Single-cell RNA-sequencing (scRNA-seq) is a powerful high-throughput technique that enables researchers to measure genome-wide transcription levels at the resolution of single cells. Because of the low amount of RNA present in a single cell, some genes may fail to be detected even though they are expressed; these genes are usually referred to as dropouts. Here, we present a general and flexible zero-inflated negative binomial model (ZINB-WaVE), which leads to low-dimensional representations of the data that account for zero inflation (dropouts), over-dispersion, and the count nature of the data. We demonstrate, with simulated and real data, that the model and its associated estimation procedure are able to give a more stable and accurate low-dimensional representation of the data than principal component analysis (PCA) and zero-inflated factor analysis (ZIFA), without the need for a preliminary normalization step. Single-cell RNA sequencing (scRNA-seq) data provides information on transcriptomic heterogeneity within cell populations. Here, Risso et al develop ZINB-WaVE for low-dimensional representations of scRNA-seq data that account for zero inflation, over-dispersion, and the count nature of the data. It represents a major advance with respect to standard “bulk” RNA-sequencing, which is only capable of measuring average gene expression levels within a cell population. Such averaged gene expression profiles may be enough to characterize the global state of a tissue, but completely mask signal coming from individual cells, ignoring tissue heterogeneity. Assessing cell-to-cell variability in expression is crucial for disentangling complex heterogeneous tissues4 and for understanding dynamic biological processes, such as embryo development5 and cancer6. Despite the early successes of scRNA-seq, to fully exploit the potential of this new technology, it is essential to develop statistical and computational methods specifically designed for the unique challenges of this type of data7.Single-cell RNA-sequencing (scRNA-seq) is a powerful and relatively young technique enabling the characterization of the molecular states of individual cells through their transcriptional profiles8. The inclusion in the library preparation of unique molecular identifiers (UMIs) reduces amplification bias9, but does not remove dropout events, nor the need for data normalization11. In addition to the host of unwanted technical effects that affect bulk RNA-seq, scRNA-seq data exhibit much higher variability between technical replicates, even for genes with medium or high levels of expression12.Because of the tiny amount of RNA present in a single cell, the input material needs to go through many rounds of amplification before being sequenced. This results in strong amplification bias, as well as dropouts, i.e., genes that fail to be detected even though they are expressed in the sample14, the inference of developmental trajectories18, spatio-temporal ordering of the cells19, and, of course, as a visualization tool21. Hence, the choice of dimensionality reduction technique is a critical step in the data analysis process.The large majority of published scRNA-seq analyses include a dimensionality reduction step. This achieves a two-fold objective: (i) the data become more tractable, both from a statistical  and computational point of view; (ii) noise can be reduced while preserving the often intrinsically low-dimensional signal of interest. Dimensionality reduction is used in the literature as a preliminary step prior to clustering23. In addition to PCA, dimensionality reduction techniques used in the analysis of scRNA-seq data include independent components analysis (ICA)15, Laplacian eigenmaps24, and t-distributed stochastic neighbor embedding (t-SNE)25. Note that none of these techniques can account for dropouts, nor for the count nature of the data. Typically, researchers transform the data using the logarithm of the  read counts, adding an offset to avoid taking the log of zero.A natural choice for dimensionality reduction is principal component analysis (PCA), which projects the observations onto the space defined by linear combinations of the original variables with successively maximal variance. However, several authors have reported on shortcomings of PCA for scRNA-seq data. In particular, for real data sets, the first or second principal components often depend more on the proportion of detected genes per cell  than on an actual biological signal26 proposed a zero-inflated factor analysis (ZIFA) model to account for the presence of dropouts in the dimensionality reduction step. Although the method accounts for the zero inflation typically observed in scRNA-seq data, the proposed model does not take into account the count nature of the data. In addition, the model makes a strong assumption regarding the dependence of the probability of detection on the mean expression level, modeling it as an exponential decay. The fit on real data sets is not always good and, overall, the model lacks flexibility, with its inability to include covariates and/or normalization factors.Recently, Pierson & Yau28, which accounts for zero inflation and over-dispersion and for which unobserved sample-level covariates may either capture variation of interest or unwanted variation. We demonstrate, with simulated and real data, that the model and its associated estimation procedure are able to give a more stable and accurate low-dimensional representation of the data than PCA and ZIFA, without the need for a preliminary normalization step. The approach is implemented in the open-source R package zinbwave, publicly available through the Bioconductor Project (https://bioconductor.org/packages/zinbwave).Here, we propose a general and flexible method that uses a zero-inflated negative binomial (ZINB) model to extract low-dimensional signal from the data, accounting for zero inflation (dropouts), over-dispersion, and the count nature of the data. We call this approach Zero-Inflated Negative Binomial-based Wanted Variation Extraction (ZINB-WaVE). The proposed model includes a sample-level intercept, which serves as a global-scaling normalization factor, and gives the user the ability to include both gene-level and sample-level covariates. The inclusion of observed and unobserved sample-level covariates enables normalization for complex, non-linear effects (often referred to as batch effects), whereas gene-level covariates may be used to adjust for sequence composition effects, such as gene length and GC-content effects. ZINB-WaVE is an extension of the RUV modeln samples  and J features  that can be counted for each sample, we denote with Yij the count of feature j  for sample i . To account for various technical and biological effects, typical of single-cell sequencing technologies, we model Yij as a random variable following a ZINB distribution (see Methods for details).ZINB-WaVE is a general and flexible model for the analysis of high-dimensional zero-inflated count data, such as those recorded in single-cell RNA-seq assays. Given μ) and the probability of dropouts (π) are modeled in terms of observed sample-level and gene-level covariates  that need to be inferred from the data. The matrix X can include covariates that induce variation of interest, such as cell types, or covariates that induce unwanted variation, such as batch or quality control (QC) measures. It can also include a constant column of ones for an intercept that accounts for gene-specific differences in mean expression level or dropout rate . The matrix V can also accommodate an intercept to account for cell-specific global effects, such as size factors representing differences in library sizes . In addition, V can include gene-level covariates, such as gene length or GC-content.Both the mean expression level . The model extends the RUV framework to the ZINB distribution . It differs in interpretation from RUV in the Wα term, which is not necessarily considered unwanted; this term generally refers to unknown low-dimensional variation, that could be due to unwanted technical effects (as in RUV), such as batch effects, or to biological effects of interest, such as cell cycle or cell differentiation.The unobserved matrix W is the same, the matrices X and V could differ in the modeling of μ and π, if we assume that some known factors do not affect both. When X = 1n and V = 1J, the model is a factor model akin to PCA, where W is a factor matrix and αμ and απ are loading matrices. However, the model is more general, allowing the inclusion of additional sample and gene-level covariates that might help to infer the unknown factors.It is important to note that although We applied the ZINB-WaVE procedure to several publicly available real data sets, from microfluidics, plate-based, and droplet-based platforms (see Methods).23, the first few principal components of scRNA-seq data, even after normalization, can be influenced by technical rather than biological features, such as the proportion of genes with at least one read (detection rate) or the total number of reads (sequencing depth) per sample. Figure As previously shownZIFA suffered from the same problem: the clustering of the samples in two dimensions was not qualitatively different from PCA Fig.  and the Conversely, ZINB-WaVE led to tighter clusters, grouping the cells by layer of origin Fig. . Further22 for additional data sets in which principal components are strongly correlated with detection rate.We repeated these analyses on the S1/CA1 data set , computed using the labels available from the original study: these were either known a priori  or inferred from the data  by the authors of the original publication . For all four data sets, ZINB-WaVE led to generally tighter clusters, as shown by an increased per-cluster average silhouette width in the majority of the groups  the identification of developmental lineages and (ii) the characterization of rare cell types.29. In the original publication, the data were normalized by full-quantile normalization, followed by a regression-based adjustment for sample quality. Clustering on the first 50 principal components identified cellular states that were then ordered into developmental lineages by Slingshot30 using the first five PCs. In the original analysis, Slingshot was able to correctly infer the lineages in its supervised mode, by manually specifying lineage endpoints . Figure 31 for a complete workflow that involves ZINB-WaVE for dimensionality reduction and Slingshot for lineage reconstruction.First, we re-analyzed a set of cells from the mouse olfactory epithelium (OE) that were collected to identify the developmental trajectories that generate olfactory neurons (mOSN), sustentacular cells (mSUS), and microvillous cells (MV)32. This example allowed us to demonstrate how ZINB-WaVE can be applied to a state-of-the-art data set that comprises tens of thousands of cells, while also illustrating that existing clustering algorithms can be used on the low-rank matrix inferred by ZINB-WaVE. In particular, we applied a popular clustering method, based on the identification of shared nearest neighbors33, similar to that of Macosko et al.2 and implemented in the R package Seurat34. We modified the clustering procedure to use ZINB-WaVE (with K = 10) instead of PCA as the dimensionality reduction step. To visualize the clustering results, we applied t-SNE to the inferred W matrix  assayed with the 10× Genomics Chromium systemrix Fig. .32 , natural killer cells , and B-cells  , which express FCGR3A/CD16, AIF1, FTL, LST135; CD1C+ dendritic cells , which express CD1C, LYZ, HLA-DR35; plasmacytoid dentritic cells , expressing GZMB, SERPINF1, ITM2C35; megakaryocyte , expressing PF432  Fig. . In addi432 Fig. . We also32 used k-means on the first 50 PCs). We hence repeated the clustering using a sequential procedure based on k-means (see Methods for details). This led to similar  results . Other more complex, non-linear effects, such as those collectively known as batch effects, require more sophisticated normalization28. Accordingly, a typical scRNA-seq pipeline will include a normalization step, i.e., a linear or non-linear transformation of read counts, to make the distributions of expression measures comparable between samples. The normalization step is usually carried out prior to any inferential procedure . In this work, we considered three popular between-sample normalization methods: total count (TC), trimmed mean of M values (TMM), and full-quantile (FQ) normalization (see Methods); we also compared the results to unnormalized data (RAW). TC, along with the related methods transcripts per million (TPM) and fragments per kilobase million (FPKM), is by far the most widely used normalization in the scRNA-seq literature; hence, TC-normalized data were used for the results shown in Fig. As for any high-throughput genomic technology, an important aspect of scRNA-seq data analysis is normalization. Indeed, there are a variety of steps in scRNA-seq experiments that can introduce bias in the data and whose effects need to be corrected for36.Normalization highly affected the projection of the data in lower dimensions  acts as a global-scaling normalization factor, making a preliminary global-scaling step unnecessary. As a consequence, ZINB-WaVE can be directly applied to unnormalized read counts, hence preserving the distributional properties of count data. ZINB-WaVE applied to unnormalized counts led to results that were comparable, in terms of average silhouette width, to PCA and ZIFA applied using the best performing normalization  can act as a global-scaling normalization factor, this may not be sufficient to accurately account for complex, non-linear technical effects that may influence the data . Hence, we explored the possibility of including additional sample-level covariates in X to account for such effects (see Methods).Although the sample-level intercept 37 and which comprises two batches of mESCs grown in three different media (see Methods). ZINB-WaVE applied with no additional covariates led to three clusters, corresponding to the three media  removed such batch effects, consolidating the clustering by medium . Hence, it is relatively easy to correct for batch effects and, unsurprisingly, both ComBat and ZINB-WaVE successfully do so. The glioblastoma data set is an example of a more complex situation, in which there is confounding between batch and biology, each patient being processed separatelyhes Fig. . We usedhes Fig. . Includihes Fig. . One key41) and a hurdle model (as implemented in MAST23).We compared the goodness-of-fit of our ZINB-WaVE model to that of a negative binomial (NB) model  rather than counts and does not have a dispersion parameter but only a variance parameter for the Gaussian component (see Methods for details). We found that MAST under-estimated the overall mean log2(TPM + 1) and over-estimated the zero probability, but had stable variance estimates over the observed proportion of zero counts . We observed that our estimators are asymptotically unbiased and have decreasing variance as the number of cells n increases  for the parameters of the model of Fig. μ and π, as well as the log-likelihood function, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC), for models with misspecified number of unobserved covariates K , gene-level covariate matrix V, and dispersion parameter φ  and one that did not (V = 0J). When the intercept was correctly included in the model, misspecification of K (with K > 2) resulted in no or very small bias  and π were unbiased over the whole range of mean expression and zero inflation probability  for estimators of r φ Fig. –25. In Fias Fig. , small Mias Fig. , and a gias Fig. . When noMSE Fig. . This isK led to almost perfect correlation between distances in the true and estimated low-dimensional space .It is important to note that the previous results were obtained for data simulated from the ZINB-WaVE model underlying our estimation procedure. It is hence not surprising that ZINB-WaVE outperformed its competitors. To provide a fairer comparison, we also assessed the methods on data simulated from the model proposed by Lun & Marionin. Although ZIFA worked well with 60% or fewer zeros, its performance too decreased at 80% of zeros, especially when only 100 cells were simulated , all methods performed well in terms of average silhouette width Fig.  and prected Fig. . Convers2, make it easy and inexpensive to collect hundreds of thousands of scRNA-seq profiles, allowing researchers to study very complex biological systems at high resolution. The resulting libraries are often sequenced at extremely low depth , making the corresponding read count data truly sparse. Hence, there is a growing need for developing reliable statistical methods that are scalable and that can account for zero inflation.Recent advances in single-cell technologies, such as droplet-based methodsZINB-WaVE is a general and flexible approach to extract low-dimensional signal from noisy, zero-inflated data, such as those from scRNA-seq experiments. We have shown with simulated and real data analyses that ZINB-WaVE leads to robust and unbiased estimators of the underlying biological signals. The better performance of ZINB-WaVE with respect to PCA comes at a computational cost, as we need to numerically optimize a non-convex likelihood function. However, we empirically found that the computing time was approximately linear in both the number of cells and the number of genes, and approximately quadratic in the number of latent factors  is the ability to include sample-level and gene-level covariates. In particular, by including a column of ones in the gene-level covariate matrix, the corresponding cell-level intercept acts as a global-scaling normalization factor, allowing the modeling of raw count data, with no need for prior normalization.W inferred by ZINB-WaVE will capture such confounding effects. It is therefore important to explore the correlation between the latent factors estimated by our procedure and known measures of quality control that can be computed for scRNA-seq libraries, using, for instance, the Bioconductor R package scater43 , the low-rank matrix see Fig. . If one 38 or unsupervised way44. Recently, Lin et al.45 proposed a model that can extend PCA to adjust for confounding factors. This model, however, does not seem to be ideal for zero-inflated count data. In the scRNA-seq literature, MAST23 uses the inferred cellular detection rate to adjust for the main source of confounding, in a differential expression setting, but is not designed to infer low-dimensional signal.Several authors have recognized that high-dimensional genomic data are affected by a variety of unwanted technical effects  that can be confounded with the biological signal of interest, and have proposed methods to account for such effects in either a supervised46. With large collaborative efforts, such as the Human Cell Atlas47, on the horizon, we anticipate that the ability of our model to include gene-level covariates that can potentially help accounting for differences in protocols will prove important.The removal of batch effects is an important example of how including additional covariates in the ZINB-WaVE model may lead to better low-dimensional representations of the data. However, ZINB-WaVE is not limited to including batch effects, as other sample-level  and/or gene-level  covariates may be included in the model. Although we did not find any compelling examples in which adding a gene-level covariate leads to improve signal extraction, it is interesting to note the relationship between GC-content and batch effects15.Although the low-dimensional signal inferred by ZINB-WaVE can be used to visually inspect hidden structure in the data, visualization is not the main point of our proposed method. The low-dimensional factors are intended to be the closest possible approximation to the true signal, which is assumed to be intrinsically low-dimensional. Such a low-dimensional representation can be used in downstream analyses, such as clustering or pseudotime ordering of the cells25 has become the most popular for scRNA-seq data. Recently, Wang et al.48 have proposed a novel visualization algorithm that can account for zero inflation and showed improvement over t-SNE. As t-SNE takes as input a matrix of cell pairwise distances, which may be noisy in high dimensions, a typical pipeline involves computing such distances in PCA space, selecting, for example, the first 50 PCs. An alternative approach is to derive such distances from the low-dimensional space defined by the factors inferred by ZINB-WaVE. This strategy was used effectively in Fig. Visualization of high-dimensional data sets is an equally important area of research and many algorithms are available, among which t-SNEβ corresponding to known sample-level covariates in the matrix X . Differentially expressed genes may be identified via likelihood ratio tests or Wald tests, with standard errors of estimators of β obtained from the Hessian matrix of the likelihood function. In addition, posterior dropout probabilities can be readily derived from the model and used as weights to unlock standard bulk RNA-seq methods49, such as edgeR41. We envision a future version of the zinbwave package with this added capability.In this article, we have focused on an unsupervised setting, where the goal is to extract a low-dimensional signal from noisy zero-inflated data. However, our proposed ZINB model is more general and can be used, in principle, for supervised differential expression analysis, where the parameters of interest are regression coefficients μ ≥ 0 and θ > 0, let fNB denote the probability mass function (PMF) of the negative binomial (NB) distribution with mean μ and inverse dispersion parameter θ, namely:For any φ = θ−1 . In both cases, the mean of the NB distribution is μ and its variance is:φ = 0 ⇔ θ = +∞.Note that another parametrization of the NB PMF is in terms of the dispersion parameter π ∈ , let fZINB be the PMF of the ZINB distribution given by:δ0(⋅) is the Dirac function. Here, π can be interpreted as the probability that a 0 is observed instead of the actual count, resulting in an inflation of zeros compared to the NB distribution, hence the name ZINB.For any n samples  and J features  that can be counted for each sample, let Yij denote the count of feature j  for sample i . To account for various technical and biological effects frequent, in particular, in single-cell sequencing technologies, we model Yij as a random variable following a ZINB distribution with parameters μij, θij, and πij, and consider the following regression models for the parameters:Given X is a known n × M matrix corresponding to M cell-level covariates and β =  its associated M × J matrices of regression parameters. X can typically include covariates that induce variation of interest, such as cell types, or covariates that induce unwanted variation, such as batch or quality control measures. It can also include a constant column of ones, 1n, to account for gene-specific intercepts.V is a known J × L matrix corresponding to J gene-level covariates, such as gene length or GC-content, and γ =  its associated L × n matrices of regression parameters. V can also include a constant column of ones, 1J, to account for cell-specific intercepts, such as size factors representing differences in library sizes.W is an unobserved n × K matrix corresponding to K unknown cell-level covariates, which could be of “unwanted variation” as in RUV28 or of interest (such as cell type), and α =  its associated K × J matrices of regression parameters.Oμ and Oπ are known n × J matrices of offsets. X and V contain a constant column of ones, to account, respectively, for gene-specific  and cell-specific  variation. In that case, X and V are of the form X =  and V =  and we can similarly decompose the corresponding parameters as β =  and γ = , where β1 and γ1 to each have elements summing to zero.By default, W is the same, the matrices X and V could differ in the modeling of μ and π, if we assume that some known factors do not affect both μ and π. To keep notation simple and consistent, we use the same matrices, but will implicitly assume that some parameters may be constrained to be 0 if needed.Although μ and π, we can model and test for differential expression in terms of either the NB mean or the ZI probability.By allowing the models to differ for θij could be investigated, such as a model similar to μij or a functional of the form θij = f(μij), but we restrict ourselves to a simpler model that has been shown to be largely sufficient in bulk RNA-seq analysis.We limit ourselves to a gene-dependent dispersion parameter. More complicated models for X, V, Oμ, and Oπ and the integer K; the parameters to be inferred are β = , γ = , W, α = , and ζ. Given an n × J matrix of counts Y, the log-likelihood function isμij, θij, and πij depend on  through Eq. , and ζ (using the unbiased sample variance statistic). The penalty tends to shrink the estimated parameters to 0, except for the cell and gene-specific intercepts which are not penalized and the dispersion parameters which are not shrunk towards 0 but instead towards a constant value across genes. Note also that the likelihood only depends on W and α through their product R = Wα and that the penalty ensures that at the optimum W and α have the structure described in the following result, which generalizes standard results such as Srebro et al.50 (Lemma 1) and Mazumder et al.51 (Lemma 6).To infer the parameters, we follow a penalized maximum likelihood approach, by trying to solveLemma 1: For any matrix R and positive scalars s and t, the following holds:R = RLRΣRR is a singular value decomposition (SVD) of R, then a solution to this optimization problem is:51 (Lemma 6) has optimum value T concludes the proof.Proof: Let W and This lemma implies in particular that at any local maximum of the penalized log-likelihood, To balance the penalties applied to the different matrices in spite of their different sizes, a natural choice is to fix W and α, which shows that the entries in the matrices W and α have similar standard deviation after optimization:In particular, from Lemma 1, we easily deduce the following characterization of the penalty on n × J matrix R and positive scalars R = RLRΣRR is a SVD decomposition of R, then a solution to this optimization problem is:i = 1, …, min,Corollary 1: For any The penalized likelihood is however not concave, making its maximization computationally challenging. We instead find a local maximum, starting from a smart initialization and iterating a numerical optimization scheme until local convergence, as described below.: To initialize the set of parameters we approximate the count distribution by a log-normal distribution and explicitly separate zero and non-zero values, as follows:Set Lij = ln(Yij) − (Oμ)ij for all Set Set βμ and γμ by solving the convex ridge regression problem:Estimate InitializationnJ rows and MJ + nL columns. To solve it efficiently, we alternate the estimation of βμ and γμ. Specifically, we initialize parameter values as:γμ, which can be performed independently and in parallel for each cell:Optimization in βμ, which can be performed independently and in parallel for each gene:Optimization in W and αμ by solvingEstimate K is large enough, one can first solve the convex optimization problem:K is at least equal to the rank of the solution of the unconstrained problem (6), which we solve with the softImpute::softImpute function51. If K is smaller, then (6) becomes a non-convex optimization problem whose global optimum may be challenging to find. In that case we also use the rank-constrained version of softImpute::softImpute to obtain a good local optimum.Denoting by βπ, γπ, and απ by solving the regularized logistic regression problem:Estimate This is a standard ridge regression problem, but with a potentially huge design matrix, with up to nJ rows and MJ + nL columns. To solve it efficiently, we alternate the estimation of βπ, γπ, and απ. Specifically, we initialize parameter values as:γπ:Optimization in i) independently and in parallel. When there is no gene covariate besides the constant intercept, the problem is easily solved by setting Note that this problem can be solved for each cell  = 0; in practice, we use a derivative-free one-dimensional optimization vector over the range . We then optimize the objective function by a quasi-Newton optimization scheme starting from the constant solution found by the first step. To derive the gradient of the objective function used by the optimization procedure, note that the derivative of the NB log-density is:Ψ(z) = Γ′(z)/Γ(z) is the digamma function. We therefore get the derivative of the ZINB density as follows, for any π ∈ :y > 0, fZINB = (1 − π)fNB therefore-If y = 0, -For ζj, for j = 1,…, J, is then easily obtained byJ − 1 term in the denominator comes from the use of the unbiased sample variance statistic in the penalty for ζ.)2.Left-factor (cell-specific) optimization:i = 1, …, n. For this purpose, we consider a subroutine solveZinbRegression  to find a set of vectors  that locally maximize the log-likelihood of a ZINB model for a vector of counts y parametrized as follows:i we call solveZinbRegression with the following parameters:Note that this optimization can be performed independently and in parallel for each cell 3.j = 1,…, J, by calling solveZinbRegression with the following parameters:Right-factor (gene-specific) optimization:4.Orthogonalization:To solve this problem, we start by estimating a common dispersion parameter for all the genes, by maximizing the objective function under the constraint that Var using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method. Let us now give more details on how the gradient of F is computed.Starting from an initial guess (as explained in the different steps above), we perform a local minimization of this function y , we first explicit the derivatives of the log-likelihood of y with respect to the  parameters of the ZINB distribution. We first observe thaty is null:y > 0, then δ0(y) = 0 and fZINB = (1 − π)fNB, so we obtain:If y = 0, then δ0(y) = 1, and we getIf N ≥ 1, using standard calculus for the differentiation of compositions and the facts that:G and H are the N-dimensional vectors given byGiven a single count J = 1000 genes were then sampled at random for each data set. The ZINB-WaVE model was fit to the count matrix Y with the number of unknown cell-level covariates set to K = 2, genewise dispersion (ζ = lnθ = −lnϕ), Xμ, Xπ, Vμ, and Vπ as columns of ones , and no offset matrices, to get estimates for W, αμ, απ, βμ, βπ, γμ, γπ, and ζ. The parameters which were varied in the simulations are the number of cells, the proportion of zero counts, and the ratio of within to between-cluster sums of squares for W. Details on the parameter choices follow.Simulating from the ZINB-WaVE model: In order to simulate realistic data, we fitted our ZINB-WaVE model to two real data sets (V1 and S1/CA1) and used the resulting parameter estimates as the truth to be estimated in the simulation. Genes that did not have at least five reads in at least five cells were filtered out and n = 100; 1000; 10,000.The number of cells was set to γπ: zfrac ≈ 0.25, 0.50, 0.75. As logit(π) = Xβπ + (Vγπ)T + Wαπ, the value of γπ is directly linked to the dropout probability π, thus to the zero fraction. Note that by changing only γπ but not γμ, we change the dropout rate but not the underlying, unobserved mean expression, i.e., this varies the number of technical zeros but not biological zeros.The proportion of zero counts, W was set in the following way. Let C denote the number of clusters and nc the number of cells in cluster c. For a given column of W (out of K columns), let Wic denote the value for cell i in cluster c, n cells, c, and TSS the total sum of squares. Then,W stay in the same range as the estimated W from the real data set; this prevents us from simulating an unrealistic count matrix Y.The ratio of within to between-cluster sums of squares for a2 and the within-cluster sum of squares by a2b2, i.e., replace a ≥ 0 and b ≥ 0 such that TSS and TSS remains constant, i.e.,W. Thus,Let us scale the between-cluster sum of squares by b2, while keeping the overall mean and variance constant.The above transformation results in a scaling of the ratio of within to between-cluster sums of squares by C = 3 clusters and considered three values for b2, where the same value of b2 is applied to each of the K columns of W: b2 = 1, corresponding to the case where the within and between-cluster sums of squares are the same as the ones of the fitted W from the real data set; b2 = 5, corresponding to a larger ratio of within to between-cluster sums of squares and hence a harder clustering problem; b2 = 10, corresponding to a very large ratio of within to between-cluster sums of squares and hence almost no clustering.In our simulations, we fixed n) × 3 (zfrac)) × 3 (clustering) = 54 scenarios were considered in the simulation.Overall, 2 ) × 3 .Simulate Create the ZINB-WaVE model using the function zinbModel from the package zinbwave.Simulate counts using the function zinbSim from the package zinbwave.For each of the 54 scenarios, we simulated 42 model: To simulate data sets from a different model than our ZINB-WaVE model, we simulated counts using the procedure described in Lun & Marioni42 . Although the Lun & Marioni42 model is also based on a ZINB distribution, the distribution is parameterized differently and also fit differently, gene by gene. In particular, the negative binomial mean is parameterized as a product of the expression level of interest and two nuisance technical effects, a gene-level effect assumed to have a log-normal distribution and a cell-level effect (cf. library size) whose distribution is empirically derived. The zero-inflation probability is assumed to be constant across cells for each gene and is estimated independently of the negative binomial mean. The ZINB distribution is fit gene by gene using the zeroinfl function from the R package pscl. We used the raw gene-level read counts for the mESC data set as input to the script reference/submitter.sh, to create a simulation function constructed by fitting a ZINB distribution to these counts. The script simulations/submitter.sh was then run to simulate counts based on the estimated parameters . We simulated C = 3 clusters with equal number of cells per cluster. The parameters which were varied in the simulations are as follows.Simulating from the Lun & Marionin = 100; 1000; 10,000.The number of cells was set to 42. However, to simulate data sets with greater zero fractions, namely zfrac = 0.6 and zfrac = 0.8, we added respectively 0.3 and 0.6 to the zero-inflation probability ) × 3 (zfrac) = 9 scenarios, we simulated B (B = 10) data sets, resulting in 9) × 10 = 90 simulated data sets in total.For each of the 3  or specific to each gene (genewise dispersion).ZINB-WaVE: We applied the ZINB-WaVE procedure using the function zinbFit from our R package zinbwave, with the following parameter choices. Number of unknown cell-level covariates 26, as implemented in the ZIFA python package (Version 0.1) available at https://github.com/epierson9/ZIFA, with the block algorithm . The output of ZIFA is an n × K matrix corresponding to a projection of the counts onto a latent low-dimensional space of dimension K.Zero-inflated factor analysis: We used the zero-inflated factor analysis (ZIFA) methodPCA: We used the function prcomp from the R package stats for the simulation study and, for computational efficiency, the function jsvds from the R package rARPACK for the real data sets.As normalization is essential, especially for zero-inflated distributions, PCA and ZIFA were applied to both raw and normalized counts. The following normalization methods were used.52 and fragments per kilobase million (FPKM)53 methods.Total count normalization (TC): Counts are divided by the total number of reads sequenced for each sample and multiplied by the mean total count across all the samples. This method is related to the popular transcripts per million (TPM)54: The quantiles of the distributions of the gene-level read counts are matched across samples. We used the function between Lane Normalization from the Bioconductor R package EDASeq.Full-quantile normalization (FQ)55: The TMM global-scaling factor is computed as the weighted mean of log-ratios between each sample and a reference sample. If the majority of the genes are not differentially expressed (DE), TMM should be close to 1, otherwise, it provides an estimate of the correction factor that must be applied in order to fulfill this hypothesis. We used the function calcNormFactors from the Bioconductor R package edgeR to compute these scaling factors.Trimmed mean of M values (TMM)56. Briefly, RSEC implements a consensus clustering algorithm which generates and aggregates a collection of clusterings, based on resampling cells and using a sequential tight clustering algorithm57. See Fletcher et al.29 for details on the parameters used for RSEC in the original analysis and Perraudeau et al.31 for details on the parameters used for RSEC in the ZINB-WaVE workflow.Clustering of the OE data set: We used the resampling-based sequential ensemble clustering (RSEC) framework implemented in the RSEC function from the Bioconductor R package clusterExperimentClustering of the 10× Genomics 68k PBMCs data set: We used two different clustering methods to assess the ability of ZINB-WaVE to extract biologically meaningful signal from the data.34 (Version 2.0.1). In particular, we used ZINB-WaVE (K = 10) instead of PCA for dimensionality reduction. The clustering is based on shared nearest neighbor modularity33. We used the following parameters: k.param=10, k.scale=10, resolution=0.6. All the other parameters were left at their default values.First, we used a a clustering procedure similar to the one implemented in the R package Seuratk-means clustering approach57, implemented in the clusterSingle function of the clusterExperiment package56. We used the following parameters: sequential=TRUE, subsample=FALSE, k0=15, beta=0.95, clusterFunction="kmeans".We also clustered the data using a sequential 23.We compared the goodness-of-fit of our ZINB-WaVE model to that of two other models for count data: a standard negative binomial model, that does not account for zero inflation, and the MAST hurdle model, that is specifically designed for scRNA-seq dataGoodness-of-fit was assessed on the V1 data set using mean-difference plots (MD-plots) of estimated vs. observed mean count and zero probability, as well as plots of the estimated dispersion parameter against the observed zero frequency.ZINB-WaVE model: For our ZINB-WaVE model, the overall mean and zero probability areK = 0 unknown cell-level covariates, gene-level intercept (X = 1n), cell-level intercept (V = 1J), and genewise dispersion.ZINB-WaVE was fit to the V1 data set using the function zinbFit from our R package zinbwave, with the following parameter choices: π = 0. Thus,Negative binomial model: The negative binomial (NB) distribution is a special case of the ZINB distribution that does not account for zero inflation, i.e., for which 41 (Version 3.16.5) with only an intercept  and genewise dispersion.A NB distribution was fit gene by gene to the V1 data set, after full-quantile normalization, using the Bioconductor R package edgeR23 is defined as follows:Yij is log2(TPM +1) for cell i and gene j, Zij indicates whether gene j is truly expressed in cell i. For each gene j, the parameters of the MAST model are: the regression coefficients 23, which is different from that in the ZINB-WaVE model of Eq.  hurdle model proposed by Finak et al.l of Eq. .For the MAST model, the overall mean and zero probability are58 . We use the function zlm to fit MAST with an intercept and a covariate for the cellular detection rate  for both the discrete and continuous parts.MAST is implemented in the Bioconductor R package MASTNote that in contrast to the NB and ZINB models, the MAST hurdle model is for log2(TPM+1) instead of counts and has no dispersion parameter. To be able to compare the fits of the three models, the MAST goodness-of-fit plots display estimated vs. observed mean log2(TPM+1) and estimated variance si of a sample i is defined as follows:i belongs, and i and the samples in cluster Clustering: Silhouette width: Given a set of labels for the cells , silhouette widths provide a measure of goodness of the clustering of the cells with respect to these labels. Silhouette widths may be averaged within clusters or across all observations to assess clustering strength at the level of clusters or overall, respectively. The silhouette width W and, for each scenario, silhouette widths were computed and averaged over B data sets. For real data, the authors’ cluster labels or known cell types were used.Average silhouette widths were used to compare ZINB-WaVE, PCA, and ZIFA on both real and simulated data sets. For simulated data, the cluster labels correspond to the true simulated Clustering: Precision and recall: Two different clusterings  may be compared quantitatively using the precision and recall coefficients. These measures involve assessing whether pairs of cells cluster together in each of the two clusterings.  Let YY  be the total number of pairs of cells which are in the same cluster in both Clustering 1 and Clustering 2 . Then, using Clustering 1 as a reference, the precision coefficient is defined as the proportion of cells clustered together in Clustering 2 which are also (correctly) clustered together in Clustering 1Similarly, the recall coefficient is defined as the proportion of cells (correctly) clustered together in Clustering 1 which are also clustered together in Clustering 2W for ZINB-WaVE, the first two principal components for PCA, and the first two latent variables for ZIFA. We simulated 3 clusters and set the number of clusters equal to 3 in kmeans (argument centers). Precision and recall were computed using the extCriteria function from the R package clusterCrit59.Precision and recall were used to compare ZINB-WaVE, PCA, and ZIFA on simulated data sets, where the reference Clustering 1 corresponds to the true simulated labels and Clustering 2 was performed using the R function kmeans in the reduced-dimensional space: the first two columns of Dimensionality reduction: Correlation with QC measures: To evaluate the dependence of the inferred low-dimensional signal on unwanted variation, we computed the absolute correlation between each dimension  and a set of quality control (QC) measures.http://www.bioinformatics.babraham.ac.uk/projects/fastqc/) and Picard tools (https://broadinstitute.github.io/picard/) were used to compute a set of 16 QC measures. These measures are available as part of the Bioconductor R package scRNAseq (https://bioconductor.org/packages/scRNAseq). For the glioblastoma and mESC data sets, we used the scater Bioconductor R package60 (Version 1.2.0) to compute a set of 7 QC measures. For the S1/CA1 data set, we used a set of 6 QC measures provided by the authors (http://linnarssonlab.org/cortex/).For the V1 data set, FastQC (K when the other parameters are set correctly (V is a column of ones 1J and genewise dispersion). For each simulation scenario, the correlation between true and estimated pairwise distances was computed and averaged over B data sets.Dimensionality reduction: Correlation of pairwise distances between observations: For simulated data, we assessed different dimensionality reduction methods  in terms of the correlation between pairwise distances between observations in the true and in the estimated reduced-dimensional space. In particular, we monitored the influence of the number of unknown cell-level covariates θ and b = 1,…, B, respectively denote the true parameter and an estimator of this parameter for the bth simulated data set. Then, for each scenario, the performance of the estimator Bias and MSE of the ZINB-WaVE estimators: For data simulated from the ZINB-WaVE model, let βμ, βπ, γμ, γπ, ζ, Wαμ, Wαπ, ln(μ), and logit(π). When the parameter to be estimated was an n × J matrix, the matrix was converted to a 1 × nJ row vector and bias and MSE were averaged over the elements of the vector.Bias and MSE were computed for Model selection for ZINB-WaVE: The Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are widely used for model selection and are defined as follows:n is the sample size, and N is the total number of estimated parameters, i.e., N = J(Mμ + Mπ) + n(Lμ + Lπ) + 2KJ + nK + J when the model is fit with genewise dispersion and N = J(Mμ + Mπ) + n(Lμ + Lπ) + 2KJ + nK + 1 when the model is fit with common dispersion.where MLE (Eq. ), n is tK).We use AIC and BIC in the simulation to select the number of unknown cell-level covariates  in adult male mice, using a set of established Cre lines. Single cells were isolated by FACS into 96-well plates and RNA was reverse transcribed and amplified using the SMARTer kit. Sequencing was performed using the Illumina HiSeq platform, yielding 100 bp-long reads. We selected a subset of three Cre lines, Ntsr1-Cre, Rbp4-Cre, and Scnn1a-Tg3-Cre, that label layer 4, layer 5, and layer 6 excitatory neurons, respectively. This subset consists of 379 cells, grouped by the authors into 17 clusters; we excluded the cells that did not pass the authors’ quality control filters and that were classified by the authors as “intermediate” cells between two clusters, retaining a total of 285 cells. Gene expression was quantified by gene-level read counts. Raw gene-level read counts and QC metrics (see below) are available as part of the scRNAseq Bioconductor R package (https://bioconductor.org/packages/scRNAseq). We applied the dimensionality reduction methods to the 1000 most variable genes.V1 data set: Tasic et al.4 characterized 3005 cells from the primary somatosensory cortex (S1) and the hippocampal CA1 region, using the Fluidigm C1 microfluidics cell capture platform followed by Illumina sequencing. Gene expression was quantified by UMI counts. In addition to gene expression measures, we have access to metadata that can be used to assess the methods: batch, sex, number of mRNA molecules. Raw UMI counts and metadata were downloaded from http://linnarssonlab.org/cortex/.S1/CA1 data set: Zeisel et al.37 sequenced the transcriptome of 704 mouse embryonic stem cells (mESCs), across three culture conditions , using the Fluidigm C1 microfluidics cell capture platform followed by Illumina sequencing. We selected only the cells from the second and third batch, after excluding the samples that did not pass the authors’ QC filtering. This allowed us to have cells from each culture condition in each batch and resulted in a total of 169 serum cells, 141 2i cells, and 159 a2i cells. In addition to gene expression measures, we have access to batch and plate information that can be included as covariates in our model. Raw gene-level read counts were downloaded from http://www.ebi.ac.uk/teichmann-srv/espresso/. Batch and plate information was extracted from the sample names, as done in Lun & Marioni42. We applied the dimensionality reduction methods to the 1000 most variable genes.mESC data set: Kolodziejczyk et al.6 collected 672 cells from five dissociated human glioblastomas. Transcriptional profiles were generated using the SMART-Seq protocol. We analyzed only the cells that passed the authors’ QC filtering. The raw data were downloaded from the NCBI GEO database (accession GSE57872). Reads were aligned using TopHat with the following parameters: –rg-library Illumina –rg-platform Illumina –keep-fasta-order -G -N 3 –read-edit-dist 3 –no-coverage-search -x 1 -M -p 12. Counts were obtained using htseq-count with the following parameters (http://www-huber.embl.de/HTSeq/doc/count.html): -a 10 -q -s no -m union. We applied the dimensionality reduction methods to the 1000 most variable genes.Glioblastoma data set: Patel et al.29 characterized 849 FACS-purified cells from the mouse OE, using the Fluidigm C1 microfluidics cell capture platform followed by Illumina sequencing. Gene-level read counts were downloaded from GEO . As done in Perraudeau et al.31, we filtered the cells that exhibited poor sample quality using SCONE36 (v. 1.1.2). A total of 747 cells passed this filtering procedure. To compare with the original results, we also re-analyze the final repertoire of 13 stable clusters found in Fletcher et al.29, consisting of 616 cells, downloaded from https://github.com/rufletch/p63-HBC-diff. See Fletcher et al.29 for details on the original analysis and Perraudeau et al.31 for details on the ZINB-WaVE based workflow.OE data set: Fletcher et al.32 characterized 68,579 peripheral blood mononuclear cells (PBMCs) from a healthy donor. The gene-level UMI counts were downloaded from https://www.10xgenomics.com/single-cell/ using the cellrangerRkit R package (Version 1.1.0). We applied the dimensionality reduction methods to the 1000 most variable genes.10× Genomics 68k PBMCs data set: Zheng et al.https://bioconductor.org/packages/zinbwave). See the package vignette for a detailed example of a typical use. The code to reproduce all the analyses and figures of this article is available at https://github.com/drisso/zinb_analysis.The ZINB-WaVE method is implemented in the open-source R package zinbwave, available as part of the Bioconductor Project (Supplementary InformationPeer Review File


Background/Aim. Evaluating the success of dose prediction based on genetic or clinical data has substantially advanced recently. The aim of this study is to predict various clinical dose values from DNA gene expression datasets using data mining techniques. Materials and Methods. Eleven real gene expression datasets containing dose values were included. First, important genes for dose prediction were selected using iterative sure independence screening. Then, the performances of regression trees (RTs), support vector regression (SVR), RT bagging, SVR bagging, and RT boosting were examined. Results. The results demonstrated that a regression-based feature selection method substantially reduced the number of irrelevant genes from raw datasets. Overall, the best prediction performance in nine of 11 datasets was achieved using SVR; the second most accurate performance was provided using a gradient-boosting machine (GBM). Conclusion. Analysis of various dose values based on microarray gene expression data identified common genes found in our study and the referenced studies. According to our findings, SVR and GBM can be good predictors of dose-gene datasets. Another result of the study was to identify the sample size of n = 25 as a cutoff point for RT bagging to outperform a single RT.  Microarray technology can simultaneously measure the expression levels of thousands of genes in a biological sample. In genome experiments, researchers frequently encounter high-dimensional data with a small sample size . RegressThe aim of this study is to evaluate clinical-dose estimation by genome data (with various sample size) using several data mining techniques. For example, in the International Warfarin Pharmacogenetics Consortium report, “Estimation of the Warfarin Dose with Clinical and Pharmacogenetic Data” whose authors Klein, Altman, and Eriksson became committee members in 2009, therapeutic warfarin dose estimation was obtained using genetic factors, such as gene expression values, and some environmental factors as independent variables . SimilarEleven real dose-gene expression datasets were used as real datasets to implement the prediction process. For this purpose, we searched the gene sequences in the GEO database and selected datasets containing a numerical measurement such as dose or concentration. DNA expression profiles of humans, rat types, and yeast species were downloaded from the National Center for Biotechnology Information Gene Expression Omnibus (NCBI GEO). These datasets were used in different studies that examine expression profiles of gene sequences at varying dose or concentration levels  for different living species. Two of these belong to yeast, seven belong to rats, and the remaining two contain human gene sequences. Our main criterion in the selection of these datasets is that they have both a gene sequence and a numerical response value . Therefore, a common characteristic of the datasets is that each has gene expression levels separately constituting thousands of columns, and each consists of a quantitative clinical measurement considered as response variable. In addition, sample size of the datasets ranges from 15 to 98. Detailed information about datasets are shown in 2 transformation was applied to nontransformed gene expression datasets. This normalization process adjusts the individual hybridization intensities to balance them appropriately to ensure that meaningful biological comparisons can be made [Some datasets had transformed counts. The log be made . In the Feature selection is another important step in selecting a small number of predictor variables having significant effects on the response variable, especially on high-dimensional gene data. Since the number of features is much larger than the sample size, classical methods such as ordinary least squares fail to fit the linear regression model. In addition, it is assumed that only a few of the features (genes) are actually associated with the response values. Hence, we must first identify the genes that are responsible for the dose of a clinical measurement to reduce the number of effective genes . An itery) as response variable and gene expression profiles as predictors (x). Then, we identified small sets of predictor genes using iterative SIS method and built regression models . Training data (70% of data) was utilized to determine the optimal value of parameters and fit the models. Finally, model performance was estimated using the remaining (testing) data.First, we considered clinical-dose values (ε-insensitive loss function (ε-SVR) to generalize support vector algorithms to apply to regression situations. The purpose of ε-SVR is to find the function f(x) with a maximum deviation of ε from the yi target values for all training datasets. The linear function condition of f(x) is defined as follows:w is the flatness of the function and the following optimization problem is solved to minimize the ‖w‖2 Euclidean form.Unlike the classical regression methods, SVR focuses on minimizing the generalization error instead of minimizing the observed training error. Vapnik has defined an Objective is ε-insensitive loss function [ε, they are ignored (considered zero). The C > 0 regularization parameter defines the balance between the flatness of f and the tolerated ε [K provides the objective function for the nonlinear solution:αi and αi∗ are Lagrange multipliers.Equation  is the efunction . As longerated ε , 15. DefY by explanatory variable vector X = X1, X2,…, Xn, which can be a random mixture of quantitative, ordinal, and nominal variables [The purpose of RT analysis is to explain a continuous response variable ariables . A tree R1, R2,…, Rm as the mth area is modelled as a constant cm [The response variable in each area for a split of stant cm :(5)fx=∑mI is the indicator function and cm is the prediction value for Rm. Using the minimization criterion of the sum of squared errors ∑(yi − f(xi))2 reveals that the best value of yi values in the region Rm:Here, j and split point s. Then, the first splitting variable j and split point s are obtained by solving the the following [In the RT formation step, two regions are created by applying a greedy algorithm for each explanatory variable ollowing : (7)minjEnsemble methods aim to improve the estimation performance of a given statistical learning or model-building technique. The basic principle of ensemble methods is to create a linear combination of model fitting methods instead of using only a single method. Bagging and boosting are two examples of aggregation methods used to increase the accuracy of classifiers or estimators. Yang et al.  proposedClassical bagging yields more robust and accurate models using bootstrap resamplings of the training data , 19. TheL) [Boosting was first introduced in 1990 by Freund and in 1995 by Schapire to improve classification . As in b, f(xi)) , 25. Boon = 69 has been used for this purpose. This dataset has been randomly selected to be an example. The number of the selected q∗ = 16 genes with iterative SIS method then has been reduced to 8 important genes by considering multicollinearity and the significance of the regression coefficients. The simulation data have been derived from the multivariate normal distribution by using the correlation matrix between gene expression measurements and dose values. In order to capture the true relation structure in the dataset, the zero mean vector and the real correlation matrix were used [zi is the standardized score, yi is the raw dose score, and σy are the mean and the standard deviation of the raw dose scores, respectively. These data generation steps were repeated 500 times.In order to ensure the effect of the sample size on the used ensemble methods, simulation data have been derived according to selected genes utilizing iterative SIS method. The gene expression-dose dataset having access number GSE2409 with a sample size of ere used . Data weFunction types whose model performance was evaluated for SVR were linear, polynomial, radial basis, and sigmoid. However, only the solutions of linear function providing the smallest RMSE estimation were considered in the results section.C (cost), ε (epsilon) and γ  well [C and ε for linear function was achieved while the optimization of all the three parameters for other nonlinear kernel functions was achieved simultaneously using tune function in R. The valid search interval of C (cost parameter) in tune.svm command was determined between 10−2 and 102. On the other hand, the search interval of γ (gamma parameter) was determined between 10−3 and 102 . Searches for 0.05, 0.10, and 0.20 values of ε in the related ranges of C and γ parameters were conducted; then, the combination of parameters which gives the smallest prediction error (MSE) for 10-fold cross-validation was identified. Similarly, minimum number of observations in a node, complexity parameter, and node number with subdivision (interaction level) parameters for RT were searched using cross-validation. Optimized parameter values were fixed for the method versions within the same cycle. Generalization performance of SVR depends on setting some hyperparameters on) well , 27, 28.Statistical analyses were performed in R 3.1.2 programming language. Each dataset was divided into training (70%) and test  sets to avoid overfitting. When creating the regression models, the R packages e1071, rpart, ipred, and gbm were used for SVR, RTs, RT bagging, and GBM, respectively. R code was written to build a SVR-bagging model. The average performances of 100 training/test divisions and 50 bagging repetitions were considered in the analyses.R2) measures, defined as follows:yi and n is the observation number, and SSR is the sum of squared regression, SSE is the sum of squared errors, and SST is the sum of squared of total variation of y. The prediction performances of related models were compared with the root mean squared error (RMSE), mean absolute deviation (MAD), and coefficient of determination , R2 values were generally found to be sufficient. Overall, the best prediction performance was obtained by SVR in nine of 11 datasets. In nine datasets, after SVR, the second best accuracy performance was provided by GBM. Average R2 values changed from 0.37 to 0.97.Thereafter, training-test performances with 100 random splits of single, bagging, and boosting models of the prediction methods were evaluated for the datasets. Prediction results of the SVR, RT, SVR bagging, RT bagging, and GBM learning techniques for each dataset are also shown as average R2 values for anticancer drug dose, approximately 81%. When the two human datasets (GSE14954 and GSE9539) were considered, their R2 values were found to be sufficiently high. The best average estimates were 80.4% and 86.7%, respectively.For the GSE1938 dataset, the two genes that most affected the mannose concentration were CWP1 and NCA3. These two genotypes together best explained the mannose concentration, approximately 96%. In another yeast dataset with access number GSE8982, a total of nine important genes were determined to predict the concentrations of the alpha mating factor pheromone. Selected genes included DIG2, GYP8, YHR097C, ACM1, LCB3, PRM4, PRM3, FYV10, and UTP7, and all had the best explained variation, approximately 74%. In the analysis of the GSE12817 dataset, important genes such as Adm, Aldob, Pkm2, Crem, and nod3l were identified. Their explanation success of glucose concentration was found to be approximately 97%. Similarly, in the rat dataset with access number GSE2409, the selected 16 genes were RGD1309228, Ccdc21, Setd5, RGD1303130, Vps26a, Sept2, BF396256, Adprhl2, BE109616, Phf3, Tfb2m, Lyplal1, Arg1, Ndufs2, Tmem208, and Nsun2. Together, they had the best Twenty-two genotypes affecting copper concentrations were determined as MCL1, DDX28, MRPS26, RPUSD2, DDIT3, PELO, SLC30A1, C20orf111, SOCS3, SOX9, DNAJB4, NXF1, MAF1, MAFG, AMOTL2, ADM, ZFAND2A, ZFAND5, DUSP1, TBCC, HPS6, and INTS5.n ≤ 25 condition and six datasets in the n > 25 condition are shown in Figures n ≤ 25 datasets . Standard dose scores obtained based on  and single performance (blue straight line) of RT are very close; however, when n > 25, error predictions of bagging and boosting steadily decrease, but boosting gives a better performance compared to the others. These results are consistent with those of the original datasets.When the training set size is 2. All participants received two different diets and then their LDL-cholesterol concentrations and insulin sensitivity levels were compared [μM copper sulfate. A related study [R2 = 0.867). Harrill et al. [R2 success of these 14 genotypes was about 55%.In this study, the performances of two commonly used machine learning techniques, SVR, and RT, and their ensembles in predicting various dose values were compared on high- dimensional microarray datasets. A total of 11 real datasets obtained from the GEO database were used. Analysis of various dose values based on microarray gene expression data identified common genes found in our study and the referenced studies. For instance, the study that analysed rat pancreatic islets cultured for 18 h in 2, 5, 10, or 30 mM glucose concentrations of raw data with accession number GSE12817 identified the 40 genes most affected by glucose . These ied study  identified study . An impol et al.  used twol et al. . HoweverR2 was obtained as 0.367, the highest R2 was 0.978.When the prediction performances were compared, the fact that SVR performs better than other methods closely resembles the results of some other studies , 14, 33.n = 25 was identified as a cutoff point for RT bagging. When RMSE estimates from RT to RT bagging were examined with changing sample size, it was seen that bagging did not improve single RT performance up to the datasets with sample size of 25. However, the R2 estimates of RT bagging gained consistency from the dataset with ID code GSE8982 (n = 33), and this improvement became more visible with an increase in the number of observations. Consequently, GBM provided more optimistic performance in datasets with n ≤ 25 compared to RT bagging. It was also found that the results obtained from the simulated data were consistent with the application of real gene data. However, this condition is not valid for SVR performance because SVR bagging did not outperform single SVR. When SVR performance was taken into consideration, in either condition (n ≤ 25 or n > 25), bagging could not provide a significant reduction in the RMSE average or variance. This finding is consistent with the results of some other studies in the literature [An important finding of this study is that the dataset size of terature , 34.Furthermore, frequent utilization of iterative SIS feature selection for genomic data was supported in this study, because it enables the selection of a smaller number of genes to contribute to regression estimation from thousands of raw genes.


Although ultrahigh-throughput RNA-Sequencing has become the dominant technology for genome-wide transcriptional profiling, the vast majority of RNA-Seq studies typically profile only tens of samples, and most analytical pipelines are optimized for these smaller studies. However, projects are generating ever-larger data sets comprising RNA-Seq data from hundreds or thousands of samples, often collected at multiple centers and from diverse tissues. These complex data sets present significant analytical challenges due to batch and tissue effects, but provide the opportunity to revisit the assumptions and methods that we use to preprocess, normalize, and filter RNA-Seq data – critical first steps for any subsequent analysis.We find that analysis of large RNA-Seq data sets requires both careful quality control and the need to account for sparsity due to the heterogeneity intrinsic in multi-group studies. We developed Yet Another RNA Normalization software pipeline (YARN), that includes quality control and preprocessing, gene filtering, and normalization steps designed to facilitate downstream analysis of large, heterogeneous RNA-Seq data sets and we demonstrate its use with data from the Genotype-Tissue Expression (GTEx) project.http://bioconductor.org/packages/yarn.An R package instantiating YARN is available at The online version of this article (10.1186/s12859-017-1847-x) contains supplementary material, which is available to authorized users. RNA-Seq experiments using ultrahigh-throughput sequencing-by-synthesis technologies were first performed in 2008 and have since been used for large-scale transcriptome analysis and transcript discovery in mammalian genomes –3. AlthoThere are now many large cohort studies, including the Genotype-Tissue Expression project (GTEx) and The Cancer Genome Atlas (TCGA) that have generated transcriptomic data on large populations and across multiple tissues or conditions to study patterns of gene expression , 9. The Established methods for RNA-Seq analysis can be used to make direct comparisons of gene expression profiles between phenotypic groups within a tissue. However, they are not well suited for comparisons across multiple, diverse tissues, of which each exhibit a combination of commonly expressed and tissue-specific genes. This characteristic is a feature that confounds most normalization methods, which generally assume the majority of expressed transcripts are common across samples. Widely-used normalization methods make assumptions that are valid only in fairly consistent samples and assume that most genes are not differentially expressed, that housekeeping genes are expressed at equivalent rates, or that the expression distributions vary only slightly due to technology –6. In laYet Another RNA-Seq normalization pipeline (YARN), illustrated in Fig. http://bioconductor.org/packages/yarn.YARN, shown in Fig. The first step in any good data processing pipeline is quality assessment to assure that samples are correctly labeled. Reliable metadata is critical for studies and a high rate of mis-assignment raises issues about the quality of the rest of the annotation provided for each sample. Some disease states and sex annotation metadata can be checked with the RNA-Seq expression values using disease biomarkers or sex chromosomal genes. Misannotation is a common problem, with 46% of studies potentially having had misidentified samples . We ours2-transformed the data, and used Principal Coordinate Analysis (PCoA) with Euclidean distance to cluster individuals within each tissue [As a measure of the quality of the GTEx annotation, we tested for the fidelity of sample sex assignment. We extracted count values for genes mapped to the Y chromosome in each sample, logh tissue   and created two cell lines (fibroblasts from skin and lymphoblastoid cells from whole blood). However, not every site was sampled in every individual. Further, there were often multiple sites sampled from the same “organ” , but the GTEx consortium did not report testing whether such samples exhibited fundamental differences in gene expression or if they were effectively indistinguishable. Our interest in analyzing GTEx was to increase our effective power by maximizing the sample size in each tissue by grouping samples that were otherwise transcriptionally indistinguishable .2-transformed raw count expression data  by taking, for example, all skin-derived samples. We excluded the X, Y, and mitochondrial genes, identified the 1000 most variable autosomal genes, and performed PCoA using Euclidean distance on the logWe then visually inspected the PCoA plots to determine whether subregions were distinguishable from each other based on the two first PCs. If they were, the subregions were considered independent tissues in all downstream analyses . Those regions that could not be resolved were merged to improve the power of downstream analyses. If we observed complex patterns, as described for brain below, we performed multiple rounds of PCoA analysis to assure that we had identified transcriptionally distinct regions. In many cases, we found clear separations between tissue subregions, such as for the various arterial or esophageal subregions, which we retained as separate tissues. However, for other tissues, such as sun-exposed and non-exposed skin, we found no distinguishable difference in the PCoA plots Fig.  and therThe greatest consolidation occurred in brain, where GTEx had sampled 13 subregions. In examining the PCoA plots, we found that samples from cerebellum and cerebellar hemisphere subregions were indistinguishable from each other, but these were very distinct from the other brain regions. We merged the cerebellum and cerebellar hemisphere subregions (brain cerebellum) and removed these from the remaining brain subregions. We then performed a second PCoA on the remaining regions. We found that basal ganglia  clustered separately from the remaining subregions that did not further separate into other groups ; this leaves 30,333 genes out of the 55,019 mapped transcripts for which reads are available in GTEx. Of these 30,333, 60%  are classified as protein coding genes and 11% (3220) are pseudogenes. This contrasts with the tissue-agnostic method in which genes are removed if they appear in fewer than half of the total number of samples in the data set; this filtering method retains only 15,480 genes, of which 84%  are protein coding and 4% (659) are pseudogenes  and lung (n = 360), two tissues with relatively large numbers of samples, and for which we expect to find many differentially expressed genes . The tissue-agnostic filtering identified the largest fraction (80%), but many of the differentially expressed genes were noncoding genes. The tissue-aware filtered data yielded an intermediate fraction of differentially expressed genes (69%), but the greatest number of differentially expressed protein coding genes. Consequently, we chose to use tissue-aware filtering as it provides for identification of tissue-specific, differentially expressed genes , those that are missing, or those mapping to a specific chromosome, respectively. The use of these functions helps retain tissue-specific genes while removing extremely low abundance genes that may represent sequencing noise , 23 Add.Normalization is one of the most critical steps in data preprocessing and there are many normalization approaches that have been used in expression data analysis. Many early and widely used methods for RNA-Seq normalization were based on scaling –26. MoreQuantile normalization forces every sample’s statistical distribution to the reference’s distribution where the reference is defined as the average of all sample count quantiles. When the distributional shapes are dissimilar across tissues, the reference is not representative of any particular tissue and scaling of quantiles is dependent on the largest tissue’s distribution. In GTEx, we wanted to use a single normalization method for all tissues. Here, with a very diverse set of tissues, the assumptions underlying quantile normalization clearly break down  using an all-sample reference  than we saw using qsmooth’s tissue-specific references Fig. . The rooLarge-scale transcriptional studies, such as GTEx, present unique opportunities to compare expression in a relatively large population and across a large number of tissues. However, as with all analyses of gene expression, it requires careful quality assessment, gene filtering, and normalization if meaningful conclusions are to be drawn from the data. We developed a simple and robust software pipeline, YARN, to allow us to perform quality control assessment of the metadata associated with a large, heterogeneous data sets such as the collection of RNA-Seq assays that are available as part of the GTEx v6 release.YARN was designed to process RNA-Seq data to allow comparisons between diverse conditions and consists of four basic steps: quality assessment filtering to remove questionable samples, comparison of “related” sample groups to merge them or split them into separate groups, filtering genes that have too few counts while preserving tissue-specific genes, and normalizing the data. For each step, YARN contains multiple options that allow user to adapt the pipeline for their use.In our analysis of GTEx v6 data, we began by using PCoA to filter samples based on misidentification by sex. We then used PCoA to compare samples from the same general body site so as to merge those that were indistinguishable. Next, we used a tissue-aware filtering method to retain genes that were expressed in one or a small number of tissues, while eliminating those in too few samples to perform a reliable normalization. Finally, we used qsmooth to perform a tissue-aware normalization .http://bioconductor.org/packages/yarnProject home page: Operating system(s): Platform independent.Programming language: R.Other requirements: Dependencies: Biobase. Imports: biomaRt, downloader, edgeR, gplots, graphics, limma, matrixStats, preprocessCore, readr, RColorBrewer, stats, quantro. Suggests: knitr, rmarkdown, testthat (> = 0.8).License: GPLv3.Any restrictions to use by non-academics: None.Additional file 1:Supplementary Material for Tissue-aware RNA-Seq processing and normalization for heterogeneous and sparse data. (DOCX 37 kb)Additional file 2: Figure S1.PCoA analysis of multiple tissues on Y-chromosomal genes can highlight poor sex annotation, related to Fig. Additional file 3: Figure S2.PCoA analysis of multiple tissue groups, related to Figs. Additional file 4: Figure S3.Animated density plots of log-transformed counts when including more tissues, related to Fig. Additional file 5: Table S1.Breakdown of gene types remaining in each data set after different filtering approaches. Filtering in a tissue-specific manner, we keep genes that appear in a least half the number of samples present in of the smallest phenotype group ; this leaves 30,333 genes of which 60%  are classified as protein coding genes and 11% (3220) are pseudogenes. This contrasts with our tissue-agnostic method in which genes are removed if they appear in fewer than half of the samples in the data set; this retains only 15,480 genes for which 84%  are protein coding, and 4% (659) are pseudogenes. (XLSX 36 kb)Additional file 6: Figure S4.Heatmap of the 15 most variable genes in the GTEx heart samples post filtering, related to Figs. Additional file 7: Figure S5.2 raw expression distribution of samples pre-normalization; count distribution for each sample normalized in a tissue-aware manner. Colors represent different tissues. (PDF 7035 kb)Count distributions pre- and post- normalization, related to Figs.


Dynamic network biomarkers (DNB) can identify the critical state or tipping point of a disease, thereby predicting rather than diagnosing the disease. However, it is difficult to apply the DNB theory to clinical practice because evaluating DNB at the critical state required the data of multiple samples on each individual, which are generally not available, and thus limit the applicability of DNB. In this study, we developed a novel method, i.e., single-sample DNB (sDNB), to detect early-warning signals or critical states of diseases in individual patients with only a single sample for each patient, thus opening a new way to predict diseases in a personalized way. In contrast to the information of differential expressions used in traditional biomarkers to “diagnose disease”, sDNB is based on the information of differential associations, thereby having the ability to “predict disease” or “diagnose near-future disease”. Applying this method to datasets for influenza virus infection and cancer metastasis led to accurate identification of the critical states or correct prediction of the immediate diseases based on individual samples. We successfully identified the critical states or tipping points just before the appearance of disease symptoms for influenza virus infection and the onset of distant metastasis for individual patients with cancer, thereby demonstrating the effectiveness and efficiency of our method for quantifying critical states at the single-sample level. The concept of dynamic network biomarkers (DNB) was proposed for detecting the critical state or tipping point of a complex disease (a pre-disease state immediately preceding the disease state), and has been applied to study the mechanism of cell fate decision and immune checkpoint blockade. But DNB cannot be used to identify the critical state or tipping point for a single patient because evaluating DNB for critical state required the data of multiple samples. The proposed method can identify the critical state of a complex disease for a single patient by implementing the concept of DNB. This method not only can be applied to detect the critical state or tipping point of a single sample, but also can be used to study the mechanism of complex disease at a single sample level. The ability of accurately and efficiently identifying the critical state for a single sample can benefit the development of personalized medicine. PLOS Computational Biology Methods paperThis is a Biomarkers, which are indicators of physiological states for living things, are commonly used to examine organ functions or disease states in biology or medicine. Generally, complex disease progression can be divided into three states, i.e., normal, pre-disease and disease  1, 2], , 2, 1, 2SDin: standard deviation) drastically increases,[Condition 1] deviation for molecules inside the module  rapidly increases, and[Condition 2] correlation between molecules inside the module  rapidly decreases [[Condition 3] correlation between molecules inside and outside the modules (ecreases –3.Im of Eq (SDin is the average standard deviation (SD) for molecules inside the DNB module, PCCin is the average Pearson correlation coefficient (PCC) in absolute value for molecules inside the module, and PCCout is the average PCC in absolute value for molecules between the inner and outer molecules of the module. Clearly based on the three conditions, Im will drastically increase when the biological system approaches the critical state, and thus it can signal the immediate disease state or predict disease state. In contrast to the information of differential expressions widely used in traditional biomarkers to “diagnose disease”, DNB is based on the information of differential associations, thereby having the ability to “predict disease” or “diagnose the un-occurred disease”.The above three statistical conditions are generic features of critical states, which hold for general biological systems regardless of their detail differences. Thus, we can simplify these three conditions as an index Im of Eq  to evaluDNB is a type of network biomarker, which can be used for the diagnosis of a pre-disease state rather than a disease state. In other words, DNB can be used for early diagnosis of a disease or to distinguish the pre-disease state from the normal state in complex diseases. According to the above three statistical conditions, DNB is clearly independent of differential expressions and is based on higher-order statistical information  rather than the first-order statistics  used for traditional molecular biomarkers. However, although the theory of DNB can ensure the recognition of early-warning signals of complex diseases, it requires multiple data samples to evaluate the three statistical conditions of DNB, which limits its application to clinical practice because multiple samples for each individual are generally not available. Here, by exploiting the high-dimensional information of the observed data  and its differential distribution  , we propsDNB is the first such a method to predict the pre-disease state or quantify the tipping point based on only one sample. Note that, completely different from the traditional classification or machine learning methods which require a large number of case/control samples (for supervised or unsupervised learning) to obtain the predictor , sDNB is a model-free method and does not require any learning process on sample data. In other words, the predictor “sDNB” is constructed by the three statistical conditions for each specific sample that are actually based on the essential dynamical features of critical states for general biological systems, and thus inherently has no overlearning problem  and in particular is an individual-based predictor.To identify the critical state using DNB from a single sample, a control sample set is required as a reference. The information from the single sample can be extracted by comparing it with the reference samples . In genehttp://www.ncbi.nlm.nih.gov/geo/) and datasets on lung adenocarcinoma (LUAD), stomach adenocarcinoma (STAD), and thyroid carcinoma (THCA) from the TCGA database (http://cancergenome.nih.gov), were used to validate the sDNB method. Dataset GSE30550 was normalized by the robust multi-array average (RMA) method, and the IDs of probe sets were mapped to the gene symbols. Probe sets without corresponding gene symbols were not considered in this study. The LUAD, STAD, and THCA datasets contained RNA-Seq data and included both tumor and tumor-adjacent samples. The tumor samples were divided into different stages based on clinical (stage) information from TCGA, while samples without stage information were ignored.Four datasets, including dataset GSE30550  from thed  can be compared with its reference distribution to estimate the deviation of its expression from the reference samples (n samples). The expression deviation of a gene in the new sample can be expressed as the distance from the expectation of its reference distribution  for gene x, can be defined asx is the expression of gene x in the new single sample, and x in the reference samples.We estimated sDNB score by using the three statistical conditions of DNB. Based on a number of reference samples , we can obtain expression distribution for each gene as its reference distribution. The expression of the gene in a new sample ribution . Specifin, and thus the Pearson correlation coefficient (PCC) between two genes  in the reference sample data can be calculated asxi and yi are the expressions of gene x and gene y for the ith sample in the reference samples, respectively. x and gene y in the reference samples, respectively.We assumed the number of samples in reference data to be PCCn is the correlation between two genes  in n reference samples. After a new single sample is added to the reference samples  based on total n + 1 samples , i.e., PCCn+1. The difference between PCCn+1 and PCCn for the two genes is caused by the new single sample added to the reference data  of the two specific genes  against n reference samples as follows . Note that the minimum or single-linkage clustering was used as the linkage criterion of the hierarchical clustering in this paper.Decomposing a network into multiple modules: Hierarchical clustering is employed to decompose the single sample network into multiple modules based on the Is (conditions 1–3): Eq (6) is used to estimate every module, and the module with the maximal score from Eq (6) is regarded as the potential sDNB module for this sample. If this score is significantly high, this sample is considered in the critical state based on DNB theory and this module is the DNB module.Choosing sDNB module with the highest score With such an algorithm, we can get the candidate sDNB for each sample one by one. If the sDNB for a sample during a biological process or disease progression has the highest score among all samples, this sample is considered to be in the critical state, and the corresponding period is also the critical period.http://www.ncbi.nlm.nih.gov/gene). The enrichment analyses were separately obtained using web service tools from the Gene Ontology Consortium  and g:Profiler (http://biit.cs.ut.ee/gprofiler/) and client software from INGENUITY IPA (http://www.ingenuity.com/products/ipa).Functional annotations were performed by searching the NCBI gene database (http://www.ncbi.nlm.nih.gov/geo/) and LUAD, STAD, and THCA from the TCGA database (http://cancergenome.nih.gov), were chosen to validate the effectiveness of this method of quantifying the critical states of diseases.In this study, four datasets, GSE30550 from the GEO database  by microarray , i.e., tFrom the LUAD (lung cancer), STAD (stomach cancer), and THCA (thyroid cancer) datasets, 459 tumor samples and 58 tumor-adjacent samples were obtained for LUAD. The tumor samples were grouped into seven stages  of lung cancer . One hunPCC was set to the p-value of 0.01 in the process of constructing the single-sample network  (The gene expression profiles of samples at time point −24 h (24 hours before inoculation) were chosen as reference samples, and totally 16 normal samples were included in the reference data. The candidate sDNB for each adult was identified by comparing the case sample with the reference samples. The threshold of s network , and theearance) . In contearance) . Notablyearance) . AnotherFor most adults (16 of 17 symptomatic and asymptomatic adults) in dataset GEO30550, our method could correctly detect critical states or early-warning signals before disease symptom appearance based on the sDNB scores (single samples). False-positive warning signals for only one adult appeared in the asymptomatic samples, possibly due to the causes described above.Homo sapiens, and results are shown in The module size of sDNB in every symptomatic adult was different, e.g., there were 1553 sDNB genes for adult s7, 696 for adult s5 , and onlEnrichment analysis of the 25 overlapped genes among all 9 sDNBs of symptomatic samples  was perfThe sDNB modules identified in the symptomatic samples are shown in Nineteen of the 25 overlapped genes are reported to be related to virus response, and 6 of the 19 are associated with the influenza virus . Hence, PCC was set as the p-value of 0.01 to construct the single-sample network  in the cancer progression of LUAD , and theFunctional enrichment showed that the common genes in at least 80% of sDNBs are identified as genes involved in the biological processes of the nuclear division, the mitotic cell cycle, the organelle fission, and so on  by GOC ; this isin vivo [There are also seven stages  in the cancer progression of STAD , and thein vivo . CTHRC1 in vivo –36 and min vivo . ESM1 rein vivo . The ovein vivo . High exin vivo , 41. PRAin vivo , 20. PRAin vivo  and lungin vivo , 43. TheFunctional enrichment analysis showed that the common genes in at least 50% of sDNBs were involved in the biological processes of collagen catabolic process, multicellular organismal catabolic process, etc.  accordinin vitro and in vivo [There are four stages  in the cancer progression of THCA . The pea in vivo . LIPH is in vivo . PROS1 c in vivo . Enhance in vivo . SLC34A2 in vivo . TENM1 i in vivo . TMPRSS4 in vivo . The aboFunctional enrichment showed that the common genes in at least 50% of the sDNBs are associated with thyroid cancer, papillary thyroid cancer, thyroid gland tumor, etc.  accordinIn this study, by exploiting the high-dimensional information of the observed data and the volcano distribution of differential networks, a new method was proposed to identify tipping points or critical states (which appear just before the disease state) based on single-sample DNB (sDNB). In contrast to the information of differential expressions used in traditional biomarkers to diagnose disease, sDNB is based on the information of differential associations, thereby having the ability to predict disease or “diagnose the un-occurred disease”. This method was applied to quantify the early-warning signals for the process of influenza virus infection and cancer metastasis on a single-sample basis. The results for the influenza virus infection show that high sDNB scores indeed signaled the imminent emergence of disease symptoms (at least 8 hours before their appearance) for every symptomatic sample, and there were no significant high scores for asymptomatic samples with the exception of adult s17. A potential explanation for this false-positive result on adult s17 is that this asymptomatic adult was the only non-Caucasian/White subject among the asymptomatic adults, and may thus have had a different threshold. Another possibility is that adult s17 did reach the critical state but recovered to the normal state before further deterioration into the disease state, thereby causing a significant signal.sPCC was set at the p-value of 0.05 to construct the single-sample network , for determining the critical state, which is based on the whole disease samples.Note that sDNB is a model-free method, and does not requires the learning on sample data; it is completely different from the traditional classification or machine learning methods which are population-based predictors requiring a large number of case/control samples to train the model and eliminate the overlearning problem. In other words, sDNB is an individual-based predictor based on the three statistical conditions for each specific sample, and thus inherently has neither overlearning problem nor assumption on the model. Hence, even for the same disease, the composition of sDNB as well as the size of sDNB for each sample or individual may be different, but its The critical state is considered as a stage early reversible to the normal state. Thus, appropriate treatment for subjects in the critical state is considered much effective in contrast to the subjects in the disease state. However, how to make such a treatment is beyond the scope of this work, and will be a future topic. In addition, theoretically, any omics data  which can dynamically reflect the change of the disease progression, can be used to detect the critical state or tipping point. Thus, depending on the disease type, we may choose an appropriate type of the omics data. With current high-throughput technologies, generally RNAs can be quantified in a relatively stable way in contrast to proteins and metabolites. Therefore, the transcriptomic data (e.g. RNA-Seq or microarray) are effective for sDNB identification from the computational viewpoint, although metabolomics and proteomics data can also be used to identify the critical state.In summary, the method described in this paper developed a novel method, sDNB, which is the first such a method to predict disease state based only on a single sample, opening a new way to quantify the critical state of diseases in individual patients. Thus, the method can be directly applied not only to personalized pre-disease diagnosis but also to the molecular mechanism analysis of disease progression at the network level. In a similar way, sDNB could also be used to detect the tipping points or critical states of many nonlinear biological processes, such as cellular differentiation and cellular proliferation –6.S1 Fig(PDF)Click here for additional data file.S2 Fig(A) Line chart for early-warning signals in all symptomatic adults. (B) Line chart for early-warning signals in all asymptomatic adults. (C) Table of sDNB diagnoses and clinical diagnoses for all adults and samples.(PDF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S8 Table(XLSX)Click here for additional data file.S9 Table(XLSX)Click here for additional data file.S10 Table(XLSX)Click here for additional data file.S11 Table(XLSX)Click here for additional data file.S12 Table(XLSX)Click here for additional data file.S13 Table(XLSX)Click here for additional data file.S1 Text(DOC)Click here for additional data file.