43.3% vs. 38.2%).The statistical validation of the proposed method was performed using data from two large databases that were randomly split into a training set and a test set of equal sample size. The first data set, published by Cangelosi and collaborators, included information on 786 patients affected by NB, the most frequently occurring solid malignancy in infants, and 13,696 gene expression profiles [n = 186) and without follow up information (n = 78) were excluded from the analyses. Characteristics of the 499 considered patients are presented in n = 241, 48.3%) followed by Group 3 , WNT (8.0%), and SHH . Classic histology was observed in 279 patients (55.9%), desmoplastic in 65 (13.0%), large cell/anaplastic in 57 (11.4%), and extensive nodularity in 14 (2.8%). Metastatic disease was observed in 148 patients (29.7%), and 139 patients died of MB (27.9%). Random splitting allowed for a quite balanced allocation of the patients’ characteristics except for the male gender, which was slightly more represented in the test set (70.3% vs. 59.2%).The second data set, published by Cavalli et al., included the expression profiles of 18,479 genes in 763 samples of medulloblastoma (MB), the most common malignant central nervous system tumour in children . PatientDue to the heavy computational burden, a convenience sample of 1000 genes in each database (the first ones included) was used for the analysis, as described in the following paragraph.HR estimate, which was obtained from the corresponding univariable Cox model, using the method described in HR was estimated applying Firth’s correction, which is based on a penalized likelihood function [For each gene included in the validation analysis, overall survival was estimated in the training set by selecting the optimal cut-off using a running procedure and adjusting the function .HRs from the training set and the corresponding HRs from the test set, expressed on a logarithmic scale. The reduction in the overestimation bias was estimated by the corresponding difference obtained by replacing the unadjusted HRs with the adjusted ones. The same procedure was also performed using the median value as a cut-off. The results of this latter analysis are expected to provide an internal referent as this approach is not prone to an overestimation bias. All analyses were performed by separating the genes into potentially over- and under-expressed categories  on the basis of the corresponding coefficient of the Cox regression model, evaluating the expression value of each gene in the entire data set.The overestimation bias was estimated by computing the difference between the unadjusted Both the survival and permutation analyses were performed using the R programming language . The R lHR estimates, on a logarithmic scale, in the training set and in the test set of the Cangelosi et al. database [HR distribution around the null as a consequence of the overestimation bias. Such a gap was no longer evident after correction for the overestimation bias according to the procedure described in p < 0.001 for unadjusted estimates, and r = 0.847, p < 0.001 for adjusted estimates, respectively). Similar figures were observed for the cut-offs based on median values .database . UnadjusHR) estimates calculated in the training set and in the test set of the Cangelosi et al. database [HR < 1 and higher for HR > 1  and were slightly negative for HR > 1 . Using the median value of each gene expression as a cut-off, the corresponding unadjusted estimates were: median value: 0.026; IQR: −0.126–0.195 for HR < 1 and median value: −0.012; IQR: −0.204–0.159 for HR > 1 . Similar estimates were observed for cut-offs based on median values .database . In Figuion bias B. The coHR) estimates calculated in the training set and in the test set. Median values of the optimal, unadjusted estimates in the training set were lower than those in the validation set for HR < 1 and higher for HR > 1  and for HR > 1 . Using the median value as a cut-off, the corresponding estimates for unadjusted values were: median value: −0.051; IQR: −0.240–0.192 for HR <1 and median value: 0.043; IQR: −0.189–0.252 for HR > 1  estimates were obtained by 2000 random permutations for each simulated gene expression.A preliminary analysis under the null hypothesis of no association between gene expression profiles and patient survival was carried out using a simplified model. Five artificial data sets, each including 1000 randomly simulated expression values , were randomly extracted from a normal distribution, arbitrarily setting the mean to four and the variance to one. The sample size varied from 20 to 100 (step 20), and a further sample of 200 statistical units (the “patients”) was also generated. Each sample was associated with a follow-up time randomly generated under the assumption of an exponential model for the survival probability, setting the event rate (lambda) to 0.1 arbitrary units. The follow-up time was right-truncated at 10 units to generate censored observations. The simulation process was entirely repeated after changing the lambda parameter to 0.3, thus obtaining, on the whole, 12,000 independent gene expression profiles. Adjusted ln(HR) estimate at the optimal cut-off and its expected value under the null, calculating the corresponding standard error (SE). The reduction of the overestimation bias by the proposed method was assessed by performing the same analysis on the adjusted ln(HR). The corresponding estimates, obtained using the median values as a cut-off, were also calculated to obtain a referent distribution. The overfitting related to the running method for the selection of an optimal cut-off was assessed, estimating the corresponding Type I error by the proportion of statistical significances of the likelihood ratio test associated with the HR estimates in the univariable Cox regression model. The usual nominal alpha level of 0.05 was assumed.The overestimation bias was estimated by the average absolute difference between each ln. Gene expression levels for the two hidden groups were generated, assuming a normal distribution with mean = 0 for the first group and mean = 1 for the second group and setting both variances to 1. Thus, two partially overlapped distributions were obtained. All the analyses were repeated and a mean = 5.0 was set for the second group, corresponding to a nearly completely separated distribution. Assuming such a binormal model for the gene expression distribution allowed us to easily obtain both the value of the best expected cut-off, which corresponded to the average between the means of the two hidden classes , and the corresponding “true” HR expected at the optimal cut-off according to the following equation, the demonstration for which is reported in the λ0 and λ1 represent the event rates in the two hidden groups, respectively, µ0 and µ1 the means of the two corresponding distributions, respectively, σ0 and σ1 the corresponding standard deviations, respectively, and Φ is the standard normal cumulative distribution function.In order to obtain a preliminary estimate of the potential impact of sample size and event rates on the adjusted HR were identified in each analysis. These corresponded to values more biased than the unadjusted ones . Outliers were defined as HRs estimated at the optimal cut-off more than three times higher than the expected value calculated according to Equation (4). The overestimation bias and its reduction by the proposed method were estimated by comparing the adjusted and unadjusted HR estimates with the corresponding expected HR. Finally, a statistical power at the alpha nominal level of 0.05 was also estimated.Non-valid estimates of the adjusted p-values for the HR at the optimal cut-off were obtained by 5000 random permutations.The sample size was allowed to vary from 20 to 160, and the number of simulated gene expressions was set to 2000 for each data set. The adjusted All simulation analyses were carried out by ad hoc developed scripts in the R programming language  files S, and anaHR) estimates for the pool of the 12,000 simulated gene expressions, obtained: (a) at an optimal cut-off, without adjustment for the overestimation bias (panel A); (b) at an optimal cut-off, adjusting for the overestimation bias (panel B); and (c) using the median value as an a priori selected cut-off (panel C). The unadjusted optimal ln(HR) is clustered into two groups above and below the expected value under the null (zero) as a consequence of the overestimation bias . Such a bias was positively associated with the sample size and seemed to be unrelated to the event rate. Estimates adjusted by permutation analysis produced values very close to the nominal alpha level (0.05) for both the pool of samples and for each considered sample size, indicating a very good control of the overfitting. Such estimates were consistent with those obtained using the median value as a cut-off. An analysis of the corresponding standard errors, reported in the right part of The results of the analysis by event rate and sample size are reported in HR by sample and the proportion of the observed outliers. When the difference between the two hidden subgroups was small , the proportion of the non-valid, adjusted HR was low in all considered groups. A higher proportion (8.2%) was observed for a very small sample size (n = 20), corresponding to a lower overlap between the two hidden distributions . For a higher sample size, the proportion was very small and rapidly decreased with rising the number of samples. The occurrence of outliers was higher in the first group  and decreased with the increasing sample size, more rapidly in correspondence with the highest separation between the two hidden classes (Δµ = 5).HR estimates by sample size. A strong reduction in the overestimation bias was evident in all analyses. Corresponding to a small difference between the two hidden classes (Δµ = 1), the adjusted HR estimates remained slightly higher than the corresponding expected true values. This indicated a small residual bias which did not seem related to the sample size. In the presence of a higher separation between the two hidden classes (Δµ = 5), the correction for overfitting was excellent for n < 80 and quite good for n = 80 but tended to be overconservative for a higher number of samples, producing estimates lower than the expected .HR estimates is reported in µ = 1), ranging from 11.0% for n = 20 to 58.5% for n = 160. In correspondence with a smaller overlap between the two classes (Δµ = 5), the statistical power was still low for n = 20 (45.8%) and rapidly increased with an increase in the sample size (from 73.8% for n = 40 to 100% for n = 160).The statistical power of the permutation test for the inference for the Stage 4S NB  is a metastatic disease occurring in the first year of life. It is characterized by metastasis that is limited to liver, skin, or bone marrow, with an infiltration of less than 10% of ,14. In gE2F1, E2F2, and E2F3) and the event-free survival (EFS) of 134 Stage 4S NB patients. Data were drawn from three publicly available databases, stored in the on-line data bank R2 Genomics Analysis and Visualization Platform : namely, Kocak-649, Oberthuer-251, and SEQC-RPM [HR estimates were calculated using the Cox regression model, applying the Firth correction in the case of no events in either group [HR (mHR) across the three databases considered was obtained by the random effect model proposed by DerSimonian and Laird [E2F3 , but not of E2F1  or E2F2  [In recent years, many genes have been investigated in relation to NB progression, including Stage 4S disease ,15. For SEQC-RPM ,17,18. Fer group . For eacHR, adjusted for the overestimation bias, was produced according to Equation (3), and the corresponding mHR was obtained by applying the method of DerSimonian and Laird [In this investigation, we performed a reanalysis of these data, splitting the patients on the basis of an optimal cut-off identified using a running analysis instead of the median value, as described above, to show the utility of the proposed method in practice. An estimate of the nd Laird . OriginaE2F1 expression, evaluated at the optimal cut-off, and the EFS of the patients in the three studied cohorts are presented in E2F1 expression and EFS was found using the optimal cut-off as a threshold . After the adjustment of the overestimation bias, the association was reduced but remained statistically significant, with an adjusted mHR = 3.1 (95%CI: 1.1–8.9) that was approximately twice that obtained by the previous analysis, which was based on the median value of the gene expression . However, after correcting for the overestimation bias the association was reduced and no longer significant .E2F3 expression and EFS in the three studied cohorts. The related Kaplan–Meier survival curves are displayed in E2F3 were associated with a poorer outcome both in the original analysis, based on the median value cut-off, and in the new analyses, based on the optimal cut-off. In particular, the meta-analysis estimates of association were similar after adjusting the overestimation bias .An immunofluorescence assay was performed to evaluate the expression level of the transcription factor E2F1 using formalin-fixed, paraffin-embedded, NB primary samples (4-μm thick) from an independent cohort of 38 patients with Stage 4S NB.MYCN status, DNA index, histology, and outcome, were collected. The patients were staged according to the International Neuroblastoma Staging System [Patients belonged to a multi-institution, retrospective series of primary NB tissue sections with Stage 4S disease, diagnosed between December 2000 and October 2011 in 27 centres of the Italian Association of Paediatric Haematology and Oncology (AIEOP) . The tumMYCN status and all were treated in accordance with the therapeutic guidelines of an ad hoc SIOPEN  protocol [The studied cohort included 38 patients aged <12 months; 34 of them had a normal protocol . FourteeAn immunofluorescence assay was carried out as previously described  using thp < 0.001, Mann–Whitney U test). In more detail, the median value was 6.55 among the not-relapsed patients (IQR: 4.0–9.5) and 67.5 among the relapsed ones , ranging from the very conservative Bonferroni’s correction to resampling procedures that include permutation analysis [HR under the null hypothesis, we developed a very simple, test-based method to remove the overestimation bias, beginning with an adjusted estimate of the corresponding p-value obtained from a set of random permutations [HR estimates. However, simulated data revealed some residual overestimation bias under the null that was larger in correspondence to either a lower event rate or a smaller sample size. Estimates of the associated alpha value indicated that such a residual bias was not associated to an inflation of the type I error, which, conversely, was very high for the unadjusted HR estimates. On the contrary, the bias correction under H1, when estimates far from the null are more likely to be observed, could provide an over-conservative adjustment; this conclusion emerged from the analyses of both real and simulated data set. For instance, the shape of the plot in HR) distribution. A similar pattern was also observed when analysing the Cavalli et al. data set [Running tests are frequently applied in early studies to evaluate the association between potential tumour markers and patient survival. The overestimation bias, i.e., the production of an “overoptimistic” estimate of association, is a well-known limitation of such investigations. Many algorithms are available for obtaining adjusted analysis ,7. Exploutations . A statidata set  . Sometimes they represent a quite forced choice when information on the follow-up time is not available, a situation often occurring in the retrospective analysis of published data. Nevertheless, these approaches should provide reliable results only in the absence of censoring, i.e., in the analysis of closed cohorts [Our method is not intended to replace validation procedures that remain the gold standard for assessing the generalizability of observed results. On the contrary, it should be applied when neither an external cohort is available, or when internal validation is unreliable due to an insufficient sample size. In the latter situation, the application of standard methods of internal validation for classification tasks, such as the  cohorts , or when cohorts .E2F1 gene expression in patients with Stage 4S NB. For instance, HRs estimates from cut-offs selected a priori could not clearly assess the association between a patient’s survival and the gene expression, while a mere running approach, without adjustment for the overfitting, would have provided a biased, meta-analytic estimate of the corresponding HR. Our proposed method, coupled with the standard meta-analysis technique by DerSimonian and Laird [E2F1 as a new gene with potential oncogenic activity in NB 4S, though it had escaped previous standard methods of analysis in the original study [E2F3 expression and NB patient survival. Both results were confirmed by biological validation using immunofluorescence analysis, in the present study with regard to the expression of E2F1, and in the original investigation for E2F3 [E2F1 and E2F3 are members of the E2F family, which plays an important role in regulating gene transcription, cell cycle, proliferation, and apoptosis [E2F1 in NB prognosis has recently been demonstrated in a large investigation by Wang et al. [MYCN amplification and a higher age at diagnosis, two major indicators of poor prognosis in NB patients. The authors also reported that E2F1 and E2F3 shared similar downstream transcriptional features, and that the high expression of both genes was significantly enriched in the cell cycle signalling pathway [E2F1 in Stage 4S patients, highlighted by the results of this study, needs to be validated in independent cohorts.In order to illustrate our method in an actual framework, we chose the data set previously included in the study by Parodi et al. . Analysind Laird , allowedal study . Using ofor E2F3 . E2F1 anpoptosis . Interesg et al. , who rep pathway . Even if pathway . AccordiMYCN proto-oncogene. In a more general framework, in the early stage of selection of new potential markers for diagnostic or prognostic purposes, only simple, univariable analyses are usually carried out [HR estimates [HR remains an estimator of an average relative risk across the whole follow-up time. Such an estimate can be useless or hardly interpretable from a clinical point of view, but it would not invalidate the statistical validity of the estimates obtained by our approach.A limitation of our method is the absence of a control for potential confounders, such as the clinical and demographic characteristics of the patients. A confounding bias was unlikely in the reanalysis of the dataset of patients affected by Stage 4S neuroblastoma because the analysed patients were quite homogeneous for the major known prognostic factors, including age at diagnosis, stage, and amplification of the ried out ,28. Howeried out . Additioried out . HoweverIn conclusion, the results of our study, even if they are partially still preliminary, indicate that the proposed simple, test-based method is a new, useful tool for supporting the identification of new potential tumour markers for prognostic purposes.HR by a running procedure. A preliminary statistical validation indicated that our method is able to remove such a bias and, accordingly, it could be useful for many applications in oncology studies.In this paper we describe a simple, test-based method to control the overestimation bias in the estimate of the E2F1 as a new, potential oncogene for paediatric patients affected by Stage 4S NB. This finding was confirmed by an immunofluorescence analysis.Combining the method with a standard meta-analysis approach allowed for the identification of HR and to different study designs.Further studies could extend our method to clinical estimators in oncology other than the