HM13 is featured by LOI and expression upregulation, which is linked to DNA demethylation. Other imprinted genes typically demonstrate lower expression in cancer, often associated with copy number variation and aberrant DNA methylation. Downregulation in cancer frequently leads to higher relative expression of the (imperfectly) silenced allele, yet this is not considered canonical LOI given the lack of (absolute) re-expression. In summary, our novel methodology highlights the massive deregulation of imprinting in breast cancer.Genomic imprinting plays an important role in growth and development. Loss of imprinting (LOI) has been found in cancer, yet systematic studies are impeded by data-analytical challenges. We developed a methodology to detect monoallelically expressed loci without requiring genotyping data, and applied it on The Cancer Genome Atlas  and Genotype-Tissue expression project  breast tissue RNA-seq data. Here, we report the identification of 30 putatively imprinted genes in breast. In breast cancer (TCGA),  In growth and development genomic imprinting is important in regulating gene expression. Here, the authors study loss of imprinting (LOI) in cancer, developing a mixture model to detect monoallelically expressed loci without genotyping data - applying this novel methodology to TCGA breast cancer data they find massive deregulation of imprinting. It is a very heterogeneous disease with major differences in incidence, clinical outcome, prognosis and response to therapy3. Gene expression profiling led to the division of breast cancer in five different molecular subtypes: Luminal A, Luminal B, HER2-enriched, Basal-like and Normal-like4. These subtypes differ amongst others in expression of the oestrogen receptor, progesterone receptor, human epidermal growth factor receptor 2 (HER2) and in histological grade3.Breast cancer is the most common type of cancer in women5. Imprinting refers to the monoallelic expression of genes in a parent-of-origin-specific manner. In diploid eukaryotic organisms, the maternal and paternal copies of most genes are expressed at similar levels. For imprinted genes, however, only a single allele is transcriptionally active8. Imprinting patterns may vary between tissues9. Imprinted genes are mostly clustered and regulated by imprinting control regions, which are typically under DNA methylation control, though also H3K27me3 was demonstrated to be involved11. Imprinted genes play an important role in development and placental biology12. Furthermore, as dosage of imprinted genes is crucial, disruption of imprinting can result in a number of human imprinting syndromes and may predispose to cancer by promoting tumourigenic or suppressing antitumour mechanisms16. Some well-known diseases are Angelman Syndrome , Prader–Willi Syndrome  and Beckwith–Wiedemann Syndrome (LOI on chromosome 11)17.An early occurring aberration in cancer is loss of imprinting (LOI)18. For instance, aberrant biallelic expression of the imprinted IGF2 locus is thought to promote tumourigenesis by inhibiting apoptosis in colorectal cancer19 and to lead to over-proliferation defects in lung, colon and ovarian cancer20. LOI of other imprinted genes, such as H19, PEG3, MEST and PLAGL1, was also discovered in varying cancers21.LOI results in biallelic expression due to activation of the silent allele. Indeed, experiments in mice demonstrated that demethylation at imprinted genes leading to LOI made cells susceptible to cellular transformation and tumourigenesis5. Indeed, recent studies identified major expression downregulation of reportedly imprinted genes in cancer23. Moreover, in oesophageal cancer, LOI of IGF2 was specifically associated with expression downregulation, and improved survival24. Also in prostate cancer, no increased expression was found for IGF2 despite LOI25. Notwithstanding the major relevance of LOI in cancer, this fragmentary evidence demonstrates that the current paradigm of the role of LOI in cancer (i.e. growth & tumour promoting expression) requires additional evaluation. A recent study by Ribaraska et al. found downregulation of several imprinted genes in prostate cancer, but stable DNA methylation23. These results suggest the existence of an imprinted gene network in which these genes are co-regulated, as was also observed in mice26. Recently, also copy number variation (CNV) was identified as an important cause of imprinting deregulation in cancer27.However, several studies suggest a far more complicated story, where LOI is associated with silencing of the normally active allele9. To date, the impact of aberrant monoallelic expression on cancer has typically been studied at single imprinted loci18. Moreover, the practical applicability of existing high-throughput methods is greatly hampered by the necessity for genotyping next to  RNA-seq data. Thus, there is a need to systematically profile (i) monoallelically expressed/imprinted loci and (ii) their deregulation (LOI) in cancer, preferably solely based on RNA-seq data.Systematic analyses of LOI are still lacking. Indeed, although monoallelic expression is a well-investigated topic, only few regions are well-characterised in humans, and only a single study thoroughly evaluated tissue-specific imprinting patterns22—applied on breast control  and cancer data (TCGA), leading to the identification of 30 putatively imprinted genes in breast of which 8 are featured by increased biallelic expression in at least one breast cancer subtype. Comparison with whole-exome sequencing (WES) data demonstrate that (i) the RNA-seq-based results are generally reliable, and (ii) that avoiding the use of WES data leads to a far higher genome-wide character. Intriguingly, the results indicate that the increased frequency of biallelic expression is far more often associated with lower expression than higher expression of the corresponding locus, though exceptions exist (e.g. HM13). Therefore, this study demonstrates that deregulation of imprinting is an important feature in (breast) cancer but is not automatically associated with canonical LOI. Furthermore, these results underline the efficacy of the proposed strategy for the identification of imprinted regions and their deregulation.Here, such a methodology is presented and—given indications for massive differential expression of imprinted genes in this tumour30). The novel imprinting model describes the data for each SNP as a mixture of homozygous and heterozygous samples, more specifically as a mixture of genotype-dependent binomial distributions, with weights derived from Hardy–Weinberg equilibrium. The model allows for sequencing errors and partial imprinting. Indeed, one parameter describes the degree of imprinting, and it can be evaluated whether its estimate is significantly higher than 0 using a likelihood ratio test.First, a methodology was developed and applied to screen for imprinted loci in RNA-seq data, using single nucleotide polymorphisms (SNPs) to discriminate between alleles. Contrasting previous genome-wide methods, no DNA genotyping data is required, as we solely rely on genotyping of RNA-seq data. The basic rationale is that in case of 100% imprinting, no heterozygous samples can be found in RNA-seq data, as they perfectly resemble homozygous samples  . Table IGF2 and SNRPN are shown in Fig. IGF2 imprinting is only partial (97% imprinted), underscoring the suitability of the flexible distribution model used here. Similar figures for the other genes can be found in Supplementary Figs. Upon application on 113 TCGA breast control samples, 127 SNPs were considered to be possibly imprinted  ≤ 0.05), and dbSNP annotation was found for 125 SNPs. The 125 possibly imprinted SNPs corresponded with approximately 35 genes, the majority already known to be imprinted  or indications (HOTAIRM1) of transcript-specific imprinting with more complex mixture distributions and consistent differences between exons . However, monoallelic methylation is only a crude proxy for the presence of imprinting associated differentially methylated regions (DMR). We therefore analysed methylation in known DMR locations, provided in Table 32. As summarised in Supplementary Data PTX3, PLIN1 and BCR, which may be regulated in a different manner. Typically, each of these DMRs featured multiple putatively monoallelically-methylated probes in the control samples, and often even largely coincided with putatively monoallelically-methylated regions . For ZDBF2 and DLK1, the DMR methylation status could not be evaluated since no probes were present.As an additional validation step, we examined whether DNA methylation levels were skewed towards putative monoallelic methylation for the imprinted loci. For the 18 genes represented in the TCGA Infinium HumanMethylation data, at least one putative monoallelically-methylated probe was found (median methylation in between 33.3 and 66.7%) (Supplementary Data PAPT highest fraction of samples (cf. Hardy–Weinberg theorem) allows us to only take the most likely heterozygotes into account. DI in cancer for a specific SNP was thus defined as a significant difference of the allelic ratios between putative heterozygous cancer and control samples . Though only technically feasible for a limited set of the data, this allelic ratio was verified to be a good measure for DI using WES data  is defined here as different relative expression of both alleles in cancer vs controls. We reserve the term LOI solely for DI caused by re-expression of the silenced allele (i.e. absolute higher expression). We determine biallelic expression per sample by the allelic ratio , which varies from 0  to 1  and is independent of expression level differences in cancer. For these analyses, it should be noted that power is compromised by the fact that DI cannot be observed in homozygous individuals, which constitutes the majority for each locus. We try to compensate this by allowing more false positives in the results (FDR of 10%), but also by enriching for likely heterozygous samples. As samples with a high allelic ratio represent heterozygotes, looking at the 2MEST, H19 and HM13. Figure MEST (and to a minor extent for HM13) also some control samples are featured by residual biallelic expression. This may suggest that this locus is less stringently imprinted and further lost its imprinting signature in breast cancer. Alternatively, this may be due to the fact that a mixture of imprinted and non-imprinted transcripts is present, with a shift towards expression of the latter in cancer.When considering the full set of 506 breast cancer samples, four SNP loci with significant DI, i.e. higher relative expression of the silenced allele, could be identified , HER2-enriched (HER2), luminal A (LumA) and luminal B (LumB), were analysed individually for DI compared to normal samples , though complicated due to the low coverage WES data significant results  analysis in control vs tumour and control vs breast cancer subtypes for the here detected imprinted SNPs and genes. Significant DE was found in almost all (92%) of the imprinted SNPs for all tumour samples. Imprinting is thus indeed heavily deregulated in breast cancer  analysed putatively imprinted genes to be differentially expressed in breast cancer1% analysHM13, for which DI implied higher expression in most subtypes  sufficient WES data were available to accurately evaluate DI and DE results. In ZNF331, significant downregulation was found in biallelically expressing tumour samples compared to monoallelically expressing control samples, but also when compared to monoallelically expressing tumour samples. HM13, on the other hand, was significantly upregulated in biallelically expressing samples , further confirming the results presented above. For the other SNPs no differences were detected, particularly due to low power (insufficient WES coverage).We verified these results in heterozygous samples, as DI cannot be observed in homozygotes  p-value was observed for SNP rs6059873  whereas this was not the case for the other imprinted loci , probes differentially methylated between cancer and controls were found. However, though these included many probes located in known DMRs and/or featured by putative monoallelic methylation in controls , there was no clear enrichment for putative imprinting regulating loci among differentially methylated probes  in breast cancer. Contrasting controls, significant associations were found between imprinted gene expression and CNV in cancer samples for 17 of the 23 genes present in TCGA CNV data  did exhibit DE but no DI. For SNPs featured by significant DI, we estimated that over 50% of all samples may be affected  were analysed in TCGA. Methylation was significantly lower for two probes  in tumour compared to control samples  imprinted allele due to downregulation of the expressed allele. Given that the imprinted allele itself is not affected, we refrain from using the term LOI, and proposed the more generic term differential imprinting to indicate a relative shift in allelic expression independent of the underlying cause. The sole example where DI could be attributed to LOI was HM13, which exhibited overexpression in cancer, particularly in LumB tumours, due to re-expression of the normally silenced allele.Genomic imprinting is important for normal development and growth. The genome-wide evaluation of imprinting deregulation in cancer and diseases is currently hampered by a lack of appropriate data-analytical strategies. We hence developed a new methodology for the genome-wide detection of imprinting and its deregulation. After application on breast tissue, we were able to detect many imprinted genes and confirm major deregulation of imprinted genes in breast cancer and the varying subtypes. Imprinted genes exhibited clear differential expression, particularly downregulation, in tumour samples. Strikingly, in HER2 and BL tumours, downregulation was associated with massive induction of biallelic expression. A similar pattern has been described earlier for individual genes, e.g. for L3MBTL1  was not evaluated by our methodology due to low coverage, whereas imprinted SNPs for the second gene (SNURF) were detected yet annotated as the overlapping gene (SNRPN). Of the 19 genes detected by our method only, at least 7 are known imprinted genes, also detected by Joshi et al.33, or genes located in the neighbourhood of imprinted genes. It should be noted that accuracy of these results largely depends on the accuracy of the underlying annotation. Nevertheless, inconsistent results between SNPs in the same gene were evaluated, and appeared to be mainly caused by technical reasons, i.e. low coverage of intronic SNPs, low goodness-of-fit to the model or low allele frequency, as demonstrated for HM13 in Supplementary Data ZNF300P1, LOC100294145, ZNF331 and GNAS-AS1/GNAS, we observed transcript-specific imprinting to be a more likely explanation.Compared to the study by Baran et al., which only used 27 breast samples, 13 genes were detected by both Baran’s and our methodMEST, showed significant DI and two genes, H19 and HM13, were borderline significant. MEST is already known to show DI in varying cancers, including breast cancer37. Aberrant H19 imprinting is often seen in cancer as well and is thought to have an important role in cancer development39. When taking into account the different tumour subtypes, we detected 24 SNPs  exhibiting DI in at least one subtype compared to the normal tissue samples. DI was particularly present in BL and HER2 tumours. Many of these genes had been linked with DI and cancer development before43. DI was typically not associated with survival, except for 2 SNPs in ZDBF2, a zinc finger-containing protein, yet this finding requires additional validation.Subsequently, we analysed 506 breast cancer samples for DI. One gene, 27. Methylation was also found to be significantly different between tumours and controls, though without clear enrichment for imprinting associated DMRs. For these loci, DI is thus most likely the consequence of transcriptional silencing. Previously, studies in murine and human prostate tissue and cancer detected a transcriptional network of co-regulated imprinted genes44, with PLAGL1 as putative key player47. Results from preliminary analyses . As recently demonstrated, particularly CNV was associated with expression deregulation of imprinted genesHM13 clearly exhibited canonical LOI, i.e. re-expression of the normally silenced allele leading to overexpression in cancer, particularly in the LumB subtype. Both significant SNPs appear to be present in the third (and last) exon of transcript variant 4, possibly the UTR of this transcript. Though other evidence for imprinting of HM13 exists, only little information is available on its function—a signal peptide peptidase involved in the immune system49. Importantly, deregulation of HM13—located on 20q—has been revealed in colorectal carcinoma: the often observed 20q gain in this tumour is associated with higher HM13 expression, which was demonstrated to lead to accelerated growth of the tumour50. Also in the study at hand, CNV gain led to increased HM13 expression, yet this was independent of LOI. Interestingly, in an imprinting study in normal blood samples by our group, HM13 also appeared to be featured by LOI and higher expression in a subset of samples, particularly in older individuals . With respect to the mechanism of HM13 deregulation in breast cancer, we demonstrated that aberrant methylation in the neighbourhood of the HM13 promoter was linked to deregulation of its expression. Differential methylation may lead to different polyadenylation (as described in mice51) and hence varying transcripts, yet we found differential expression of all exons in HM13. Our methodology also did not allow to exclude promoter switching from an imprinted promoter to a non-imprinted one, as already described for IGF2 and MEST36, as cause of HM13 LOI in cancer. Further research is, therefore, necessary to unravel the exact mechanism(s) and consequences of (de)regulation of HM13 in breast cancer.Contrasting other loci, 9. Some methodological improvements could however further increase sensitivity and specificity. For example, the current method relies on Hardy–Weinberg equilibrium, but could be modified to take into account population substructure. Additionally, the current mixture of binomial distributions could be updated to a mixture of beta-binomial distributions, as the latter captures more natural variation in expression between alleles. Nevertheless, the current study , and could not find a significant correlation between infiltrating lymphocytes and HM13 LOI, thereby rejecting confounding due to lymphocyte infiltration. As a final limitation, it is important to note that no distinction between primary and secondary imprints is possible with our methodology.Throughout the manuscript, results were verified by comparison with available WES-based genotyping data. However, low or absent coverage of WES for the corresponding loci led to a massive loss of imprinted SNPs that could be evaluated. This further underscores the benefits and more general applicability of the introduced methodology, which solely focuses on RNA-seq data. Also, this may explain why novel imprinted loci were found in our analysis, compared to methods where genotyping data is used to identify heterozygous samples prior to detecting imbalanced allelic expression in the latter, e.g. Baran et al.HM13, with LOI and upregulation in cancer samples. We were able to detect these putatively imprinted genes and their deregulation with a newly developed method solely based on RNA-seq data. The effectiveness of our novel methodology and the advantage of solely using RNA-seq data was hence also confirmed.In conclusion, this study demonstrates that imprinting is indeed heavily deregulated in breast cancer, though the mechanism of its deregulation is complex. Many imprinted genes are downregulated in cancer, likely leading to DI without actual higher expression of the silenced allele. One clear exception was found, 52. RNA-seq BAM-files were downloaded from the prior TCGA data portal . Invasive ductal carcinoma, which starts in the milk ducts of the breast, and invasive lobular carcinoma, which originates in the lobules, were both studied28. For all cancer samples, additional expression subtypes based on the PAM50 classifier were obtained from the UCSC cancer genome browser 52. In all of these samples, variants were called using Samtools mpileup/bcftools (v0.1.19)53. Female breast samples (92 samples) from GTEx data (in dbGaP under accessions phs000424.v6.p1) were used for validation29.RNA-seq data of 113 human healthy control and 506 diseased samples (only those for which a PAM50 subtype was available) of the TCGA breast invasive carcinoma dataset were used in this study54. For detection of imprinting and differential expression analysis, an FDR of 5% was used as significance threshold. For analyses where loss of power is anticipated due to non-informative homozygous samples , an FDR of 10% was used.Throughout the manuscript, the Benjamini–Hochberg procedure was used for false discovery rate estimation55, a fast Bayesian genotype-calling algorithm based on the expectation maximisation (EM) algorithm to estimate the prior allele frequencies and the nucleotide-read error rate in an iterative way. Note that imprinting biases RNA-seq-based genotyping (i.e. less heterozygous samples will be detected), yet that allele frequency estimates are unbiased as both alleles have an equal chance to be imprinted. Genotyping with SeqEM was done without the HWE option, only for estimation of the number of biallelically expressing samples in RNA-seq data HWE was assumed 56. However, in case of monoallelic expression, heterozygous samples will no longer be detected in RNA-seq data resulting in deviation from the HWE, which can be measured , yet this of course applies to all possible nucleotides.Rationale: The rationale behind the proposed methodology is that biallelic expression yields RNA-seq data (or other similar sequencing data) that is in HWE for each locus, i.e. if SNPs are present for a locus, both homozygous and heterozygous subjects will be detected at a predictable rate (under HWE assumptions)red Fig. . So for 30.Note that the same is true for enrichment-based sequencing data. Indeed, monoallelic histone modifications, as well as monoallelic DNA methylation, lead to ChIPseq and MethylCap-seq data, respectively, that is no longer in HWE, e.g.56. Sequencing error rates (median per chromosome) are here taken into account. Subsequently, maximum likelihood estimation was used to estimate the degree of imprinting (i) and a likelihood ratio test was constructed to detect significant imprinting. A detailed discussion of the different elements of this PMF and the analytical framework can be found in the following subsections. All analyses were performed in R (v3.3.2)57, scripts are available upon reasonable request.To enable screening for loci featuring imprinting, a probability mass function (PMF) describing the probability of observing specific coverages for each allele for a specific SNP locus was developed. As the probabilities depend on the underlying genotypes, the PMF was created as a mixture model of genotype-dependent binomial distributions with weights corresponding to the probabilities under Hardy–Weinberg Fig. 56. Sequei.x1 and x2 equal to the sum of the two highest allele frequencies of the sample divided by two, and x3 and x4 are equal to the sum of the two lowest sample allele frequencies divided by two. Note that the two alleles corresponding to these latter two frequencies could only be obtained due to sequencing errors.The posterior probability of obtaining a specific observation given a heterozygous sample was determined using a multinomial distribution:p and q the mean allele frequencies over all samples of the standard and non-standard allele, respectively.The probability that the sample is heterozygous is calculated as:ii.x2, x3, x4 are determined as the sum of the lowest three allele frequencies divided by three, while x1 represents the allele frequency of the ‘true’, standard allele .Similar to the approach for heterozygous samples, the posterior probability of the obtained nucleotide sequence in case of a homozygous sample is again defined with a multinomial distribution:p again represents the mean allele frequency of the standard allele over all samples.The probability of the sample originally being homozygous is next defined as:entclass1pt{minimaiii.P(data) is equal for both P(heterozygote|data) and P(homozygote|data), this can also be written as:Finally, following criterion was used to identify putative heterozygous samples:Data filtering using an empirical Bayes approach: After SNP calling, for each SNP position samples were filtered and corrected to obtain nucleotide sequences containing a maximum of two alleles. Using a maximum of two alleles per locus ensures high-quality sequences, but was also a prerequisite for the genotype calling step later on (by SeqEM). As dbSNP was used for SNP calling, the dbSNP alleles were chosen as the two standard alleles. In case dbSNP contained three or more alleles for a particular SNP position, the standard alleles were chosen as the two dbSNP alleles with the highest mean allele frequencies for that locus over all samples. A quality filtering procedure was included to retain only those samples featuring one (homozygous) or both (heterozygous) standard alleles . By default, samples already containing the two standard alleles as most frequent alleles were retained, whereas samples for which the allele with the highest frequency was not a standard allele were filtered out. However, for samples characterised by a non-standard allele as the second most abundant allele, an empirical Bayes approach was implemented to filter out putative heterozygous samples  yet keeping homozygous samples . This procedure goes as follows:Genotype calling and filtering: Calculation of genotype probabilities and corresponding nucleotide-read/sequencing error rate was done using SeqEM (v1.0), a fast Bayesian genotype-calling algorithm based on the expectation maximisation (EM) algorithm to estimate the prior genotype frequencies and the nucleotide-read error rate in an iterative way.As model-based approaches (such as SeqEM) are prone to false positives due to pre-processing induced artefacts , only reliable loci were used for further analysis. The standard approach of filtering is based on HWE and not applicable here, leading to the necessity to use a combination of alternative criteria. Therefore, after obtaining estimates of both the allele frequencies and sequencing error rate, the SNP loci were subjected to extra filtering steps: (i) minor allele frequency > 0.1, (ii) median coverage > 4, (iii) estimated sequencing error rate ≤ 0.035 and finally, (iv) the number of samples covering the specific locus had to be at least 75. Loci which successfully passed these previous filters were subsequently tested with two final quality checks based on ‘goodness-of -fit’ criteria.Additional data filtering using a goodness of fit procedure: SNPs that already passed the basic filtering steps were subjected to two final checks based on two methods assessing their goodness-of-fit in the model, independent of the presence of  imprinting. This approach is particularly aimed to remove loci exhibiting good sequencing characteristics, yet with properties that indicate deviation from the standard genetic models. This may be due to technical (e.g. mismapping) but also biological (e.g. presence of SNP dependent expression differences) reasons.χ² test is used for goodness-of-fit. Though the exact distribution depends on the level of imprinting, this is not the case for the fractions of samples with respectively a higher reference allele , the likelihood of each individual measurement was multiplied by its coverage+1. The mean of these corrected log-likelihoods was next used as measure for the goodness-of-fit: loci with a mean ≤ 1.2 were filtered out. Though empirical in nature, this filter setting largely removed remaining loci featured by aberrant allelic distributions.Next to a After prior filtering of the data, the remaining SNPs were screened for imprinted regions by a likelihood ratio test (LRT).PMF calculation: First, the probability mass function describing the probability of observing specific coverages for each allele for a specific SNP locus was established. As the probabilities depend on the underlying genotypes, we established the PMF as a mixture model of genotype-dependent binomial distributions with weights given by the expected probabilities under Hardy–Weinberg equilibrium Fig. . Importax the coverages for alleles A and T, i.e. x = PA and PT the estimated population allele frequencies for a specific locus over all samples (obtained by SeqEM)SE the estimated sequencing error rate i the degree of imprinting (varying from not (i = 0) to fully (i = 1) imprinted)B the binomial probability for x given the probabilities for each allele, i.e. pA and pT, which depend on the specific genotype, SE and imprinting factor iWithpA  whereas the ‘total number of trials’ equals nA + nT.One already familiar with binomial distributions will notice that this is a somewhat alternative representation than typically used. However, it is simple to see that here, the chance of ‘success’ is represented by Note that this PMF can be easily extended towards four alleles by considering a mixture of multinomial instead of binomial distributions. However, for simplicity - and as SeqEM can only handle two alleles per locus—we considered only two alleles.From a practical point of view, the binomial coefficient is identical for each binomial distribution  and expressed as:pA) is 1-SE, while the chance of observing allele T (= pT) is equal to SE, as T can only be present in the data due to a sequencing error.As ideally only a single allele is observed for homozygous samples, potential imprinting cannot be deduced from the allelic coverages. Here, the binomial probability will depend only on the SE - which is obtained by SeqEM. Because this error rate is assumed to be equal for all loci but can be ill-estimated when imprinting is present, the median SE over all loci is used. For homozygote AA, for example, the chance of observing allele A  then becomes:P is multiplied by the probability of the sample being homozygous AA. Assuming Hardy–Weinberg equilibrium (HWE), this equals the respective population allele frequency squared, i.e. PA².In the PMF this value of pA and pT can be set to 0.5. However, when imprinting is present, the probability of observing the imprinted allele diminishes with a factor i/2. As the probabilities for both alleles need to sum to one, both probabilities are normalised by dividing them by a factor 1−i/2 (= 0.5 + 0.5−i/2). Also sequencing error rates have to be taken into account, as a fraction SE of the normalised probability of one allele will be observed as the other allele and vice versa. Thus, when allele A is imprinted, the probability of observing allele A (= pA) equals:For heterozygotes, for example AT, potential imprinting has to be taken into account. This is done by including an imprinting factor i that can vary between 0 (no imprinting) and 1 (fully imprinted) and is estimated using Maximum Likelihood Estimation . Without imprinting, in theory both alleles A and T will be expressed to a similar extent so that pT this becomes:While for the probability of Leading to the following formula:However, the possibility of imprinting of allele T also has to be taken into account:PAPT. As from the underlying biology both alleles can be assumed to have an equal chance of imprinting (= 50%), this ultimately leads to the mixture PMF denoted in Eq.  ies (Eq. ) over alLikelihood ratio test: Finally, in order to screen for imprinted loci a likelihood ratio test is performed. The respective null and alternative hypotheses for a locus are:H0: the locus is not imprintedH1: the locus is imprintedWith the previous definitions this translates into:H0: i = 0H0: i > 0i = 0) is compared to the alternative hypothesis that the locus is imprinted (i > 0). Practically, in a first step, the PMF  for theχ² distributed and H0 will be rejected if its value is greater than χ² distributions is used: under the null hypothesis, the test statistic is distributed as an equal mixture of two χ² distributions, namely 58. Finally, a locus is called imprinted if the corresponding FDR-corrected p-value was smaller than the nominal FDR level of 0.05 (Benjamini–Hochberg correction for multiple testing).As the null hypothesis is a special case of the alternative hypothesis, the test statistic for nested models Ri,s for SNP i and sample s) are calculated as the lowest allele count over the highest allele count, yielding values between 0  and 1 . Next, the values of these ratios are sorted over all samples and the value of the ‘median putatively heterozygous sample (sm)’ is calculated. This sample corresponds with rank round(samplesize*(1−PA−PT−PAPT)) = round(samplesize*(PAPT)). The median imprinting value is then calculated as 2* . In a last step, SNP positions with a median imprinting level ≥ 0.8 were considered as robust (TCGA). For GTEx , we used a median imprinting level of 0.4 as cut-off, given that typical artefacts had already been eliminated.Median imprinting: A robust measure for degree of imprinting, called median imprinting, was developed to enable the identification of a robust set of imprinted loci from the significant set identified higher. For each SNP locus, sample-specific ratios  are calculated for each single SNP, over all samples. These ratios are sorted per SNP in an ascending order separately for control and tumour samples. As the lowest ratios are expected for homozygous samples , one can consider samples with the highest 2PAPT ratios as putative heterozygous samples for that specific locus. In practice: samples with rank higher than sample_size*(PA2+PT2) are considered as the heterozygous samples for a specific locus. After determining the mean ratio of these heterozygotes , parameter Ri,diff is calculated as the difference between these values, i.e. Ri,diff = Ri,stumour − Ri,scontrol. Upon random assignment of the tumour and control labels to the present samples by permutation, 10,000 random values of Ri,diff are simulated to generate a null distribution. Loci with an FDR-adjusted p-value smaller than the nominal 10% FDR level were concluded to be differentially imprinted between control and tumour samples. We were solely interested in DI in cancer and hence we exclusively tested for higher ratios in tumour compared to control data. The different breast cancer subtypes were also tested for DI  in which the p-value was corrected over all samples. Here, it should be noted that considering the ratios allows for detecting differences independent of alterations in expression levels of imprinted genes, which are also prominent in breast cancer59.Next to the detection of imprinted loci, we also examined possible deregulation of imprinting in cancer. This was done by testing for different relative expression of both alleles, here termed DI. When associated with absolute re-expression of the originally silenced allele, this is coined LOI. Briefly, ratios of the lowest allele count over the highest allele count .Subsequently, for loci featured by DI, the latter was linked to survival. A continuous DI variable, which was defined as the allelic ratio , was associated with survival and adjusted for age with a Cox proportional hazard model. To anticipate assumption violations, a null distribution was constructed by 10,000 permutations by randomly shuffling the ratios over the samples. Loci with an FDR-adjusted Differential expression of the silenced (lowest expressed) allele was analysed as well to assess whether expression of the normally silenced allele was higher in tumour data. Here, counts per million (CPM) reads of the least expressed allele count were calculated as described in the next paragraph. The same permutation test as mentioned higher yet based on the logCPM-values rather than ratios, was performed on the SNPs showing significant DI.60. Afterwards, CPM-values for the imprinted SNPs were computed with these normalisation factors and library sizes . EdgeR-based DE analysis was developed to increase power, at the cost of several assumptions. As the sample size and thus power is sufficiently high in the case at hand, we opted to use more robust standard non-parametric methods. Differential expression in control versus tumour samples was analysed with a Wilcoxon Rank Sum test for detected SNPs as well as the corresponding genes . To test for DE in the different breast cancer subtypes, a Kruskal-Wallis test and Dunn’s post-hoc test were performed on the CPM-values of the varying subtypes.DE analysis was performed to further evaluate deregulation of imprinted genes in cancer. EdgeR normalisation factors were calculated from the breast cancer RNA-seq expression count file downloaded from firebrowse.orgHM13, logCPM-values of exonic expression data  were normalised and analysed for DE between control and tumour samples as described in the previous paragraph. Exon data were available for 468 tumour samples  and 100 control samples. Exonic RPKM values, available from firebrowse.org as well, were used for additional verification and consistently yielded the same conclusions.To study transcript-specific effects in 60 and CNV data from the GDC portal of TCGA. Infinium methylation data (450k) could be retrieved for 84 control and 207 tumour samples , whereas CNV data was available for 92 control and 506 tumour samples. A Wilcoxon Rank Sum test was performed to screen for significant differential methylation in probes located in imprinted genes. In the CNV data, gains and losses were called as segment mean > 0.2 and < −0.2, cf.61. A linear model was constructed to model expression (gene-based logCPM counts) as a function of CNV (factor), adjusting for breast cancer subtype.Infinium HumanMethylation450k data were downloaded from firebrowse.orgHM13, also the link between CNV and LOI was of interest. A χ² test comparing LOI/not LOI  and exonic expression data  were correlated to identify which methylated locus might control expression. Both expression and methylation data were available for only 72 control and 192 tumour samples. A Spearman correlation test was performed for detecting correlation between the β-values of the 10 probes and (i) logCPM-values of the whole HM13 gene  and (ii) logCPM-values of the 3rd exon of transcript 4 (as most of the imprinted SNPs were located in the neighbourhood of this exon). Again, RPKM values were successfully used for verification.For To additionally verify the imprinting and deregulation results, corresponding WES data (BAM files) were downloaded from TCGA to obtain the underlying genotypes. However, only for 93 control samples and 464 tumour samples WES data were available. Concordance between WES and RNA genotypes was examined to validate the quality of genotyping with RNA-seq data (Supplementary Note The scripts are available from the authors upon reasonable request.Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6


The application of genomic data and bioinformatics for the identification of restricted or illegally-sourced natural products is urgently needed. The taxonomic identity and geographic provenance of raw and processed materials have implications in sustainable-use commercial practices, and relevance to the enforcement of laws that regulate or restrict illegally harvested materials, such as timber. Improvements in genomics make it possible to capture and sequence partial-to-complete genomes from challenging tissues, such as wood and wood products.Quercus) species with a high level of accuracy with very small amount of genomic data. The method is robust to sequencing errors, different sequencing laboratories and sequencing platforms.In this paper, we report the success of an alignment-free genome comparison method, This method offers an approach based on genome-scale data, rather than panels of pre-selected markers for specific taxa. The method provides a generalizable platform for the identification and sourcing of materials using a unified next generation sequencing and analysis framework.The online version of this article (10.1186/s12864-018-5253-1) contains supplementary material, which is available to authorized users. The annual trade in natural resources represents $3.35 T of global imports and $3.25 T of global exports , and it Quercus subg. Quercus). Unlike traditional genetic analysis, our approach uses whole genome DNA sequence data without a priori selection of marker loci. This work extends studies showing that background-adjusted alignment-free sequence comparison measures (CVTree , SRR2053125 [Q. robur], SRR2053082 [Q. dentata]) as extreme outliers  sequencing data of 99 white oaks from North America, Europe and Asia were downloaded from NCBI BioProject PRJNA269970. The sequence data for these samples was derived from leaf tissue sampled from specimens collected in the field, which were previously published . Four saMean dissimilarity measures used in this study are weakly and inversely correlated with sequence quantity. To reduce confounding effects caused by different sequence quantities, we down-sampled data for all 92 samples to produce three different datasets. Two datasets consisted of random samples of reads totaling to 50 Mbp and 100 Mbp for each sample, respectively. The third consisted of reads totaling to 300 Mbp. All samples were divided into three geographic categories based on their continental origin. Samples from the United States and Canada were categorized as North America (NA), samples from west of 60°E longitude were categorized as Europe (EU), and samples from east of 60°E longitude were categorized as Asia (AS).k-mers  to compare any pair of samples. These are the traditional Manhattan, Euclid, and d2 , SRR2053125 [Q. robur], SRR2053082 [Q. dentata], were identified. However, the other samples cluster together. (PDF 224 kb)Additional file 6:Details on the definitions of six alignment-free distance/dissimilarity measures between two genomes based on NGS data. (PDF 123 kb)Additional file 7:Table S1. Library construction, sequencing, and genome enrichment methods used for all DNA libraries in this study. (PDF 29 kb)


The miRNA isoforms (isomiRs) have been suggested to regulate the same pathways as the canonical miRNA and play an important biological role in miRNA-mediated gene regulation. Recently, a study has demonstrated that the presence or absence of all isomiRs could efficiently discriminate amongst 32 TCGA cancer types. Besides, an effective reduction of distinguishing isomiR features for multiclass tumor discrimination must have a major impact on our understanding of the disease and treatment of cancer.In this study, we have constructed a combination of the genetic algorithms (GA) with Random Forest (RF) algorithms to detect reliable sets of cancer-associated 5’isomiRs from TCGA isomiR expression data for multiclass tumor classification.We obtained 100 sets of the optimal predictive features, each of which comprised of 50–5’isomiRs that could effectively classify with an average sensitivity of 92% samples from 32 different tumor types. We calculated the frequency with which a 5’isomiR found in these sets as measuring its importance for tumor classification. Many highly frequent 5’isomiRs with different 5′ loci from canonical miRNAs were detected in these sets, supporting that the isomiRs play a significant role in the multiclass tumor classification. The further functional enrichment analysis showed that the target genes of the 10 most frequently appearing 5’isomiRs were involved in the activity of transcription activator and protein kinase and cell-cell adhesion.The findings of the present study indicated that the 5’isomiRs might be employed for multiclass tumor classification and the suggested that GA/RF model could perform effective tumor classification by a series of largely independent optimal predictor 5′ isomiR sets. The accumulation of genetic alteration drives cancer development and progression . The CanThe filter, wrapper and embedded methods are typically utilized for feature selection, though all of them are not good at dealing with data which contain a large number of collinear variables. , 21. TheFurthermore, 5’isomiR may target very different transcripts as compared with their canonical miRNAs attributed to shifting in the seed region , which is recognized to be very critical in determining miRNA target specificity –31. Varihttps://tcga-data.nci.nih.gov). Only primary solid tumor samples with infix ‘01’ in the TCGA sample barcode, with the exception of the blood samples derived from acute myeloid leukemia  were included in the study. After excluding all samples that were annotated as ‘potentially problematic’ datasets (file_annotations.txt files), 9085 eligible datasets (isoform.quantification.txt files) were finally included for further analysis  from the TCGA data portal (randomForest was used (https://cran.r-project.org/web/packages/randomForest/randomForest.pdf). Besides, we use SVM classification for comparison, and the e1071 package in R with linear kernel function was run (https://cran.r-project.org/web/packages/e1071/index.html).In this study, we used the GA/RF based model for tumor classification. GA/RF utilizes a GA to select a set of salient features from input and classification module using RF . The selFor tumor, classification prediction may vary based on different samples assigned to the training set. We repeated the above the GA/RF procedure100 times. During each of the 100 runs, the training and testing were carried out, each time using one distinct subset of randomly selected for training and the remaining subsets for testing. In a given run, the training sets were generated by randomly selecting 75% of each cancer’s available tumor datasets, and the testing sets were generated by the remaining 25% datasets. Finally, we achieved optimal 5’isomiR sets after 300 generations of GA/RF steps.http://www.targetscan.org/vert_50/seedmatch.html) prediction of the target genes of 5’isomiRs with original seed region along with different seed region of canonical miRNA, respectively, were performed [Using the TargetScanHuman (http://www.targetscan.org) and the TargetScanHuman Custom  with Random Forest (RF) algorithms to detect reliable sets of cancer-associated 5’isomiRs from TCGA isomiR expression data for multiclass tumor classification Fig. . After 1p-value was calculated as less than 0.01 followed by Bonferroni correlation for multiple testing. Finally, 41 highly frequent 5’isomiRs were selected (Table For all 100 runs, we acquired 100 sets of GA/RF classifiers and each set comprised of 50 items. Then, the frequency of selected 5′ isomiR across all the optimal predictive set was calculated. The relative significance of each 5′ isomiR for tumor classification was assessed by counting how often it appeared in these predicted optimal feature sets. For the functional enrichment analysis, we included all 5′ isomiRs with the frequency of ≥11 in these sets. It is difficult to randomly select a gene for more than 11 times in a 100 subset from 100 runs for a given dataset of 2231 samples, and the significance of adjusted Next, we examined the expression level of these highly frequent isomiRs Fig. . Many ofNext, the 9 most frequently appearing 5’isomiRs from all 100 runs were selected to determine whether a rational classification could be obtained using a reduced set. The training set and the corresponding test set were randomly produced 1000 times. Then, the RF algorithm was performed to determine the prediction accuracy of multiclass tumor classification Fig. a. We couFurthermore, to investigate the candidate target genes of the 9 most frequently appearing 5’isomiRs, the TargetScanHuman was performed for the 5–5’isomiRs with canonical seed region and the TargetScan Custom was used for other 4–5’isomiRs with a shift in seed regions. The target genes predicted were subjected to the functional enrichment analysis. Finally, 2345 genes were recognized by the DAVID web tools to analyze the functional annotation and the detection of enriched functional categories. The gene ontology enrichment analysis suggested that these target genes were highly enriched in genes implicated in the activity of transcription activator and protein kinase and cell-cell adhesion (Fig. We report a novel GA/RF analytical model for multiclass tumor classification using the miRNA expression data that may reveal effective predictive and prognostic biomarkers and therapeutic targets for drug development. With an average sensitivity of 92%, we were able to accurately classify the tumor samples using 100 different 50–5’isomiR sets, though some 5’isomiRs appeared repetitively in the sets. These predictive 5’isomiRs sets could achieve similar prediction accuracies with slight overlap; suggesting that even less sensitive 5’isomiRs could be detected for the tumor classification. Notably, most of the tumor types could be easily distinguished with high sensitivity. However, there were also some cancers that exhibited low prediction accuracy due to similar histology and anatomical location , 34. In In a recent study, the RNA-seq expression data analysis revealed that many development-related genes are essential for the analysis of TCGA cancer classification . SimilarUsing only 50–5’isomiRs, the present GA/RF model could achieve comparable prediction performances consistent with previous report, with an average accuracy of 90% for all isomiRs . We alsoIn conclusion, the present study demonstrated that the 5’isomiRs might be employed for multiclass tumor classification and the suggested that GA/RF model could perform effective tumor classification by a series of largely independent optimal predictor 5′ isomiR sets.


Data normalization and identification of significant differential expression represent crucial steps in RNA-Seq analysis. Many available tools rely on assumptions that are often not met by real data, including the common assumption of symmetrical distribution of up- and down-regulated genes, the presence of only few differentially expressed genes and/or few outliers. Moreover, the cut-off for selecting significantly differentially expressed genes for further downstream analysis often depend on arbitrary choices.We here introduce a new tool for estimating differential expression in noisy real-life data. It employs a novel normalization procedure , which takes account of the overall distribution of read counts for data standardization enhancing reliable identification of differential gene expression, especially in case of asymmetrical distributions of up- and downregulated genes. The tool then introduces a polynomial algorithm (aFold) to model the uncertainty of read counts across treatments and genes. We extensively benchmark aFold on a variety of simulated and validated real-life data sets  and show a higher ability to correctly identify differentially expressed genes under most tested conditions. aFold infers fold change values that are comparable across experiments, thereby facilitating data clustering, visualization, and other downstream applications.We here present a new transcriptomics analysis tool that includes both a data normalization method and a differential expression analysis approach. The new tool is shown to enhance reliable identification of significant differential expression across distinct data distributions. It outcompetes alternative procedures in case of asymmetrical distributions of up- versus down-regulated genes and also the presence of outliers, all common to real data sets.The online version of this article (10.1186/s12864-019-5686-1) contains supplementary material, which is available to authorized users. RNA Sequencing or RNA-Seq has become a popular approach for the analysis of gene expression variation and uses the enormous recent advances in next generation sequencing technology. In contrast to array-based methods, RNA-Seq permits the quantification of gene expression without detailed prior genome information, such as gene annotations. Thus, it is widely used for both classical model organisms and also non-model taxa . A commoCurrent statistical approaches for DE analysis in RNA-Seq rely on fitting the distribution of read counts with probabilistic models. These methods often detect significant DE via an inferred probability value, usually adjusted for multiple testing through false discovery rate (FDR) estimation. FDR procedures highly depend on mean-variance relationships –4. In tht-test analysis of microarray data partially addresses this problem via testing the significance of DE on a given fold-change threshold [Alternative solutions are based on the idea of merging these cut-offs into a single statistical model or by reducing the effect of high coefficients of variation. For example, TREAT for hreshold . DESeq2 hreshold . Howeverhreshold –10. The p-value) to achieve high reliability in DE inference.We have previously developed ABSSeq as an analysis tool for RNA-Seq data, in order to solve some of the above problems . ABSSeq sensu strictu), which models the uncertainty of read count data between treatments and experiments using a polynomial function. It thereby allows calculation of fold-change values comparable across conditions and provides a statistical framework for evaluating the significance of DE, thus avoiding the problem of choosing specific cut-off values. Using real and simulated datasets, we demonstrate that the aFold tool is more efficient in DE ranking, DE visualization, and FDR reduction than several of the currently available RNA-Seq analysis approaches, including DESeq2 [Here, we introduce a novel integrated approach (aFold) of normalization and DE estimation to enhance reliability of RNA-Seq data analysis, which overcomes the problem of low variance levels. aFold includes two elements: a normalization method and then a subsequent gene expression analysis approach. For the former, we developed a new method to improve the normalization of RNA-Seq data, which we term qtotal and which uses the overall read count distribution and thus variance differences among samples for data standardization. This approach is not constrained by the assumption of presence of non-DE genes, which is common to the popular normalization methods. Therefore, qtotal is applicable to a wider range of data sets, including those with substantial DE across conditions. For the latter, we introduce a new method for differential gene expression analysis  as an indicator of sequencing depth; this procedure is however easily influenced by outliers of read count at high expression level and DE ;number of read count in the lower quartiles (a procedure termed quartile), which was introduced with the baySeq approach to avoid a possible bias due to outliers ; this prgeometric mean of all read count , which is used by DESeq  and DESeTrimmed mean of M values , which is implemented in edgeR and is based on the assumption that the majority of genes with high expression are not DE .removing technical variability using conditional quantile normalization , which removes systematic biases such as GC-content and gene length .per gene normalization after per sample median  or upper-quartile global scaling  .Read count analysis of RNA-Seq data requires normalization before DE inference in order to reduce possible biases from variation in sequencing depth, library preparation, sequencing in different lanes, or other random factors , 26. A vIn general, all above listed methods rely on the assumption of presence of no or few DE genes, such as majority of high expressed genes (TMM), genes from 1st to 3rd quartile (quartile) or median (geometry). However, this assumption may not apply in some situations. For example, presence of a large number of DE genes  will disturb the detection of non-DE genes. Asymmetrical DE in up and down regulation will impact median estimation.Here we introduce a new normalization procedure, termed qtotal, to address this problem. It is based on the idea that true DE alters the overall read count distribution (either more or less dispersed), which is reflected by a change in the coefficient of variation (CV) of reads count across genes, while variation in sequencing depth does not affect the CV . qtotal The normalization procedures affect the discriminative power of subsequent DE inference. This influence can be assessed with the help of the true and false positive rates  and the area under the Receiver Operating Characteristic (ROC) curve (AUC). The AUCs were inferred with the ROC package in Bioconductor , wherebySimilar results are also obtained using root mean square deviation (RMSD) analysis of external RNA control consortium (ERCC) data, which compares log2 fold changes with pre-defined fold changes  on ABRF  to the data: 1) GLM is fitted on read count to obtain maximum-likelihood estimates (MLEs) for the log fold changes and a zero-centered normal distribution of MLEs from all genes; 2) a second GLM is fitted again on the read count data using the zero-centered normal distribution as a prior. Interestingly, the second GLM, which relies on the zero-centered normal distribution of MLEs from all genes, might be influenced by the number of genes with significant DE. If the number of DE genes is high, then the inferred normal distribution shows a flat structure and thus little moderation of fold-change (see below). This could potentially introduce a bias in the obtained fold change values.aFold estimates fold change through modelling uncertainty of read count data. In particular, the observed read count of RNA-Seq data are characterized by several levels of uncertainty (resulting in observed variance) as a consequence of biological variation, but also due to systematic or non-systematic biases during libarary preparation and sequencing , 31. aFop-value and/or minimum expression level). To achieve this, aFold does not directly model read count distributions. Instead, it employs a zero-centered normal distribution on estimated log fold changes and compares them with the global standard deviation . For this test comparison, the DESeq2-based shrinkage procedure leads to almost no change in the fold-change distribution and thus no apparent data shrinkage, while that by aFold still results in similar shrinkage as seen for the first test comparison . These pseudo reads counts were added to the above used data set, resulting in a data set with about 40% of DE . Therefore, the expected or truly DE genes should be sex-related and only includes a total of seven genes on sex chromosomes as highlighted by us previously  identify seven genes on sex chromosomes with significant DE. If ranked by p-value, then all seven sex chromosome genes are within the top 10 DE genes. However, if genes are ranked by fold change, then only aFold is able to find these seven gene within the top 10. These results may suggest that fold changes calculated with aFold are more robust than the conventional fold change calculations (Voom and DESeq2) in ranking truly DE genes. In contrast, consideration of fold-change is not sufficient for identification of truly DE genes by the alternative methods (Voom and DESeq2), but must additionally take into account the associated p-vales. Consideration of statistical significance of DE highlights that aFold has similar power than Voom, yet higher specificity in comparison to DESeq2.Statistical assessment of genes with significant DE confirmed the above results Table . Under aWe next evaluated the discriminative power of several different methods with the help of three additional data sets. In above Table The considered ABRF data set consists of RNA-Seq data from the same mRNA sample generated by three different laboratories . This dap-values to detect true DE [The results of the analyses are shown in Fig.  true DE –10. HoweFurthermore, normalization by qtotal further improves the performance of all methods on all three data sets except of the ROTS approach on ABRFAB and MAQC-II and baySeq on ABRFAB  and estimated fold changes (RNA-Seq), as inferred with aFold and DESeq2, using corresponding SEQC data. To avoid any biases, we consistently used qtotal for normalization. Lowly expressed genes  distribution is most commonly used to increase reliability of DE detection methods as RNA-Seq data shows over-dispersed variance , 10, 15.625625, Fig. n = 5) and Voom (n = 10) . While DESeq2 directly employs a NB model to identify DE, its performance improves as the sample size increases  still has 625 up- and 625 down-regulated genes, in addition to random outliers. Additional outlier dectection produres were applied for edgeR (GLM_robust) and DESeq2 (Cook’s distance) to analyze R625625. For these simulated data sets, aFold demonstrates a significant advantage  over alternative methods at large sample sizes (n = 5 or 10) and even reaches an AUC of 0.9 at n = 10  decreases the power of DE detection for all methods, which leads to either low sensitivity and FDR  or high sensitivity but also high FDR . Interestingly, in the presence of outliers in the R625625 data sets, aFold maintains its comparatively high sensitvity and now additionally causes reduced FDR  of all methods with the help of above simulated data sets. As discribed in , the sen20002000, Additional file 01250 and NB04000, Additional file Similar results are obtained for the simulated data sets with large number of DEs  and minimize the type I error rate  while identifying a large number of DE genes , 38. To p-value of 0.05, whereby Voom reports the largest number (29120), followed by DESeq2 (28997) and aFold . These results suggest that the above observed differences between aFold and the other two methods result from genes with low expression level and/or fold change, which is consistent with findings from previous studies [We first evaluated the three methods using the ABRF data set, based on the same structure as above  have an eFDR of 0.216, while those jointly identified by DESeq2 and Voom (denoted as the gene subset I) produce an eFDR of 0.529. Note that other subsets were not considered because they included only a small number of genes, which does not permit reliable eFDR calculation. The higher eFDR for gene subset I relative to gene subset II may suggest a larger bias caused by DESeq2 and Voom. Similar results are also observed in the SEQC and MAQC-II data sets  or the geometric mean approach (DESeq2), both subsets are reduced . These results suggest that high eFDR of subset I and II is due to low fold changes (low dispersion).Our next analysis aimed at reducing eFDR for these two gene subsets by applying more stringent adjusted ffs Fig. b or addiffs Fig. c. Both affs Fig. b and c. Since false positives often result from under-estimation of variances (with low fold change but high expression or high fold change but low expression) –10, we cp-value . These results therefore suggest that aFold is able to control FDR by reducing false positives at all expression level while retaining sensitivity, even when more stringent cut-offs are used.We then assessed use of an additional fold change cut-off of 0.5 (under log2-tranformation). In this case, eFDR reduces to around 0.05 in all quartiles for aFold but only the upper ones (3rd and 4th) for DESeq2 and Voom, which produce no change in the 1st quartile (0.164 to 0.164) and only a slight improvement in the 2nd quartile (0.075 to 0.067). In fact, reducing eFDR for DESeq2 and Voom in 1st quartile to a similar value of 0.05 requires an extremely high log fold change cut-off of 4.0. Such a cut-off additionally decreases the total number of DE genes to 3564 and 3224 for DESeq2 and Voom, respectively. At the same time, applying a log fold change cut-off of 0.5 for aFold still yields a total of 15,339 DE genes. A more efficient way to reduce eFDR at 1st quartile for DESeq2 and Voom is to use a combination of cut-offs for expression level and also Drosophila melanogaster [p-value cut-off of 0.05, only aFold is able to control the type I error rate around 0.05 for the ABRF data set while the other two methods produce a rate above 0.2. For the modencodefly data set, all three methods are able to control type I error rate around 0.05, but aFold reports the smallest number of false positives (average of 15), followed by DESeq2 (119) and Voom (867). Thus, for both data sets, aFold reduces the type I error rate to a larger extent than the alternative methods , consistent with above results for eFDR.We next compared the methods in their ability to control type I error rates . We used two gene expression data sets: 1) the ABRF data set as above, including data from the same RNA sample but generated by three different laboratory sites, each with 3 replicates; and 2) the modencodefly data set, which contains data for development processes of the fruitfly nogaster , with tep-values inferred from aFold are directly deduced from and thus monotonically correlated with fold-change, which allows to apply single cut-off values to select candidate DE genes for further analysis. More importantly, aFold also takes into consideration uneven dispersion across expression levels, which avoids possible biases in inferred DE genes due to large fold change at low expression level [Taken together, the approach implemented in aFold is able to control FDR and type I error rates more effectively than the two tested alternative approaches. Moreover, on level  and thusThe results of transcriptomic studies are often visualized using a heatmap, which usually takes log fold change as input data to compare the expression difference across treatments or conditions , 41. Hown = 3). We take genes that show significance at one lab site from each method as unique genes for each method , as illustrated in Fig. However, there are still unique genes identified at each lab site by each method, which are most likely caused by variance under-estimation due to limited sample size . These genes also often exhibit high variance combined with high fold change  of samples if the SD is independent of the mean. However, In RNA-Seq data or microarray data, the SD is not independent of ai is the coefficient that stands for the mean-variance relationship of the ith gene. This implies that there is propagation of error (uncertainty) in measurement of SD based on μi. Therefore, an accurate reads uncertainty measurement should also include the propagation of error from (2). In theory, the propagation uncertainty of SD can be written aswhere si is the sample SD of gi. Thus, the uncertainty of read counts for each gene becomeswhere ai in (3) actually serves as the CV asgi becomes a polynomial function of sample SD siThe uncertainty of εi is then used to moderate the ordinary fold change . A more detailed description of the new analysis method and also its evaluation in comparison with available approaches is given in the supplementary methods in Additional file bioconductor.org/packages/devel/bioc/html/ABSSeq.html.aFold has been implemented and integrated in the software package ABSSeq for the cross-platform environment R, available through the R Core Team . aFold iThe figures in this study have been plotted using R.Additional file 1:Supplementary Methods, Figures and Tables. (PDF 2321 kb)


Most approaches aim to identify significant genes by comparing their expression values between healthy subjects and a group of patients with a certain disease. Given that studies normally contain few samples, the heterogeneity among individuals caused by environmental factors or undetected illnesses can impact gene expression analyses. We present a systematic analysis of sample heterogeneity in a variety of gene expression studies relating to inflammatory and infectious diseases and show that novel immunological insights may arise once heterogeneity is addressed. The perturbation score of samples is quantified using nonperturbed subjects  as a reference group. Such a score allows us to detect outlying samples and subgroups of diseased patients and even assess the molecular perturbation of single cells infected with viruses. We also show how removal of outlying samples can improve the “signal” of the disease and impact detection of differentially expressed genes. The method is made available  Gene expression profiling methods such as microarrays and RNA-seq have been extensively used to examine the molecular changes associated with a biological “perturbation.” This perturbation can be drug treatments, vaccinations, infections, cancers, and autoimmune or inflammatory diseases . For humTranscriptome datasets typically contain expression values of tens of thousands of genes from a relatively small number of samples. This presents a dimensionality problem when trying to identify significant changes in gene expression . Most meThe molecular distance to health  is a methttps://bioconductor.org/packages/release/bioc/html/mdp.html) and can identify potentially problematic subject data from transcriptomic dataset, as well as to quantify the perturbation score of healthy and diseased samples. Meanwhile, our user-friendly web-based application (https://mdp.sysbio.tools/) allows scientists to run MDP without any knowledge of bioinformatics or programming languages. We demonstrated that the application of our method on inflammatory and infectious disease datasets can affect the detection of differentially expressed genes (DEGs). Finally, these tools were used to analyze RNA-seq data of single cells infected with dengue virus (DENV), revealing the individual cell heterogeneity of infected cells.Here we describe a systematic analysis on heterogeneity of several RNA-seq and microarray datasets from a diverse set of human diseases. Our approach, called the molecular degree of perturbation (MDP), is available as a Bioconductor R package , and , a measure of the variability (the standard deviation or the MAD) for each gene i in the control samples. Finally, let zi be a modified z-score transformation using and as parameters. The absolute values of zi are taken, and values less than 2 are set to 0. The values that remain represent significant deviations from the healthy control samples. The MDP score for each sample j (both in the control and perturbed groups) is then the mean of the modified absolute zi values considering all genes or just the perturbed ones. The “perturbed genes” represent the top (default is 25%) genes with the highest absolute zi values across all samples in a perturbed group. Additionally, the MDP package can automatically identify outlier samples based on the number of standard deviations (default = 2) from the mean of MDP scores of all samples within each class.The MDP score measures how much a sample is distant from a reference group of samples. Let https://www.ncbi.nlm.nih.gov/geo/). If normalized data were not available, we processed the raw CEL files using the affy Bioconductor R package  cutoffs were used and are shown in Student We used the NetworkAnalyst tool  to creathttps://cloud.r-project.org repo packages: data.table, withr, ggplot2, plotly, and pandoc was used to process the data and generate the results in HTML.The code of the tool was implemented in HTML, CSS, JavaScript, PHP, and R. To upload files, check for errors and check the structure of the data; we used the languages JavaScript and PHP. An R script containing the For defining style and appearance of pages, we used CSS with Bootstrap, which is a front-end framework with several components included. For dynamic manipulation of the page, we used JavaScript with Jquery. The latter is a framework for JavaScript itself, where its main purpose is to facilitate, streamline, and reduce the complexity in development.https://traefik.io/). It also implements SSL certificate management through the Let’s Encrypt project (https://letsencrypt.org/). The nginx container is our webserver, and the php-fpm is the backend that processes requests to php files.In the infrastructure, we used the concept of containers and microservice with the platform Docker. In parallel, we used the tool Docker Compose to orchestrate and to deploy these containers. In total, we have three containers: proxy, nginx, and php-fpm. In the proxy container, the functions of reverse proxy and load balancing were performed, which were left in charge of the traefik service  and median absolute deviation (MAD). Absolute normalized expression values less than 2 are designated as unperturbed and are set to 0. Sample MDP scores are the average of normalized expression values for a given gene set  has been developed to allow non–bioinformatics users to quickly assess the MDP in their samples without the need for any previous computational knowledge or additional software  obtained from the GEO  and SRA Staphylococcus aureus, for instance, seems to be a stronger perturbation than infection with influenza virus  were used to assess the consistency between DEGs before and after removal of potential outlier samples identified by MDP. After removal, we found 21 genes that were differentially expressed in at least four JIA datasets, and none using all original samples   and on the MDP score (cutoff MDP = 1), we split the single cells into four subsets: MDPhighVLlow, MDPhighVLhigh, MDPlowVLlow, and MDPlowVLhigh. We then performed differential expression analyses between these subsets to assess the transcriptomic alterations caused by DENV infection. highVLhigh with MDPlowVLlow subsets , rather than either of these criteria alone. Comparing cells with high MDP score (MDPhighVLlow + MDPhighVLhigh) with those with low MDP score (MDPlowVLlow + MDPlowVLhigh) resulted in 872 DEGs. The lowest number of DEGs (196 DEGs) was found when we compared cells with high VL (MDPhighVLhigh + MDPlowVLhigh) with those with low VL (MDPhighVLlow + MDPlowVLlow) , CNPq (313662/2017-7), FONDECYT-CONICYT (11161020), and PAI-CONICYT (PAI79170021). This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior–Brasil (CAPES)–Finance Code 001. MN and GP were supported by the Wellcome Trust and National Institute for Health Research Biomedical Research Centre at University College London Hospitals.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.


A significant hurdle in developing reliable gene expression–based prognostic models has been the limited sample size, which can cause overfitting and false discovery. Combining data from multiple studies can enhance statistical power and reduce spurious findings, but how to address the biologic heterogeneity across different datasets remains a major challenge. Better meta-survival analysis approaches are needed.We presented a decentralized learning framework for meta-survival analysis without the need for data aggregation. Our method consisted of a series of proposals that together alleviated the influence of data heterogeneity and improved the performance of survival prediction. First, we transformed the gene expression profile of every sample into normalized percentile ranks to obtain platform-agnostic features. Second, we used Stouffer’s meta-z approach in combination with Harrell’s concordance index to prioritize and select genes to be included in the model. Third, we used survival discordance as a scale-independent model loss function. Instead of generating a merged dataset and training the model therein, we avoided comparing patients across datasets and individually evaluated the loss function on each dataset. Finally, we optimized the model by minimizing the joint loss function.Through comprehensive evaluation on 31 public microarray datasets containing 6,724 samples of several cancer types, we demonstrated that the proposed method has outperformed (1) single prognostic genes identified using conventional meta-analysis, (2) multigene signatures trained on single datasets, (3) multigene signatures trained on merged datasets as well as by other existing meta-analysis methods, and (4) clinically applicable, established multigene signatures.The decentralized learning approach can be used to effectively perform meta-analysis of gene expression data and to develop robust multigene prognostic signatures. The limited sample size can cause overfitting and false discovery, which leads to spurious findings and overconfident results.4 Better approaches to developing robust prognostic models using gene expression data are needed.Gene expression-based prognostic  models can serve as useful biomarkers that guide clinical decision making for precision medicine.7 Previous meta-analytic studies in breast cancer,8 lung cancer,9 ovarian cancer,10 and pan-cancers11 only investigated single prognostic genes. However, a prognostic model, which integrates multiple genes synergistically interacting in biologic processes, holds the potential to further improve the prediction accuracy.12Combining data from many studies—performing a meta-analysis—overcomes the limitations of small sample sizes by increasing statistical power and by allowing the robustness of findings to be assessed across multiple cohorts. Given the availability of large-scale public databases, such as the National Center for Biotechnology Inormation Gene Expression Omnibus (GEO), ArrayExpress , and National Cancer Institute’s The Cancer Genome Atlas (TCGA), meta-analysis is becoming increasingly important for investigating high-throughput genomic and transcriptomic data.13 where the model parameters are obtained by maximizing the partial likelihood function. To avoid overfitting in the large-p-small-n scenario in genome-wide transcriptomic studies, the L1-regularized version of Cox regression is often used as well.14 Survival analysis has also been formulated as a ranking problem, where the concordance index (c-index) instead of the partial likelihood is maximized for model optimization.15 In addition, several methods have been proposed that are based on support vector machines,18 Bayesian methods,20 principle component analysis,21 area under the receiver operating characteristic curve optimization,22 or ensemble machines.23 However, existing methods are designed for model training using a single cohort. To our knowledge, there has been no previous systematic approach to training a prognostic model from multiple datasets by leveraging the power of the meta-analysis.The conventional method to train such a model is the Cox regression analysis,24 or feature transformation25 to the datasets and merge them together. However, this merging approach essentially requires a uniform or similar distribution of known prognostic factors  across different cohorts. As a consequence, certain selection criteria have to be applied to carefully adjust for the population differences at the expense of reduced statistical power. Furthermore, when the meta-analysis involves cohorts receiving different therapies, or even distinct tissue of origins , merging is questionable because it introduces confounding factors and because comparing the survival duration across cohorts no longer makes sense.Nevertheless, to extract useful information from diverse data remains a daunting challenge given the profound biologic heterogeneity among datasets and technical biases across measurement platforms. One practical solution has been to apply batch-effect correction algorithmsIn this article, we present a novel decentralized learning framework of meta-survival analysis for training a prognostic model from multiple gene expression datasets without actually merging them. Such a strategy, along with the proposed feature transformation as well as carefully selected loss function, effectively overcomes the data heterogeneity stemming from both population and measurement biases.26 to best reproduce the cell cycle progression (CCP) signature as performed by the authors.We used the R package GEOquery to retrieve the processed expression data for the GEO datasets, with the exception of GEO datasets GSE32062, GSE17260, and those used in experiment 4. For GSE32062 and GSE17260, the processed data were z-score transformed across samples and lost the original ranking order. Therefore, their raw data were directly downloaded from GEO and transformed to percentile ranks without normalization. For the datasets in Experiment 4, we also downloaded the raw expression data but further performed normalization within each individual dataset by the robust multi-array average algorithmwww.synapse.org/#!Synapse:syn1688369/) with institutional review board approval. In addition, the processed data for E.MTAB.386  and The Cancer Genome Atlas Ovarian Cancer were obtained from ArrayExpress  and the University of California Santa Cruz Cancer Genomics Browser (version 2015),27 respectively.For the METABRIC dataset, the normalized expression data were obtained from SYNAPSE . Another important advantage of ranking-based gene signatures is that they can be used in a truly individualized manner that facilitates their practical implementation.For each sample, we applied a feature transformation method that transformed the expression profiles into normalized percentile ranks.31 Specifically, for each gene, we calculated its z-score with respect to the survival in dataset k, zk, corresponding to the Harrell’s c-index test.33 The meta-z score was then given by P value was Φ(z), where Φ(⋅) is the standard normal cumulative distribution function. We ranked the genes on the basis of their meta–P values and kept the top d genes for model training. We chose d o be the number of genes whose adjusted overall P values were smaller than .05 after Benjamini-Hochberg correction.34After feature transformation, we prioritized the genes on the basis of Stouffer’s meta-z method.k is the loss of the model on dataset k. In particular, we aimed to build a linear model that minimizes the loss function, which is defined as the survival discordance  as follows:We used the decentralized learning framework to develop multigene signatures by combining multiple datasets. Mathematically, this entails minimizing the joint loss function, i is the survival time, ci is the censoring label, and where 1(⋅) is the Heaviside step function, yw. Without loss of generality, we only derived the subgradient of the loss function for dataset k and for simplicity’s sake dropped the dataset index k, because the subgradient of the total loss is the sum of the subgradients of respective losses. According to equation (2), the subgradient of a given dataset is given byBecause of the convexity of the hinge function, equation (2) is also convex. Therefore, minimization of the loss function can be achieved by plugging its gradient  to any convex optimization solver such as the quasi-Newton or Broyden-Fletcher-Goldfarb-Shanno methods. In the following equation, we provide an efficient algorithm to compute the subgradient of equation (2) with respect to w takes O(md) time, where m is the number of elements in the list u to keep track of how many times each feature vector xi is selected based on the value of u = T and for each X⋅u, where X = . This algorithm takes O(m + nd) time, which is faster than O(md) as in general m = O(n). The pseudo code for computing the loss function and its subgradient is summarized in algorithm 1.where w was obtained by minimizing Furthermore, to avoid overfitting, we regularized the joint loss with the ridge penalty. Therefore, the coefficient vector gAlgorithm 1: compute loss function L and its subgradient Input: L = 0u = T b = XTw  for each  in E doj-bi < 1 then  if bi-bj   L←L + 1 + bi←ui + 1   uj←uj-1   ug = Xu Procedure:g L, Output:33 was used to evaluate and compare the predictive performance of the gene signatures. The c-index ranges from 0 to 1, with 1 being perfect prediction and 0 being the opposite. A c-index of 0.5 indicates random prediction.33 Here, c-index was chosen as the performance measure because it assesses whether a risk model can correctly rank the survival for every pair of patients. Therefore, it is a direct characterization of the overall prediction performance. C-index has been a popular choice for benchmarking survival predictors. For example, it is the adopted evaluation criterion in the DREAM  Breast Cancer Prognosis Challenge.23 This, in fact, is also why we aimed to minimize the survival discordance  as the loss function in our model. Interestingly, it has been shown that maximizing Cox’s partial likelihood function approximately maximizes c-index.15 However, as we have shown in algorithm 1, the hinge approximated survival discordance, and its gradient can be evaluated much more efficiently than the partial likelihood.Harrell’s c-indexP values of the gene signatures with a smaller value indicating better prediction.In addition, we evaluated the performance using the univariable Cox regression analysis. That is, after a survival model (gene signature) was trained on the training datasets, it was applied to the independent testing dataset to produce a risk score. This risk score was then analyzed using Cox regression to assess its correlation with survival in the testing cohort. Importantly, the risk score was treated as a continuous covariable instead of a binary one on the basis of a certain cutoff in the Cox regression, so that the performance was irrelevant to arbitrary cutoff choices. We compared the Cox 35 our approach allows training a prognostic signature by integrating information from multiple datasets without actually merging them  or disease-specific survival information available. We used six GEO datasets for training and the METABRIC dataset for testing. We compared the proposed method with conventional meta-survival analysis methods (Appendix), including single prognostic genes, models trained on a single dataset, and models trained on the merged dataset. It should be noted that for the models trained on a single dataset and on the merged dataset, we also used ridge penalty for regularization so that it would be comparable with the proposed method, which is also regularized by ridge penalty. In addition, we compared it with the meta-analysis method of Riester et al,37 We assessed the prediction performance in a leave-one-dataset-out fashion, where we trained a model on all the datasets except the one that was to be tested. This procedure was repeated until all the datasets were independently tested. It should be noted that in such a process, model training was strictly separated from the test dataset. This means both the gene prioritization and cross-validation–based hyperparameter tuning (λ in ridge regression) were also performed using only datasets allocated for training to avoid overestimation of the result.The purpose of experiment 2 was to evaluate the proposed method for predicting OS of high-grade, late-stage ovarian cancer. The benchmark methods included the model trained on the merged dataset, Riester’s risk score, and the top-performing prognostic gene signatures reported in a previous meta-analysis study.38 was implemented. However, experiment 4 concerned OS prediction of non–small-cell lung cancer in 10 microarray datasets, and the CCP signature39 was used as the benchmark. For both experiments, signature evaluation was performed in a leave-one-dataset-out manner as described previously.Experiments 3 and 4 were designed to compare the performance of meta-survival analysis  with established multigene signatures in applications where their clinical validity has been extensively tested. In particular, experiment 3 was aimed for prediction of recurrence-free survival (RFS) in eight microarray datasets, for which the 70-gene signatureP < 2.2 × 10−16; P values are for Cox regression analysis, unless otherwise indicated) among all competing methods (P < 2.2 × 10−16) and 0.664 (P < 2.2 × 10−16) on the METABRIC dataset. We identified single prognostic genes after the meta-analysis approach of Gentles et al.11 The top 10 genes in terms of the largest absolute meta-z scores were CCNB2, AURKB, TPX2, FOXM1, TRIP13, ALG3, CDKN3, CPT1A, UBE2C, and DDX39A. When evaluated on the METABRIC dataset, the best performing gene was UBE2C . Finally, we trained gene signatures on each of the six GEO datasets and tested their performances on the METABRIC dataset. The resulting c-index scores showed a wide range, from 0.483 to 0.669.In experiment 1, we used the proposed method to train a multigene signature by combining six GEO datasets. When tested on the METABRIC dataset, the resulting signature achieved the highest c-index score of 0.681 .Experiment 2 contained all the datasets used in a previous study by Waldron et al for comparative meta-analysis of prognostic gene signatures for high-grade, late-stage ovarian cancer,P = .02 to 1.5 × 10−8) but not for GEO dataset GSE7390 in leave-one-dataset-out testing. In comparison, the model trained on the merged dataset achieved significant prediction for six datasets  but not for GEO datasets GSE7390 and GSE12093; Riester’s risk score obtained significant results for six datasets  but not for GEO datasets GSE7390 and GSE19615; the 70-gene signature achieved significant prediction for six datasets  but failed for GEO datasets GSE7390 and GSE19615. Overall, the proposed method outperformed the model trained on the merged dataset in seven of the eight datasets, outperformed Riester’s risk score in seven of the eight datasets, and outperformed the 70-gene signature in all the eight datasets in terms of c-index  in leave-one-dataset-out testing, whereas the result for GEO dataset GSE19188 was not significant. However, the model trained on the merged dataset significantly predicted OS in seven datasets  but not for GEO datasets GSE83227, GSE14814, and GSE19188; CCP significantly predicted OS in only four GEO datasets: GSE68465, GSE30219, GSE31210, and GSE68571 ; and Riester’s risk score significantly predicted OS in three GEO datasets: GSE68465, GSE30219, and GSE31210 . P values.In experiment 4, the proposed method predicted lung cancer OS in nine of 10 datasets  single prognostic genes identified using conventional meta-analysis, (2) multigene signatures trained on single datasets, (3) multigene signatures trained on merged datasets as well as by existing meta-analysis methods, and (4) clinically applicable, established multigene signatures. These results confirm that the decentralized learning approach can effectively integrate information from multiple datasets and be used to derive robust multigene prognostic signatures.There are several methodologic advantages of the proposed method that may explain its improved prediction. The decentralized learning approach allows us to perform meta-analysis of multiple datasets without the need for data aggregation. It does this by estimating a common survival model where the loss function is calculated individually on each dataset, and the model coefficients are jointly estimated by minimizing the overall loss function. However, the simple merging approach implicitly assumes that the patients in different cohorts have similar characteristics. In practice, however, significant biologic and clinical differences  exist among datasets, which can lead to suboptimal results if data are aggregated without careful selection.41 as the selection criterion for gene prioritization because it is a direct, more relevant method to measure the survival prediction performance compared with the statistical significance of a Cox regression model. For the same reason, the survival discordance was explicitly used as the loss function for developing gene signatures rather than the pseudo-likelihood of the Cox regression,13 the use of which was also proposed by Vikas et al.15 There are, however, essential differences between our work and the approach taken by Vikas et al.15 First and most important, we integrated such a ranking-based survival model in a decentralized learning framework and therefore successfully addressed the data heterogeneity problem, which to our best knowledge, is the first in meta-survival analysis studies. Second, to better match the ranking nature of the model, we preprocessed the gene expression profiles into population-independent normalized percentile ranks, which served to standardize the data as well as regularize outliers. Third, we used the hinge function to approximate the survival discordance and developed a fast algorithm to evaluate the subgradient for gradient-based optimization. It turned out that both feature transformation and hinge loss approximation can significantly accelerate convergence in model training and improve the model performance.Different from previous studies, we used Harrell’s c-index42 when patient privacy is desired. However, training a model in a merged cohort requires all data to be pooled together in a central database, which demands a huge storage capacity and tremendous computing power.From a computational perspective, the decentralized learning approach is more efficient because it allows the loss function to be calculated in situ for each dataset. The model training can be accomplished in a distributed fashion, because communication between datasets only involves the transfer of the updated model coefficients and respective losses. This is particularly attractive for large multi-institutional collaborative efforts, such as the CancerLinQ project,43 This may help reveal novel molecular mechanisms beyond transcriptome associated with a poor prognosis for patients with cancer. Furthermore, the decentralized learning approach may also be used to identify common biologic themes of aggressive disease across different histologies in a pan-cancer setting.11 Currently, our method considers only those common genes across all datasets for building the signature. As the number of datasets increase, this may result in a shrinking of available gene sets. One solution is to impute the missing gene from the common genes.44 Although in this study we applied the ridge regularization, which led to a dense model, the L2-norm can be simply replaced with the L1-norm or a combination of both35 when model sparsity  is desired.Last but not least, we emphasize that our purpose for applying decentralized learning was to integrate datasets of multiple cohorts presenting the same type of data , whereas the heterogeneity mainly stems from the sampling bias of the population. This should be distinguished from studies that used decentralized learning to integrate multiomics datasets  for the same cohort.45 An interesting future study would be to combine these two types of studies to develop more comprehensive models.In principle, our approach can be generalized to incorporate other types of omic data, such as genomic, epigenomic, proteomic, and metabolomic data.https://github.com/maycuiyan/META-SURV.In conclusion, we propose a decentralized learning framework for developing multigene prognostic signatures using genome-wide transcriptomic data. Our approach allows us to perform meta-analysis by integrating information from multiple datasets without the need for data aggregation. Given the increasing prevalence of large-scale omic data, this approach can be used to identify robust and more reliable multigene prognostic signatures that will ultimately advance precision medicine. Our codes for implementing the proposed method are publically available at