There are massive transcriptome profiles in the form of microarray. The challenge is that they are processed using diverse platforms and preprocessing tools, requiring considerable time and informatics expertise for cross-dataset analyses. If there exists a single, integrated data source, data-reuse can be facilitated for discovery, analysis, and validation of biomarker-based clinical strategy. Here, we present merged microarray-acquired datasets (MMDs) across 11 major cancer types, curating 8,386 patient-derived tumor and tumor-free samples from 95 GEO datasets. Using machine learning algorithms, we show that diagnostic models trained from MMDs can be directly applied to RNA-seq-acquired TCGA data with high classification accuracy. Machine learning optimized MMD further aids to reveal immune landscape across various carcinomas critically needed in disease management and clinical interventions. This unified data source may serve as an excellent training or test set to apply, develop, and refine machine learning algorithms that can be tapped to better define genomic landscape of human cancers. Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.9901763 There also exist vast datasets deposited at the National Center for Biotechnology Information (NCBI) Gene Expression Omnibus (GEO) in the form of microarray. Applying machine learning to exploit them, however, is not straightforward; they are often generated using diverse platforms and normalization tools, and are annotated with non-standardized texts and definitions. All of these features add computational complexity to the existing high-dimensional data, necessitating multiple and intricate analytics tools for data integration and analysis.The Cancer Genome Atlas (TCGA) increasingly serves as a ‘training’ reference to apply machine learning algorithms, having comprehensive, well-curated genomic data of over 11,000 tumors across 33 major cancer types. In recent years, this rich resource combined with machine learning has facilitated the development of cancer classifier5. The resulting MMD was used to develop a predictive multi-gene classifier, termed as tumor matrisome index (TMi), for prognosis and prediction of response to adjuvant chemotherapy among NSCLC patients6.To increase the reuse of such legacy data, we generated single, merged microarray-acquired datasets (MMD) for 11 major cancer types using a uniform R pipeline  were observed between microarray (MMD) and RNA-seq (TCGA). Next, we demonstrate the potential application of MMD as training data to develop clinical predictive models that can be applied cross platform. By applying CIBERSORT12, we further show how MMDs can be used to de-convolve tumor immune microenvironment by parsing specific subpopulations of infiltrating immune cell, comparatively with TCGA datasets of matching cancer types.Here, we extend the framework to include various carcinomas of epithelial origin. Consistent with prior works13. The generated cancer type-specific MMDs, the associated clinical metadata and R codes are available at ArrayExpress and figshare (see Data Records and Code Availability). Our open resource of curated large-scale transcriptomic data may provide the basis for the analytical and computational techniques to derive unbiased and new information, enabling predictive modeling for precision oncology.Through pan-cancer analysis of MMDs, we recently identified clinically significant matrisomal changes associated with immune response and targetable immune checkpoints for a subset of cancers across different malignancieshttp://www.ncbi.nlm.nih.gov/geo) was done to ensure the selection of MIAME compliant datasets having the following attributes in the original GEO submission: (1) raw data in CEL files, (2) tissue origin annotation , and (3) Affymetrix platform annotation. Here, only datasets generated using the GPL570 platform (Affymetrix Human Genome U133 Plus 2.0 Array) were specifically selected to ensure uniform curation of the same probe-sets . Altogether, 95 independent GEO datasets comprising a total of 8,386 samples spanning over 11 cancer types were subjected to pre-processing, normalization, batch-effect correction, data integration and analyses (Table A careful GEO search (es Table . The num14 (RStudio version 1.1.447) using the affy package (version 1.48.0)15. The ReadAffy function was called with default parameters to read all CEL files, except for the function argument “cdfname” which was set to “hgu133plus2”. The rma function was subsequently used to normalize and background correct all the annotated probe-sets-derived expression data. This preprocessing step was applied to all 95 datasets for uniform processing and feature annotation prior to merging based on cancer type. Batch effects were identified and removed using ComBat via the inSilicoMerging package (version 1.14.0)16. Probes having maximum mean expression values across samples in each MMD were collapsed to the genes, and were annotated using the hgu133plus2SYMBOL object in the hgu133plus2.db package (version 3.2.2)17 for subsequent DE analysis.Raw expression data from each dataset was first imported and loaded into R Bioconductor18 (Table 18. Only genes with at least 1 count per million (cpm) or RPMK value in at least 20% of total number of samples in each cohort were kept via the edgeR package (version 3.12.1)19. The number of genes filtered out in each TCGA dataset is summarized in Table 20. Of note, ovarian (OV) and melanoma (SKCM) TCGA cohorts were excluded in DE and RRHO analyses due to lack of NT samples (Table 18.The Cancer Genome Atlas (TCGA) data were retrieved and processed via the TCGA-Assembler package (version 2.0)18 Table . Normalies Table . Clinica21. The lmFit and eBayes functions in the limma package (version 3.26.9)20 were used to perform DE analysis. All genes annotated in each MMD and TCGA dataset were ranked by log fold change (logFC) computed based on their DE between NT and TT samples. These ranked lists were further reconstructed to only include genes that were common to both MMD- and TCGA-derived lists22 (Table http://systems.crump.ucla.edu/rankrank/rankranksimple.php). In all cases, the step size was set to 300 to generate Benjamin-Yekutieli corrected hypergeometric matrix and RRHO heatmaps.Principal component analysis (PCA) was performed using the prcomp function in the built-in R stats package (version 3.2.2). The first two PCs were visualized using the ggbiplot package (version 0.55)22 Table . These fhttp://software.broadinstitute.org/morpheus/) for sample stratification. The list of MGT genes and the associated references are summarized in Table Expression data of TMi and other gene signatures of commercially available or previously validated multi-gene tests (MGTs) were extracted from all TT samples across MMD and TCGA datasets, and were loaded into Morpheus (http://cibersort.standford.edu/)12. 1,000 samples were thus randomly selected to generate the input “mixture” file for these MMDs. All samples in the rest of MMDs were included in the CIBERSORT analysis. Each run was performed with a default LM22 (22 immune cell types) gene signature using 100 permutations. The resulting immune cell profiles were used to compute the mean fractions of 22 immune cell types and the quantitative change between the two groups (NT vs. TT), denoted as delta , per dataset.Consisting of over 1,500 samples, breast, colon, and lung MMDs exceeded the load capacity (500MB) of the CIBERSORT analysis  stratified by a pan-cancer multi-gene TMi classifier  were compared between the two groups (NT vs. TT) using MMDs. The selected housekeeping genes are stably expressed across tissues to maintain cellular function, and are commonly used for normalization in transcriptomics studies. While expression levels of cancer-associated gene were significantly different between NT and TT samples, that of all reference genes were almost the same in the two groups across all cancer types, validating the robustness of ComBat in adjusting technical batch effects while maintaining biological variation across samples Fig. .All MMDs were next subjected to genome-wide, limma-based DE analysis to rank all the genes by logFC based on DE between NT and TT samples (see Methods). These ranked lists were used to generate volcano plots visually depicting differentially expressed genes that met our statistical threshold  in TT relative to NT samples Fig. . To vali36 was used to assess the overlap intensity between MMD- and TCGA-derived lists of genes ranked by DE between NT and TT samples per cancer type  previously derived from MMD data exclusively comprising TT samples  to build best predictive model in distinguishing TT from NT samples. Predictive model built from each MMD was then tested directly on TDM-transformed-TCGA dataset. Except for breast MMD, all MMDs achieved an average AUC of 0.96 (ranging from 0.913 to 0.997) in classifying TCGA cancers  treatments. The recent advancements in computational techniques have further facilitated high-resolution, large-scale immunogenomic analyses of the tumor-immune interface54. Of the developed analytical pipelines, CIBERSORT serves as an exemplary in silico deconvolution method to estimate the relative proportion of 22 immune cell populations from heterogeneous bulk tissues. By applying CIBERSORT to MMDs, we next tested if the generated compendiums could further provide the basis for the developed computational infrastructure to reveal clinically significant immune landscape across multiple cancer types (see Methods).TCGA data are increasingly being used to study the prognostic influence of the composition of tumor-infiltrating lymphocytes (TILs)56.The extent of difference in immune cell composition between the two groups (NT vs. TT) varied depending on cancer type Fig. , where tSupplementary Information


Current normalization methods for RNA-sequencing data allow either for intersample comparison to identify differentially expressed (DE) genes or for intrasample comparison for the discovery and validation of gene signatures. Most studies on optimization of normalization methods typically use simulated data to validate methodologies. We describe a new method, GeTMM, which allows for both inter- and intrasample analyses with the same normalized data set. We used actual (i.e. not simulated) RNA-seq data from 263 colon cancers  and used the same read count data to compare GeTMM with the most commonly used normalization methods (i.e. TMM (used by edgeR), RLE (used by DESeq2) and TPM) with respect to distributions, effect of RNA quality, subtype-classification, recurrence score, recall of DE genes and correlation to RT-qPCR data.We observed a clear benefit for GeTMM and TPM with regard to intrasample comparison while GeTMM performed similar to TMM and RLE normalized data in intersample comparisons. Regarding DE genes, recall was found comparable among the normalization methods, while GeTMM showed the lowest number of false-positive DE genes. Remarkably, we observed limited detrimental effects in samples with low RNA quality.We show that GeTMM outperforms established methods with regard to intrasample comparison while performing equivalent with regard to intersample normalization using the same normalized data. These combined properties enhance the general usefulness of RNA-seq but also the comparability to the many array-based gene expression data in the public domain.The online version of this article (10.1186/s12859-018-2246-7) contains supplementary material, which is available to authorized users. In recent years, the analysis of the transcriptome has switched from using microarrays to the potentially more powerful and informative massive parallel sequencing of cDNA (RNA-seq) . In RNA-Current normalization methods allow for either inter- or intrasample comparison. The two most commonly used normalization methods when interested in DE genes between samples (intersample comparison) are edgeR  and DESeThe most commonly used normalization method that includes gene length correction is TPM (Transcripts Per kilobase Million) , as otheIdeally, a normalization method should generate a data set on which both between-sample and within-sample analyses can be performed. We therefore introduce GeTMM (Gene length corrected TMM), a novel normalization method combining gene-length correction with the normalization procedure TMM, as implemented in edgeR, to allow both inter- and intrasample comparison with the same normalized data set. We used true (i.e. not simulated) RNA-seq data of a large cohort of primary tumors of 263 colon cancer patients, and normalized these data using our new method GeTMM, alongside TMM, RLE and TPM , a cliniFresh-frozen tumor tissue of 263 colon cancer patients of the MATCH study, a multicenter observational cohort study, who underwent surgery in one of seven hospitals in the Rotterdam region, the Netherlands, were used. Inclusion criteria and additional clinical characteristics have been described .Detailed description of the RNA-isolation has been described previously , 17; briFor RNA-seq, 500 ng of total RNA after gDNA removal, clean-up and removing ribosomal RNA using Ribo Zero , was used as input for the Illumina TruSeq stranded RNA-seq protocol (paired-end). No biological replicates were used. Libraries were pooled and sequenced on Illumina HiSeq2500  or NextSeq  instruments. Pool sizes and the amount of samples per run were determined based on the percentage of tumor cells estimated from histological examination . We usedhttps://www.gencodegenes.org/). To obtain exon specific counts for CDK1 and MKI67, all unique HAVANA exons for each gene were extracted and used in FeatureCounts /(n1 + n2–2), where V1 and V2 are the variance for each of the groups, and n1 and n2 the sample group sizes.The CMS classification was performed using the “CMSclassifier” package  were considered significant when below 0.05.Statistical tests were performed using R (v3.2.2), using non-parametric tests  where appropriate. For identifying DE genes, the default tests that are included within the edgeR and DESeq2 packages were used . For edgeR, a common dispersion value of 0.4 was used, as suggested by the documentation. Additionally for edgeR and DESeq2, but also for RT-qPCR, TPM and GeTMM the Student’s t-test was used. For the calculation of Root Mean Square Error (RMSE), standardized data were used . Statistical tests are indicated in the main text, We used primary tumor tissue of a cohort of 263 colon cancer patients to generate RNA-seq data. There were no biological or technical replicates. We aligned these data to the human reference genome (GRCh38) and generated read counts per gene. This read count matrix was used for several normalization procedures: TMM (implemented by edgeR) [The library sizes (i.e. the number of mapped reads) of the samples ranged from 5.8 to 37.8 million (mean 16.0 million and median 14.2 million). Density plots were generated to get an overview of the read count distributions Fig. , which bHMBS, HPRT1 and TBP) using RT-qPCR in the same RNA isolate as was used for sequencing. The RT-qPCR data were normalized using the reference genes and were considered as the gold standard to compare against. To assess the effect of the different normalization methods on intersample analysis, we correlated the normalized RNA-seq data of the 30 genes to the RT-qPCR levels over all samples . A Spearman’s rank correlation analysis on these data – to ascertain the influence of possible non-normally distributed expression data – showed the same results , indicating an insufficient sequencing depth for these genes. ACTB was the highest expressed gene of the 30 genes and had the lowest variance in 4 of 5 methods , which may be the reason for the low correlation. For CDK1 and MKI67, we re-analyzed all 263 samples to obtain the reads per exon. We observed a lower expression of exon 1 of CDK1, which may explain the poor correlation between the RT-qPCR and RNA-seq data as the RT-qPCR product spans exon 1 and 2 . GeTMM showed a higher correlation coefficient in 262 of the 263 cases.Previously , RNA-seqp = 0.02, see Additional file p-value (Student’s t-test under H0 that the difference is 0). Similar to the intersample comparison between RNA-seq and RT-qPCR in all samples, the result for GeTMM was similar to TMM and RLE normalized data, meaning the correlation coefficients were similar for the low and high RIN group. Normalization using TPM did result in significantly lower correlation coefficients in the high RIN group compared to the low RIN group , again indicating an advantage for GeTMM compared to TPM.Next, we repeated the intersample correlation analysis with RT-qPCR data for the 76 samples that had an RNA integrity (RIN) value < 7 after the cleanup procedure (median RIN 5.3), and compared these to an equally sized group of 76 samples with the highest RIN values . The median library size of the low RIN group was slightly lower at 5.58 million versus 6.52 million for the high RIN group  for these 8 genes. Again, GeTMM performed similar to TMM and RLE normalized data, showing very comparable SNRs, but outperformed TPM  compared to edgeR (14/22), DESeq2 (7/22) and TPM (16/22). The recall was similar for all methods . When analyzing TMM (edgeR) and RLE (DESeq2) normalized data with a t-test, recall of edgeR dropped to 3 genes while DESeq2 recalled 4 genes. Both edgeR and DESeq2 called 5 genes as ‘false-positives’ .The correlation of the different normalization methods to RT-qPCR data already showed that GeTMM performed equivalent to TMM and RLE, but outperformed TPM. To further study the effect of the different normalization methods on an intersample analysis in a biological relevant context, the genes in left sided and right sided colon tumors were examined for differential expression, since tumors in the left and right hemicolon are known to be biologically different. In short, right-sided tumors are frequently hypermethylated, hypermutated, microsatellite instable and mutation . This chtype DX® [n = 109) would receive this score. Clearly GeTMM, which uses gene length correction on top of edgeR normalization, improves the range and distribution of the RS scores.An often-used tool to estimate risk of recurrence in colon cancer is the Recurrence Score (RS) algorithm of Oncotype DX® , which uFinally, the CMS classification was determined for each sample using data normalized by the different methods . In thisThe current study showed that GeTMM performed equivalent in intersample analyses to two commonly used and best performing in several RNA-seq normalization aspects – RLE (used by DESeq2) and TMM  –8, whileGRB7 (a 532 bp transcript) is higher expressed than BCL2 (a 239 bp transcript), it adds to the evidence for a HER2 subtype [GRB7 read counts will be about 2-fold higher compared to the BCL2 read counts, when both genes are expressed at equal levels. Evaluating these intrasample-type analyses in the current study, GeTMM and TPM produced significantly better results compared to data normalized by TMM (edgeR) and RLE (DESeq2) when correlating a set of genes measured by different methods within the same sample. A similar sort of analysis had been performed previously [type DX®) edgeR showed an overall much lower distribution and assigned almost half of the patients below a zero score. This was remedied by including a gene length correction (thus yielding GeTMM), resulting in scores very comparable and in the same range as the RT-qPCR generated scores. This illustrates the importance of using a normalization method like GeTMM, that results in a data set that is suited for both intersample as well as intrasample analyses.The effect of gene length correction on downstream analysis is more important than it seems at first, when realizing that several frequently used standard analyses are vulnerable to gene length induced bias. Besides the theoretical example stated in the introduction, another example is e.g. in breast cancer, wherein the AIMS  method w subtype . Withouteviously  using theviously . Given tSeveral metrics were used to evaluate the normalization methods, summarized in Table The analyses using subsets of samples with a low or high RIN value showed remarkably little difference in correlation to RT-qPCR generated data. It appears that samples with a low RIN value may yield sequencing data suitable for expression analyses. Still, this conclusion is drawn from a single correlation analysis and may be very specific to the entire protocol that was used  and may therefore not be applicable to all studies and protocols. Still, a-priori disregarding samples with a low RIN value for sequencing could prove wasteful, though it is prudent to perform a robust QC on the generated sequencing data to spot failed samples.Lastly, this study uses RT-qPCR as standard so the RNA-seq normalization methods could be compared with each other. RT-qPCR is known for its precise and reproducible measurements and may have a bigger dynamic range compared to the usual coverage of sequence data. The downside is that RT-qPCR measures just a small part of the gene, may miss or be affected by splice-variants, and can be affected by SNPs in the primer regions. In that respect, the RNA-seq generated data may be nearer the mark of the actual expression level of a gene. In the future, RNA-seq may replace RT-qPCR as the gold standard for expression data, provided a well-founded normalization method is used.This study shows that GeTMM produces a versatile normalized RNA-seq data set, appropriate for both inter- and intrasample comparisons. This quality of GeTMM should further enhance the capacity of RNA-seq as a solid method to explore and compare gene expression profiles, and thus may become increasingly interesting in the current era of data sharing efforts.Additional file 1:Impact of gene length correction on correlation. Simulated expression data of 10 genes in 2 samples. Correlation based on read counts show different results after correcting for gene length. RPK indicates reads per kilobase. (PDF 189 kb)Additional file 2:Correlation RIN BioAnalyzer vs MultiNA. RIN values as measured by the Bioanalyzer (Agilent) were compared to the 28S/total concentration as measure by the MultiNA in a training set of 60 cases (A). The resulting trend line was validated in an independent cohort (B) of 73 cases. (PDF 199 kb)Additional file 3:Details on the RT-qPCR assays. (XLSX 14 kb)Additional file 4:Details on the settings for the STAR algorithm and R commands to obtain normalized data. (DOCX 13 kb)Additional file 5:Correlation coefficients for each method compared to RT-qPCR. (XLSX 10 kb)Additional file 6:PSCA and comparison of several RNA-Seq normalization methods. (TIFF 9492 kb)Expression of Additional file 7:P-values are derived from the Mann-Whitney test. (PDF 3492 kb)Comparison correlation coefficients by method. Boxplots show correlation coefficient of 30 genes, comparing 4 methods to RT-qPCR generated data. Additional file 8:Spearman’s correlation to RT-qPCR data of 30 genes. Correlation coefficients (x-axis) of 30 genes comparing RNA-seq normalization methods to RT-qPCR generated data. (PDF 618 kb)Additional file 9:Library size and PCA plots by RIN. A shows the library size (log10) in samples with low RIN values (RIN < 7) or high RIN (> = 9). B-E show PCA plots, colored by samples with low RIN (red) or high RIN (blue), by normalization method. (PDF 2842 kb)Additional file 10:Signal-to-Noise Ratios. (XLSX 9 kb)


Adaptive multivariate two-sample test for Microbiome Differential Analysis (AMDA) to examine whether the composition of a taxa-set are different between two conditions. Our simulation studies and real data applications demonstrated that the AMDA test was often more powerful than several competing methods while preserving the correct type I error rate. A free implementation of our AMDA method in R software is available at https://github.com/xyz5074/AMDA.Differential abundance analysis is a crucial task in many microbiome studies, where the central goal is to identify microbiome taxa associated with certain biological or clinical conditions. There are two different modes of microbiome differential abundance analysis: the individual-based univariate differential abundance analysis and the group-based multivariate differential abundance analysis. The univariate analysis identifies differentially abundant microbiome taxa subject to multiple correction under certain statistical error measurements such as false discovery rate, which is typically complicated by the high-dimensionality of taxa and complex correlation structure among taxa. The multivariate analysis evaluates the overall shift in the abundance of microbiome composition between two conditions, which provides useful preliminary differential information for the necessity of follow-up validation studies. In this paper, we present a novel  The human microbiome, referred as the aggregate of microorganisms that resides on or within any human tissues and biofluids, has recently gained substantial scientific interest due to its vital role in many human health and disease conditions, including but are not limited to obesity . That is, many studies attempt to detect differentially abundant microbiome features (species/OTUs) between two predefined classes of samples, where a microbiome feature is considered differentially abundant, if its mean proportion is significantly different between two conditions. This type of analysis can improve understanding the pathology of the disease from a microbiome perspective and potentially lead to preventive or therapeutic strategies  or even all OTUs in the microbiome community. The multivariate-type microbiome differential analysis usually gains power by reducing the multiple testing correction burden and aggregating modest effects across multiple taxa. Moreover, the multivariate analysis is typically less sensitive to normalization/transformation compared to individual analysis as it has a much larger analysis unit. Motivated by this, many statistical methods for microbiome community-level analysis have been recently proposed  is that the result of the test is global and is unable to identify specific taxon in the taxa-set that are differentially abundant. Besides the limitation in results' interpretation, it may also jeopardize the power of the test when the taxa-set contains many taxa that are not differentially abundant  samples collected from two groups with sizes of n1 and n2, respectively. Here, the term community refers as a taxa-set, which typically consists of taxa from the same taxonomic rank such as genus, family, phylum, or bacteria kingdom. Let nk × p OTU matrix for group k, where p × 1 microbiome composition vector . Suppose that, p-dimensional multivariate distribution with mean parameters μ(1) and μ(2), respectively. In many practical problems, the hypothesis of interest is to examine whether microbiome abundances are different under two different conditions, that is,Assume that we have measured the microbiome abundances of a community of For microbiome data, due to the varying amount of DNA yielding materials across different samples, the count of microbiome sequencing reads can vary greatly from sample to sample. The normalization of the raw sequencing read counts to relative abundances makes the microbial abundances comparable across samples. Therefore, it is a common practice to analyze high-dimensional microbiome compositional data with a unit sum Li, . As suchA popular approach to relax the compositional constraint of microbiome data is to perform the statistical analysis through log-ratio transformations , as a common practice, a zero count is usually replaced by a pseudo count of 0.5 before the relative abundance normalization and centered log-ratio transformation Li, . For comTwo-sample testing on the equality of two high-dimensional means has been well studied in the statistical literature is to use a non-parametric test that does not need to estimate the covariance matrix. One such test is the kernel-based maximum mean discrepancy (MMD) test  is a characteristic kernel , we apply the test on a putative testing subset XS, where S⊂{1, …, p}. Our method can also be viewed as a weighted approach in the sense that a zero weight is assigned to a feature that is not selected in the testing subset, and an equal weight is assigned to each feature in the testing subset. We defer details of selecting such a testing subset to the next section and present our adaptive microbiome differential analysis (AMDA) procedure in A common adaptive approach in a multivariate association test or two-sample test is to assign different weights to variables so that important variables are up-weighted and non-informative variables are down-weighted  is applied to each dimension of X and p-values as p1, …, pp and p is typically much larger than sample size in microbiome studies, we calculate the marginal p-values rather than joint p-values for testing subset selection. For a truly differentially expressed variable Xj, as We first randomly permute the row indices of matrix It should be noted that the aforementioned permutation-based procedure is one way to achieve testing subset selection but not the only way, and it is possible to select testing subset p-value. We do not incorporate this strategy, for ease of presenting, and only evaluate the Gaussian kernel-based test for AMDA, MiRKAT, and MMD in this simulation. Correspondingly, we evaluate the OMiAT as the optimal of a series of MiSPU tests (without MiRKAT tests of different kernels) for fair comparison. With a slight abuse of notation, we still term this test as OMiAT, though it does not contain the MiRKAT component compared to the original one . For this reason, we use permutations to calculate the MAX test p-value and the resampling option in the QCAT software  were drawn from a uniform distribution Unif and we considered the banded covariance structure Σ = D1/2AD1/2, where D is a diagonal matrix with entries randomly drawn from Unif and A has nonzero entries ajj = 1, aj,j−1 = aj−1,j = −0.5. Under the null model, we set μ(2) = μ(1). Under the alternative model, we randomly picked a subset ej ~ Unif for all %p and 50%p with the indices randomly chosen from {1, 2, …, p}. Throughout this simulation, we varied n = 50, 100, 200 with n1 = n2 = n/2 to investigate the test's performance under different sample sizes, and considered p = 50, 100, 200, 500 representing taxa-sets under different taxonomic ranks.We closely followed the simulation design of the MAX test  = exp{−||x−y||2/ρ}, where x and y are two microbiome compositional vectors) was used in AMDA, MMD, and MiRKAT with the shape parameter ρ selected as the median of sample pairwise Euclidean distance ||x − y||2. The type I error was evaluated using 5,000 replicates generated under the null model and the power of test was assessed with 1,000 replicates under the alternative model. Without loss of generality, we set the nominal significance level α = 0.05 throughout this simulation.After the data were simulated, we applied AMDA, MAX, OMiAT, MMD, MiRKAT, and QCAT to examine the two-sample differences. The first three tests AMDA, MAX, OMiAT are adaptive in the sense that they either use a testing subset of the taxa (AMDA and MAX) or assign a different weight for each taxon in the set (OMiAT) to conduct the multivariate two-sample test. The Gaussian kernel -configurations. The power of different tests are reported p = 50 and 100) and p = 200 and 500). Since the effect size was arbitrarily chosen to avoid power saturation, we care about the relative power among different methods rather than their absolute magnitudes. As can be seen from both figures, adaptive tests  are consistently more powerful than the non-adaptive ones . This is because the scenarios considered in our simulation studies are relatively sparse (p*/p ≤ 50%), and the adaptive tests can largely boost the power by treating variables  differently.The type I error of different tests are reported in n = 200). When the dimension of taxa-set increases, QCAT can quickly lose power and become less powerful than both MMD and MiRKAT  and dimension is relatively low  as indicated in p = 500, there are p* = 50 even under the sparse scenario and AMDA can be more powerful than MAX by including more signals in the testing subset (bottom row of p*/p = 30%) or relatively dense (p*/p = 50%), AMDA is much more powerful than MAX under most scenarios in both p*/p ≤ 50%, which means there are much more noises than signals), the accumulated adverse effects of noise variables can still deteriorate the performance of OMiAT. As a comparison, a zero weight is assigned to a noise variable (by excluding it from the testing subset) in AMDA, which explains power gain in AMDA over OiMAT.Among the three more powerful adaptive tests, MAX seems to be slightly more powerful than AMDA and OMiAT when the density of signal is sparse (p*/p = 10%) under relative low dimensions , MAX can be slightly more powerful than AMDA.To conclude, like five other methods, the proposed AMDA method is able to preserve the nominal type I error in microbiome differential abundance analysis. Power-wise speaking, there is no uniformly most powerful test in our simulations. However, the proposed AMDA method is always the most powerful one among all six tests being evaluated in this simulation under most scenarios, and the power advantage of AMDA over the other five methods can be huge , 2. Unden = 180), non-autistic developmental delay , and typically developing . The ASD group was defined using criteria specified in the Diagnostic and Statistical Manual of Mental Disorders (DSM–5) by the American Psychiatric Association. The DD group included children who did not meet DSM-5 criteria for ASD but had developmental delay symptoms . TD children included children with negative ASD screening and met typical developmental milestones on standardized physician assessment. The oral microbiome composition of these children was quantified with next generation sequencing. The data along with details of data processing are available in the previous publication  difference of microbiome community profiles between ASD and DD. For the comparison of ASD vs. TD, the test p-values of AMDA, MAX, OMiAT, MMD, MiRKAT, and QCAT are 0.0021, 0.0017, 0.0323, 0.3039, 0.3099, and 0.1782, respectively. All three adaptive methods  are able to detect a significant difference between ASD and TD. In the original study  compared to the number of variables (p = 753), the non-adaptive tests have a low power. This explains that MMD/MiRKAT/QCAT methods are not able to detect a significant difference of microbiome profiles between two conditions in this data. Finally, the AMDA/MAX/OMiAT p-value of comparison ASD vs. TD is much smaller than that of comparison ASD vs. DD, indicating a more significant overall oral microbiome composition difference between ASD vs. TD than the between ASD vs. DD, which is consistent with the severity of disorder.We first applied these tests to examine whether there is an overall shift in oral microbiome composition between different developmental groups by testing the differential abundances of all 753 taxa as a whole community. For the comparison of ASD vs. DD, the test p-values of these tests at family-level are presented in p-values at other taxonomic ranks have the similar pattern and hence are not reported). The AMDA p-values tend to be the smallest among p-values of all six tests. Therefore, our method has a clear advantage over the other methods in terms of detecting more significant differences in this oral microbiome data differential abundance analysis.Next, we shift our analysis unit to lower ranks than the community-level to comprehensively assess taxa-set (with multiple taxa) at each taxonomic rank that are differentially abundant among different developmental status groups. The testing results are summarized here in With the ever-increasing availability of microbiome and metagenomics data generated by next generation sequencing technology, the need to develop and implement efficient statistical analysis for the data is important to ensure both statistical rigor and biological relevance. In this paper, we consider the problem of differential abundance analysis for microbiome data, which leads to a better understanding of the behavior of microbiome communities. Most existing methods tackle this problem using individual taxon-based approach followed by multiple testing adjustment. However, as taxa living in the same community do not grow independently, the complicated interactions among taxa result in complicated correlation structures among taxa relative abundances, which may violate the correlation assumptions  of existing multiple correction methods . Moreover, the adaptive strategy used in AMDA could be easily extended to other hypothesis testing framework  beyond the two-sample problem considered in this paper. We conducted comprehensive numerical simulation studies to show the superior performance of AMDA over existing approaches in terms of maintaining the correct type I error while having a higher power to detect a true difference. The potential usefulness of AMDA was further demonstrated via its application to an oral microbiome data, where AMDA tends to detect more significant differences than its competitors.For illustration of our method, we applied the Gaussian kernel-based MMD test, which has been shown to be a consistent two-sample test  to Quadrant Biosciences, Inc. Quadrant Biosciences was involved with study design, and data collection for the RNA sequencing results employed in this study's secondary data analysis (autism microbiome data). SH and FM serve on the scientific and medical advisory boards of Quadrant Biosciences Inc., and SH is a paid consultant for Quadrant Biosciences Inc. 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.


The emergence of single-cell RNA sequencing (scRNA-seq) technologies has enabled us to measure the expression levels of thousands of genes at single-cell resolution. However, insufficient quantities of starting RNA in the individual cells cause significant dropout events, introducing a large number of zero counts in the expression matrix. To circumvent this, we developed an autoencoder-based sparse gene expression matrix imputation method. AutoImpute, which learns the inherent distribution of the input scRNA-seq data and imputes the missing values accordingly with minimal modification to the biologically silent genes. When tested on real scRNA-seq datasets, AutoImpute performed competitively wrt., the existing single-cell imputation methods, on the grounds of expression recovery from subsampled data, cell-clustering accuracy, variance stabilization and cell-type separability. Single-cell RNA sequencing (scRNA-seq), on the contrary, enables the measurement of gene expressions in individual cells. Over the past few years, scRNA-seq has revolutionized the field of genomics by facilitating the characterization of phenotypic diversity among seemingly similar cells5. Hence, only a small fraction of transcriptomes of each cell is captured during the amplification process6, so, the gene expression matrix presents significant missing values or dropouts9. These dropout events introduce technical variability and high noise, making it difficult to analyze the single-cell RNA-seq data10. Also, it is quite challenging to distinguish between dropouts and the events of biological gene silencing. As a result, the state-of-the-art nuisance factor rescaling based normalization techniques often fail to denoise the data.Many single-cell transcriptomic technologies have emerged over the last few years, each having its unique capabilities and limitations in terms of throughput, sensitivity, accuracy, and precision. There are two major protocols into which they can broadly be divided: (1) ones that reverse transcribe and amplify full-length mRNA transcripts from single-cell samples in order to extract full sequence information, and (2) ones that amplify only the 5′ or 3′ ends of each transcript, with the aim of counting mRNA molecules for measuring gene expression. Unlike methods that are designed to target specific transcripts (such as microfluidic single-cell qPCR), single-cell transcriptomics suffers from low reverse transcription efficiency (which limits the ability to detect lowly expressed genes) and high levels of technical noise (owing to the paucity of starting RNA)The measured gene expression matrix can be perceived as a partially observed version of the complete gene expression matrix (with no dropout events). The problem is akin to that of collaborative filtering; therein the ratings matrix is partially observed and the goal is to estimate the complete matrix given the partially observed ones. Our problem is to recover the complete gene expression matrix by imputing the dropouts. Traditional strategies to solve the matrix completion problem include (1) nuclear norm minimization, (2) matrix factorization and (3) autoencoders. Autoencoder based methods generalize better and are less prone to overfitting for a data restricted problem like ours, as the number of parameters that are to be learned/estimated is much smaller than the number of learnable parameters in matrix factorization or nuclear norm minimization (more on this in the methods section).In this work, we propose AutoImpute Fig. , a novelWe compare the performance of AutoImpute with the existing imputation methods on nine independent datasets. Our proposed method performs competitively as evaluated on the grounds of expression recovery from subsampled data, cell-clustering accuracy, variance stabilization across cells of identical type and cell-type separability. Also, AutoImpute is the only method which is capable of performing imputation on the largest of the nine datasets in question, PBMC , without exhausting memory.13. MAGIC uses a neighborhood-based Markov-affinity matrix and shares the weight information across cells to generate an imputed count matrix.Recently, attempts have been made to devise imputation methods for single-cell RNA sequencing data, most notable among these are MAGIC, scImpute, and drImputeOn the other hand, for a zero expression value, scImpute first estimates the probability of it being a dropout. It uses a Gamma-Normal mixture model to take into account the dropout events. Zero expressions, which are likely to be dropouts are then estimated by borrowing information from similar cells. scImpute has been shown to be superior as compared to MAGIC. Another method, drImpute, repeatedly identifies similar cells based on clustering and performs imputation multiple times by averaging the expression values from similar cells.14 of sparse matrix imputation frequently encountered in recommender systems a.k.a collaborative filtering in information retrieval. The problem is well illustrated with the following example. When designing a recommender system for movies (like in Netflix), we are given a user-movie rating matrix in which each entry  represents the rating of movie j by user i only if the user i has watched movie j and is otherwise missing. The problem now is to predict the remaining entries of the user-movie matrix, to make suitable movie recommendations to the users.Our approach, AutoImpute is motivated by a similar problem16 and Neighborhood Models17. The use of latent factor models like those based on the autoencoders18 have been rising, stemming from the recent successes of (deep) neural network models for vision and speech tasks. Justifying their popularity in the recent years autoencoder based matrix imputation methods outperform the current state-of-the-art methods. So, we adopt and deploy this idea to address the problem of dropouts in scRNA-seq data.With the aim to impute the sparse user-movie rating matrix in the aforementioned problem, various algorithms have been proposed; the most popular ones amongst which are Matrix Factorization19) to be indicative of true biological silencing. We imputed the matched single cell expression data from the same cell line using various imputation methods. We conjectured that a reasonable imputation technique should retain zero expressions due to biological silencing, whereas impute the dropout cases.Due to the lack of the starting RNA material single-cell RNA-seq experiments suffer from high dropout rates. As a result, expression datasets often contain an excessive number of zero expression values compared to typical bulk expression datasets. While a majority of these zero expression values manifest technical dropouts, a sizeable fraction of these is caused by biological silencing of the concerned genes. There is no confirmatory method to zero in on the source of origin of the zero expression values. To circumvent this, we made use of matched bulk expression profiles. Bulk RNA-seq experiments involve millions of cells, thus do not suffer from dropouts. To this end, we considered zero expressions in a homogeneous bulk cell populations derived from myoblast cell line  in the imputed single-cell expression data is reported on a natural logarithmic scale in the Fig. The existing techniques were tested on the aforementioned experiment, by first processing the bulk RNA-seq data using TMM normalization, followed by log-transformation; to check for composition bias. Then, the median of gene expression across three different biological replicates taken from cells of undifferentiated myoblasts was considered to create expression bins. The genes with zero expression in the bulk data were considered to be biologically silent and are assigned a separate bin. Rest of the expressed genes were grouped based on their median expression. For each set of genes belonging to a bin (found using the bulk data), the fraction of zeros , we artificially masked (removed) a certain percentage of the total non-zero expression values at random, and used the imputation techniques to estimate the expression values at these missing locations. For this, five incomplete data matrices per dataset were created with the masking of varied portions of data (10 to 50%). As mentioned in the introductory section, we could not carry out these experiments on the PBMC dataset owing to its size (given the limitations in resources and time constraints).Though it hasn't been proven in a systematic manner, dropouts are often modeled as a Poisson process(Supplementary Table S2). From the results shown in Fig. The reconstruction error from AutoImpute is in general better than other imputation strategies, RMSE and MAE being always lesser in majority of datasets, while NMSE being less than all methods except MAGIC.As the observability of input expression matrices to various imputation strategies increases, ideally any imputation method should have improved performance. Talking of all metrics NMSE, RMSE, and MAE, this trend is only observed for AutoImpute and ScImpute and not always for MAGIC.To compare among the imputation methods, we use Normalized Mean Squared Error (NMSE), Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) between the corresponding recovered and full expression dataset as evaluation metrics; these are standard metrics for studying recovery in machine learning. Owing to the random nature of weights initialization in an autoencoder, all the experiments were run 10 times and both mean and variance of the aforementioned metrics are reported The imputations from drImpute algorithm removes some insignificant input genes, normalizes the input and log-transforms the data as part of its preprocessing. Since muting the gene-filtering step in drImpute pipeline was not possible, input and output expression matrices have different dimensions, hence, the error metrics were not calculated for drImpute.A large number of dropouts in single-cell RNA sequencing data can give a false view of expression levels, which might compromise the integration and interpretation of the data. Such kind of technical and biological noise is bound to trick a clustering algorithm which aims to cluster cells of similar types.21.This issue should be fixed by an imputation method which correctly recovers single-cell expression data. So, We applied K-means clustering algorithm on the log-transformed datasets to observe how well do the imputation strategies improve the cell clustering results. The performance metric we used to evaluate the correspondence between the original annotations and K-means assigned annotations is Adjusted Rand Index (ARI)K (number of clusters) in K-means algorithm has been set to the number of unique cell-types. The results show that our approach gives the best Adjusted Rand Index amongst all the state-of-the-art imputation strategies for five out of the eight datasets we tested on  for individual genes across these cells for unimputed data as well as data imputed with various imputation methods.It was found that AutoImpute stabilized the intra-subpopulation gene expression variance the most in three  datasets, performs better than all imputation methods except MAGIC in two datasets, and gives a reasonable improvement in CV for others too.The plot in Fig. Visually well-separated cell-types in single-cell expression data is indicative of more valid biological conclusions from the data. A good imputation strategy should improve the separability of various cell-type subpopulations. To assess this, We reduce the gene expression to two dimensions by applying Principal Component analysis on it, and further plotting the cell transcriptomes in 2D space, coloring each cell by its annotation. Quantitatively, we observe the average of silhouette index values, an unsupervised metric to inspect how well each method groups/separates the cells from various subpopulations.Figure Motivated by the recent success of neural networks, we present an imputation model which uses an over-complete autoencoder, AutoImpute. It learns the inherent distribution and patterns of gene expression in individual cells to reconstruct an imputed version of the expression matrix by projecting the expression profiles into a high dimensional latent space. AutoImpute, to our knowledge, is the very first scRNA-seq imputation method which bypasses the statistical modeling of single-cell expression by implementing a state-of-the-art machine learning technique. Of note, scImpute, a leading imputation technique for scRNA-seq data models gene expression using parametric distributions. We conjecture that such assumptions may not hold as the noise distribution changes with the introduction of novel platforms for single-cell transcriptomics. A neural network based technique works by minimizing a specific loss function and therefore, in principle, is not sensitive to the marginal distribution of the gene expressions.The various experiments demonstrated in this article portray the competitive performance of AutoImpute with respect to, the existing techniques. AutoImpute out-performs various state-of-the-art techniques on the grounds of a number of evaluation metrics (discussed), and also scales well to huge datasets with thousands of transcriptomes. Also, in the handling-dropouts experiment, AutoImpute (and scImpute) depict an intuitive trend of the true-zeros recovery along with an effective dropout imputation (with the amplification of gene expression), which implies that the algorithm successfully imputes missing values with minimal disturbance to the biologically silent genes in the recovered matrix.With the amplification of gene expression in bulk RNA-seq data, scImpute and AutoImpute have been observed to recover a higher number of dropout events as compared to MAGIC. Also, Fig. Through this work, we hope to bridge the gap between two seemingly disjoint research areas, collaborative filtering and bio-informatics and anticipate to establish a symbiotic relationship between the two.In scRNA-seq data, only a fraction of transcriptome of each cell is captured, due to insufficient quantities of input RNA. This makes the measured gene expression a partially observed version of the complete data (with no dropout events). We aim to impute these dropouts or missing values by finding this complete version of the gene expression data. The formal model for measurement can be expressed as follows:23 in information retrieval. In there, X is the unknown ratings matrix of users and items while R is its partially observed version. The goal is to recover the complete ratings matrix, so that (estimated) highly rated items can be suggested to users.This is an under-determined linear inverse problem and hence has infinitely many solutions, and therefore multiple ways to solve it. The problem is akin to that of recommender systems a.k.a collaborative filtering22, where the missing values are filled by heuristically defined interpolation weights (in the row or column direction). The advantage of this approach is its interpretability, however such naϊve techniques do not yield very good results.There are two class of methods to solve . The fir23. In the simplest form, it assumes that X is a low rank matrix and hence can be expressed as a product of one thin (U) and one fat (V) matrix: X = UV. Incorporating this model into , which is much smaller than the size of the matrix. Therefore as long as the number of measurements in R is larger than the number of degrees of freedom, one can expect to recover the X.One cannot have any insight into heuristic neighborhood based models, but the one can understand the latent factor models by analyzing the information content of . Assume 27. An autoencoder is a self-supervised neural network, i.e. the input and the output are the same. Therefore, the autoencoder basically learns to model identity. However, since the number of nodes in the representation/hidden layer is not the same as the input dimensionality, autoencoders learn interesting structures from the data.In recent times, with the advent of representation learning, autoencoder based models have been improving the accuracies for collaborative filteringGiven the success of autoencoders in collaborative filtering, we propose to employ the same model for our problem. Since autoencoders may not be well known to the community, we review them briefly in the next sub-section.Y into the latent space (H) -ϕ is the activation function; usually tanh or sigmoid.An autoencoder consists of an encoder E and a decoder D. The encoder first maps the input data D) projects the latent space (H) back to the input space; this is given by -The decoder  the Euclidean cost function.28 are created by nesting one autoencoder inside the other. Mathematically this is represented as,There are several variants of the autoencoder model. Stacked autoencodersλ is the regularization coefficient, and the regularizer ℜ can range from simple Tikhonov penalties on the encoder and decoder to more complex priors like sparsity30, rank deficiency31 and contractive penalties like the l2-norm of the Jacobian32. Traditionally autoencoders have been used for pre-training neural networks33. However there are a few studies showing their application in solving inverse problems35 and dimensionality reduction.Then there are regularized autoencoder. In a generic fashion, they can be expressed as -MX as input to the autoencoder, and then, training it to learn the encoder and decoder functions which best regenerate the imputed expression matrix X (with no dropouts), by back-propagating the errors, only for the non-zero counts present in the sparse matrix MX.Given the similarity between our problem and collaborative filtering, we leverage the autoencoder based imputation approach from the prior studies (in collaborative filtering) to address the problem at hand. We aim to use overcomplete autoencoders to capture the distribution of the given sparse gene expression data and hence, regenerate a complete version of the same. This is done by feeding the sparse gene expression matrix - E, D and λ have the same usual meaning (refer to the previous section), ||·||O implies that loss is calculated only for the non-zero counts present in the sparse expression matrix MX and σ is the sigmoid activation function applied at the encoder layer, in the neural network.The perfect imputation is achieved by minimizing the following cost function:To prevent overfitting on the non-zero values present in the count matrix, we regularize the learned encoder and decoder matrices.Once the Encoder and Decoder matrices are learned after training, the imputed expression matrix is given by equation Figure m.r (for U) + n.r (for V). Nuclear norm minimization, being largely based on the same concept requires estimation of almost the same number of parameters. The number of independent variables that need to be estimated for the autoencoder is simply 2 × m.r which is much smaller than the number of variables in matrix factorization or nuclear norm minimization. In a data restricted scenario such as ours, where the model is prone to over-fitting, fewer parameters mean that it will be less susceptible and hence would generalize better leading to better performance.Although there is no theoretical insight as to why autoencoders should perform better than matrix completion or matrix factorization, we have an explanation. Assume that the expression matrix has a significantly larger number of cells than the number of genes, i.e., E - encoder matrix and D - decoder matrix were initialized from a random normal distribution.The autoencoder network consists of a fully-connected multi-layer perceptron (MLP), with three layers: input, hidden and the output layer. It is trained using gradient descent with gradients computed by back-propagation to reach the minimum of the cost function equation . RMSPropλ - the regularization coefficient, to control the contribution of the regularization term in the loss or cost function.Size of the hidden layer or latent space dimensionality.Initial value of learning rate.Threshold value - We stop the gradient descent after the change in loss function value in consecutive iterations is less than the threshold value, implying convergence.The hyper-parameter selection was done after doing an extensive grid search on the following hyper-parameters:The best results were observed on the hyper-parameter choices shown in Table Blakeley: Single-cell RNA sequencing was performed on a human embryo to define three cell lineages of the human blastocyst36: pluripotent epiblast (EPI) cells that form the embryo proper, and extraembryonic trophectoderm (TE) cells and primitive endoderm (PE) cells that contribute to the placenta and yolk sac, respectively. This data with 30 cells, was shared by the authors of13.Jurkat-293T data: This dataset contains expression profiles of Jurkat and 293T cells, mixed in vitro in equal proportions. This data contains 3,388 cells annotated according to the expressions of cell-type specific markers37 - the cells expressing CD3D are assigned Jurkat, while those expressing XIST are assigned 293T.Kolodziejczyk: Single-cell RNA sequencing of mouse Embryonic Stem Cells (mESCs)38 forms the contents of this dataset. These mESCs were cultured under three different conditions: serum/LIF, 2i, and the alternative ground state a2i. Despite sharing a common origin and defining properties, mESCs propagated under different culture conditions also differ, and these culture conditions serve as cell annotations for this dataset.PBMC data: This single-cell RNA sequencing data features approximately 68,000 PBMCs , freshly collected from a healthy donor. Single-cell expression profiles of 11 purified subpopulations of PBMCs were used as a reference for cell type annotation37.The dataset is available at 10x Genomics website.Preimplantation data: This is a single-cell RNA sequencing data of mouse preimplantation embryos. It contains expression profiles of around 300 cells from zygote at nine stages: early 2-cell stage, middle 2-cell stage, late 2-cell stage, 4-cell stage, 8-cell stage, 16-cell stage, early blastocyst, middle blastocyst and late blastocyst stages. The first generation of mouse strain crosses were used for studying monoallelic expression.39.The count data is available at the Gene Expression Omnibus (GSE45719)Quake: Single-cell RNA sequencing on healthy human brain cell samples was done40 to examine the heterogeneity of the adult human cortex. Healthy adult temporal lobe tissue was obtained from epileptic patients during temporal lobectomy for medically refractory seizures, and their cells were classified into all of the major neuronal, glial, and vascular cell types in the brain. This data is available at Gene Expression Omnibus under the accession number GSE67835.Trapnell: This single-cell RNA sequencing data is of primary human myoblasts19. The cells obtained from culturing differentiating myoblasts were dissociated and individually captured at 24-hour intervals four times. At each of these four times, 50–100 cells were captured following the serum switch using the Fluidigm C1 microfluidic system.This data is available at Gene Expression Omnibus under the accession number GSE52529.Usoskin: This data of mouse neurons41 was obtained by performing RNA sequencing on 799 dissociated single-cells dissected from the mouse lumbar dorsal root ganglion (DRG) distributed over a total of nine 96-well plates. The cell labels  were computationally derived and assigned by performing PCA classification on single mouse neurons.http://linnarssonlab.org/drg/ .RPM normalized counts with full sample annotation are available at Zeisel: Quantitative single-cell RNA sequencing has been used to classify cells in the mouse somatosensory cortex (S1) and hippocampal CA1 region based on 3005 single-cell transcriptomes42. Individual RNA molecules were counted using unique molecular identifiers (UMIs) and confirmed by single-molecule RNA fluorescence in situ hybridization (FISH). A divisive biclustering method based on sorting points into neighborhoods (SPIN) was used to discover molecularly distinct, nine major classes of cells.The aforementioned experiments were performed on nine different single-cell RNA sequencing datasets, which are described in detail below:Raw data is available under the accession number GSE60361.Gene filtering: If a gene is detected with ≥3 reads in at least three cells, we consider it expressed, and ignore all the un-expressed genes.Median Normalization: Expression matrices are normalized by first dividing each read count by the total counts in each cell, and then by multiplying with the median of the total read counts across cells.Gene Selection: For each expression data top 1000 high-dispersion (coefficient of variance) genes are kept43 for imputation and further analyses.Log Normalization: A copy of the matrices, were log2 transformed following the addition of 1 as pseudo count.Imputation: For various experiments, log-transformed expression matrix was used as input for imputation by one of the methods.We perform the following steps for preprocessing of raw scRNA-seq data.https://github.com/divyanshu-talwar/AutoImpute.The source code of AutoImpute is available at the GitHub repository: 46 and stacked autoencoders in the filed of collaborative filtering47 (for matrix completion), we propose to deploy a deeper version of our model for imputing missing values in the future work. Such deeper model is expected to improve the results even further.The current version of our AutoImpute model has three layers of nodes, and hence essentially follows a shallow neural network architecture. Motivated by tremendous success of deep learning in image and speech recognitionSupplementary Material


With the rapid accumulation of gene expression data from various technologies, e.g., microarray, RNA-sequencing (RNA-seq), and single-cell RNA-seq, it is necessary to carry out dimensional reduction and feature (signature genes) selection in support of making sense out of such high dimensional data. These computational methods significantly facilitate further data analysis and interpretation, such as gene function enrichment analysis, cancer biomarker detection, and drug targeting identification in precision medicine. Although numerous methods have been developed for feature selection in bioinformatics, it is still a challenge to choose the appropriate methods for a specific problem and seek for the most reasonable ranking features. Meanwhile, the paired gene expression data under matched case-control design (MCCD) is becoming increasingly popular, which has often been used in multi-omics integration studies and may increase feature selection efficiency by offsetting similar distributions of confounding features. The appropriate feature selection methods specifically designed for the paired data, which is named as matched-pairs feature selection (MPFS), however, have not been maturely developed in parallel. In this review, we compare the performance of 10 feature-selection methods  on two real datasets by applied three classification methods, and analyze the algorithm complexity of these methods through the running of their programs. This review aims to induce and comprehensively present the MPFS in such a way that readers can easily understand its characteristics and get a clue in selecting the appropriate methods for their analyses. Nowadays, using the existing next-generation sequencing techniques, such as microarray and RNA-seq, developed for gene expression profiling, the paired gene expression data under matched case-control design (MCCD) is becoming increasingly popular. Such data has frequently been used in multi-omics studies and may increase the feature selection efficiency by offsetting similar distributions of confounding features . Nevertht-test to rank relevant features by evaluating significant levels which is often followed by a classification approach to improve model predictive accuracy. Such kind of methods is comparatively time-consuming and may return a preliminary feature selection results. Second, the conditional logistic regression (CLR) , γ[1]), …, } can be obtained from each iteration. Employed with MH algorithms, they estimated the posterior inclusion probabilities p and the coefficients βk, which can be used to rank features and determine the optimal models.At last, Markov chain Monte Carlo (MCMC)  sampling3.2.3Boosting is another successful strategy for high-dimensional feature selection. Adewale et al. developed two modified boosting methods for correlated binary response data .3.2.3.12Boost” [2 loss if the weights are taken to be an identity matrix. The weight matrix represents the unknown variance-covariance matrix of response. Compared to the standard functional gradient descent approach, the loss function is modified by updating the variance-covariance matrix as the boosting iteration progresses.The first method based on the functional gradient decent boosting was dubbed “WL2Boost” ,76. The 3.2.3.2The second method is called 1-step PQLBoost, which modifies the likelihood optimization boosting algorithm via a generalized linear mixed modeling approach, described by Friedman et al.  and Tutzsurement :(9)Il=E∂t-test to rank relevant features and are often followed by a classification approach to improve model predictive accuracy. The conditional logistic regression methods are widely used in MCCD studies to identify features significantly associated with case-control status and have taken the interaction between features into consideration. The boosting strategy addresses classification problems with matched case-control responses.Above all, we have described three groups MPFS methods: test statistic, conditional logistic regression, and boosting strategy. The test statistic methods use original and modified paired 4To compare the performance of the above-mentioned eight MPFS methods and two traditional unpaired feature selection methods (mRMR and MRMD ), two brBoth datasets contain gene information from tumor tissue and matched-pair normal tissue. The TCGA-BRCA dataset, downloaded from TCGA, contains 113 samples of case-control patients, and the GSE70947 dataset, downloaded from GEO, contains 143 samples of case-control patients. The experiments include three main steps: (i) data pre-processing and normalization, (ii) generalization of gene significance ranking list for each method, and (iii) comparison of the performance of all ten methods by applying three classification methods based on the generated ranking lists.p-value < 0.005 (t-test), variance >0.1, and the absolute fold-change >0.5 between case and control data.The two datasets have been pre-analyzed by the following processes: (i) Merging different probes of the same gene by selecting the maximum value to present the gene expression level; (ii) Substitution of missing value is performed using the mean of the expression values, once only <1% missing data exists. Otherwise, such a gene will be discarded; (iii) Normalizing the two datasets by scaling to 0–1; and (iv) Filtering genes by After the above pre-processing steps for the case and control data matrix, the ten feature selection methods are implemented to both datasets to obtain gene ranking lists. The lists were then integrated into a classifier to obtain the accuracy curves by ten-fold cross-validation , which ct-test methods, pttest, mpttest and fcpttest performed less satisfied as they only identify differential genes when the case data and control data are obeying to the same distribution without additional feature information. The performances of the three conditional logistic regression methods, PCU-CLR, RP-CLU and BVS-CLR, and one classic unpaired method, MRMD, were shown moderate for both small gene counts (100) and large gene counts (1500), while mRMR was only better than the t-test methods. All the ten methods showed great accuracy higher than 0.85 with gene counts grew, except for SVM-GEO. Additionally, in both datasets, the ten methods showed unsatisfied or slow-growing accuracy for SVM classifier at the lower gene counts. As a result, under the matched-pairs data setting, most MPFS methods, except the modified t-test methods, are the better choices for feature selection tasks than traditional unpaired feature selection methods.The accuracy curves of the top 1500 genes in each method are shown in t-test methods are suitable for high gene counts analysis, since their accuracy have no significant difference and required the least running time compared to other methods.On the other hand, running time is also a crucial indicator to evaluate the performance of methods. Here, we only record the running times of generation of gene list with specific gene counts, 10, 50, 100, 1000 and 1500 , as the 5This paper presented a review of current matched-pairs feature selection (MPFS) methods for paired gene expression data. With a description of feature selection application and MPFS problem, we reviewed the current approaches of MPFS through three categories, i.e., test statistic, CLR, and boosting strategy. Differ from the commonly categorized feature selection approaches , we dealt feature selection with gene expression data as unpaired and MPFS methods by considering MCCD or not.The paired data can be divided into pure-paired data and mixed-paired data under MCCD, and the mixed-paired data is regarded as pure-paired to reduce the model complexity and minimize the mixing effect. However, the unpaired data, which contains mixture case data without matched data, is usually obtained when matched data is missing or MCCD experiment is not performed. In t-test is most commonly used in practical paired gene expression data analysis, as it is easy to implement and very efficient. The modifications of paired t-test methods have higher sensitivity and specificity than the original. However, they only involve univariate tests, which do not control the effects of other features and can lead to the fallacious identification of relevant features. The CLR model is a standard and effective analytical approach to significantly identify features associated with case-control status yet with higher computational intensity and convergence problems. To solve the issue, Balasubramanian et al. designed the RPCLR algorithm [The originally paired lgorithm , and Qialgorithm . Moreovelgorithm  to provilgorithm  focused MPFS can be widely applied in bioinformatics, e.g., gene function enrichment analyses, cancer biomarker detection, drug targeting identification, etc. To be specific, here are several examples: (i) Identifying important CpG sites. CpG site refers to a double-stranded sequence where cytosine and guanine are separated by only one phosphate, and gene expression can be altered by cytosine methylation on that site. Sun et al.  selectedAlthough numbers of researchers have explored MPFS with numerous methods, challenges are still ahead of us. First of all, as discussed in Besides that, the stability of gene selection is also extremely important in bioinformatics . To thisThe last challenge, as another interesting future direction, is to integrate two or more omics data using MPFS in cancer research. Chen et al. reviewed multivariate dimensional reduction approaches that can be applied to the integrative exploratory analysis of multi-omics data . Mallik Besides the challenges discussed above, other issues on feature selection methods still exist, as the same as MPFS approaches, such as the problem of small sample size in big dimensional data sets, data class imbalance, computational complexity, especially for the conditional logistical regression model, and the assessment of MPFS.6In this review, we recalled the concepts of feature selection techniques and focused on MPFS methods for gene expression data analysis. We classified the existing algorithms into three groups: test statistic, CLR, and boosting strategy, and evaluated the performance using two breast cancer datasets. From the experimental results of 10 methods on two datasets with three classifiers, we concluded that (1) WL2Boost method may get the best performance when the feature list is not too big, and the users do not care about the running time; and (2) RP-CLR and PCU-CLR methods may get a better tradeoff between high dimensional features and time consuming. At last, we discussed some challenges and exciting directions for the development of MPFS. It is worth noting that, most of algorithms have been proposed in recent years were dedicating to address the feature selection problem associated with the paired data. Based on the development of gene expression profiling technique and the extensive use of MCCD, MPFS approach is a promising technique in the bioinformatics and machine learning cross-field in future.The authors claim no conflict of interest.