Recent high-throughput sequencing technology has identified numerous somatic mutations across the whole exome in a variety of cancers. In this study, we generate a predictive model employing the whole exome somatic mutational profile of ovarian high-grade serous carcinomas (Ov-HGSCs) obtained from The Cancer Genome Atlas data portal.A total of 311 patients were included for modeling overall survival (OS) and 259 patients were included for modeling progression free survival (PFS) in an analysis of 509 genes. The model was validated with complete leave-one-out cross-validation involving re-selecting genes for each iteration of the cross-validation procedure. Cross-validated Kaplan-Meier curves were generated. Cross-validated time dependent receiver operating characteristic (ROC) curves were computed and the area under the curve (AUC) values were calculated from the ROC curves to estimate the predictive accuracy of the survival risk models.p-value <0.001). For PFS, there was also a significant difference in PFS between the high-risk group (10.9 months) and the low-risk group (22.3 months) . Cross-validated AUC values were 0.807 for the OS and 0.747 for the PFS based on a defined landmark time t = 36 months. In comparisons between a predictive model containing only gene variables and a combined model containing both gene variables and clinical covariates, the predictive model containing gene variables without clinical covariates were effective and high AUC values for both OS and PFS were observed.There was a significant difference in OS between the high-risk group  and the low-risk group  (permutated We designed a predictive model using a somatic mutation profile obtained from high-throughput genomic sequencing data in Ov-HGSC samples that may represent a new strategy for applying high-throughput sequencing data to clinical practice. Recent high-throughput sequencing technology has generated an enormous amount of data that continues to accumulate for somatic mutations in a variety of cancers. A major issue for these studies is how to separate the useful information from these large volumes of data and how to use the data more effectively. It is important to consider how the data from somatic mutational profiles containing survival information can be applied in clinical use. From this view point, the development of predictive modeling using somatic mutation profiles that employ complete genomic data with survival information may be worthwhile. Predictive modeling has been well studied in microarray gene expression profiling and in proteomic profiling BRCA2 mutation is associated with favorable survival and platinum sensitivity The predictive model with gene signature for predicting patient survival can be used in clinical test. However, no study has attempted to generate a predictive model using a somatic mutational profile obtained from high-throughput sequencing data. Somatic mutation has the potential to reflect patient survival and cancer prognosis. In ovarian high grade serous carcinoma (Ov-HGSC), http://tcga-data.nci.nih.gov/docs/publications/ov_2001) with open access We downloaded a validated whole exome somatic mutation data set and clinical information for 316 patients with Ov-HGSC from TCGA website , divide the i-th sample from whole data as the training set and the remaining (n−1) patients as the validation set.For the i-p-values <0.01, and standardize the selected gene using the mean and standard deviation of the gene, then (2) apply multivariate Cox regression to the standardized genes.For the training set, (1) select the genes with log-rank For the validation set, (1) standardize each gene using the mean and the standard deviation calculated from the training set, then (2) calculate the risk score as the linear combination of standardized values for each gene and the corresponding coefficient fitted from the multivariate Cox regression.Repeat above steps 1–3 for all n samples.Dichotomized the predictive scores into low- or high-risk based on median value and cross-validated Kaplan-Meier curves were generated.p-value as follows; (1) compute the log-rank p-value  curves using the cross-validated predictive indices were computed to measure the predictive accuracy based on landmark time p values less than 0.05 were considered statistically significant. Statistical analysis was performed using Stata/IC statistical software  and R program (version 2.12.0: www.r-project.org).Cross-validated Kaplan-Meier curves were generated for OS and PFS, and the permutation distribution of the cross-validated log-rank statistic was used for comparing the Kaplan-Meier curves p value of the cross-validated log-rank statistic was calculated to compare the cross-validated Kaplan-Meier curves. p-value <0.001). The median survival time for OS was significantly longer in the low-risk group  than in the high-risk group  from LOOCV, which corresponds to a hazard ratio for death of 0.077 . For PFS, the cross validated Kaplan-Meier plot for PFS is shown in p-value <0.001). The median survival time for PFS was significantly longer in the low-risk group  than in the high-risk group  from LOOCV, which corresponds to a hazard ratio for recurrence of 0.216 .The primary end point was the OS and PFS. The developmental strategy and work flow of predictive models for OS and PFS are schematically depicted in We estimated the predictive accuracy of the model for OS and PFS using time-dependent RO curve. Cross-validated time-dependent ROC curves show the predictive accuracy of the survival risk group model based on a defined landmark time 36 months for OS and PFS in p = 0.026 and p = 0.033, respectively) and PFS .Association of risk groups for clinicopathological factors including platinum response status (sensitive vs. resistant), surgical outcome , histological grade (grade 2 vs. 3), tumor stage, and age, are described in To compare predictive model containing only gene variables with combined model containing both clinicopathological covariates and gene variables, we developed a combined survival risk model containing clinicopathological covariates  and gene variables. Platinum response status was not included because it cannot be measured at initial surgical treatment. Cross-validated Kaplan-Meier curves of OS  and PFS The findings in this study demonstrate that predictive modeling using somatic mutational profile obtained from whole exome sequencing has potentially useful applications. Predictive modeling using expression microarray is well established, whereas predictive modeling using mutational profiling has not been attempted until now. Most of the differences between microarray data and somatic mutation data are characteristics of value. Expression microarray data has continuous value, whereas a somatic mutation profile contains binary data. In other words, expression microarray data is a relative value, whereas somatic mutation data is an absolute value that indicates the presence or absence of mutation. Therefore, if modeling using somatic mutation data is well established, it may be more predictive for independent external samples.Currently, high-throughput sequencing in cancer is being employed more often, and large amount of data from sequencing will be generated. Therefore, our approach for generating predictive modeling using somatic mutational profiles obtained from high-throughput sequencing could be an effective method in the high-throughput sequencing era.A few noteworthy issues arose while creating the predictive model from the somatic mutation data in this study. We acknowledge that the genes considered in the modeling may include passenger mutations. Currently, a major question is that what is a driver mutated gene in the numerous mutated genes. This was also a major issue that needed to be addressed before making the predictive model using somatic mutation profiles. Together, these issues may result in non-reproducible results in external independent data set. In our present analysis, one factor underlying the construction of a successful predictive model may have been the large sample size, despite the rare frequency of repeated mutated genes. In the future, it may be necessary to develop additional algorithms that are adjusted to fit somatic mutational profiles in cases of relatively small sample sizes. On the other hand, the integration of a mutation profile, copy number change, and gene expression profile with the goal of generating a predictive model may be a more promising approach.There are several methods for predictive modeling and estimation of the predictive model BRCA2 mutation was associated with favorable survival, which was well demonstrated form the original TCGA study as well as several other studies BRCA2, were associated with poor prognosis, which was not identified in previous studies. Even though this study included some already well-known genes such as ATMAmong the genes selected by fitting Cox proportional hazards models for PFS, the In Ov-HGSC, the standard treatment is aggressive tumor cytoreductive surgery followed by platinum based chemotherapy. Ov-HGSC is usually platinum-sensitive In conclusion, we designed a predictive model using a somatic mutation profile obtained from high-throughput genomic sequencing data for Ov-HGSC samples that may represent a new strategy for applying high-throughput sequencing data to clinical practice.


As the magnitude of the experiment increases, it is common to combine various types of microarrays such as paired and non-paired microarrays from different laboratories or hospitals. Thus, it is important to analyze microarray data together to derive a combined conclusion after accounting for heterogeneity among data sets. One of the main objectives of the microarray experiment is to identify differentially expressed genes among the different experimental groups. We propose the linear mixed effect model for the integrated analysis of the heterogeneous microarray data sets.The proposed linear mixed effect model was illustrated using the data from 133 microarrays collected at three different hospitals. Though simulation studies, we compared the proposed linear mixed effect model approach with the meta-analysis and the ANOVA model approaches. The linear mixed effect model approach was shown to provide higher powers than the other approaches.The linear mixed effect model has advantages of allowing for various types of covariance structures over ANOVA model. Further, it can handle easily the correlated microarray data such as paired microarray data and repeated microarray data from the same subject. Microarray technology has important applications in pharmaceutical and clinical research. For example, microarrays can be used to identify tumor-related genes and targets for therapeutic drugs. In microarray experiments, the identification of differentially expressed genes (DEG) is an important issue. Statistical test procedures have served as useful tools for identifying the DEGs which can be candidate genes for a specific disease or can be used for the further analysis such as clustering analysis and gene regulatory network construction.t-statistics, to identify DEGs between two groups [As the cost of producing microarrays has become lower costs and the importance of replication in microarray experiments has been demonstrated by many researchers , replicao groups . The anao groups . In addio groups -11.When the magnitude of a microarray experiment increases, it is common to use the same type of microarrays from different laboratories or hospitals. Thus, it is important to analyze microarray data together to derive a combined conclusion after accounting for the differences. Recently, statistical approaches based on meta-analysis have been proposed in order to combine independent and heterogeneous microarray studies -15. In tet al. (2004) introduced the probability of expression (POE) and proposed a method to estimate the POE using MCMC [et al. (2007) proposed EM algorithm to estimate the POE instead of MCMC, which can reduce the estimation time of the POE [Shen ing MCMC . The POE the POE . Standaret al. [Park et al.  proposedIn this paper, we propose the linear mixed effect (LMe) model for the integrated analysis of the heterogeneous microarray data sets. The LMe model contains various random effects which effectively account for the heterogeneous variability in the data from many different sources. Further, the LMe model has advantages of allowing for various types of covariance structures over meta-analysis and ANOVA model approaches. Thus, it can handle easily the correlated microarray data such as paired and non-paired microarray data. The proposed method is illustrated using the liver cancer microarray data sets obtained from three different hospitals .C1, contains 10,336 human cDNA probes that were verified by single pass sequencing. The second chip, C2, contains 10,368 human cDNA probes. Two chips shared the common 9,984 cDNA probes. The chips were cDNA chips with two-colors, where the way of labeling samples and controls is described in Choi et al. (2004). A further detailed description of the chips has been uploaded to the Gene Expression Omnibus (GEO) site (http://www.ncbi.nlm.nih.gov/geo/) with GEO accession number GPL2911.Four independent microarray data sets were generated from three hospitals using two different chips . The firThe chip type (1 and 2), labeling scheme, hospital and number of samples are shown in this table. Here, the data were normalized by locally weighted scatterplot smoothing . For LOWESS normalization, the value of the span parameter was 0.75 and the tricubic function was used as a weight function. For robustness analysis, Tukey’s biweight function was used . HepatocC2 was used only on 21 microarrays from 13 patients in Hospital C. Other microarrays were produced by Chip C1. Microarrays from Hospital C were divided into two data sets (D3 and D4) according to the chip type. All microarray data were obtained using the reference design with the placenta as the reference.Table H multiple data sets denoted by h = 1, …, H. There are hn patients for the hth data set. In our study, H = 4 and treatment groups consist of two levels denoted by k = T, C, where one (k = T) is the tumor tissue group and the other (k = C) is the control tissue group. For the paired observations, k has two values T and C. For the non-paired observation, k has only one value of T or C. Assume there are N common probes on each chip for all data sets. We denote genes by l .The linear mixed effects (LMe) model consists of both fixed effects and random effects. The LMe model for the lth gene is given bySuppose there are Yhil = Xhilβl + Zhilbhil + εhil,h = 1, …, H, i = 1, …, hn, l = 1, …, N, (1)Yhil is a response vector for the ith subject (patient) of the hth data set, βl is the fixed effect parameter vector, bhil is the random effect parameter vector, and εhil is the error vector. Random effects and errors are assumed to be independent and normally distributed:where bhil ~ N,  εhil ~ N. (2)Φh can have several forms. When the off-diagonal terms are zero, then the random effects are uncorrelated. Otherwise, they are correlated. By allowing different forms of Φh, we can model variability among samples efficiently. When there are no random effects, say Zhil = 0, the LMe models become equivalent to the ANOVA models.The variance of random effects For the liver cancer data, there are three fixed effects: treatment, hospital, and chip type. The LMe model is given by following equation:l = 1,…, 9984, h = 1,…, 4, Tlβ represents the treatment effect of differences between tumor tissue and control tissue, Clβ represents the effect of differences between two chips, and two parameters, βH1l and βH2l, represent the effect of differences among hospitals.where bhil. We consider four types of covariance forms for the integrated analysis of microarray data. For simplicity, we start with the case when the data consist of all paired observations.The most general form of covariance matrix in the LMe models assumes the covariance matrix of gene expressions within each data set is unstructured and differs among data sets. However, this covariance matrix requires many parameters to be estimated, which could result in a possible loss of power. Therefore, we need to consider simplified forms of the covariance matrices of bhil:1. Type 1: General form Covariance matrix of bhil:2. Type 2: One common unstructured covariance matrix for all data sets Covariance matrix of bhil has only one component hilb and its variance is given by3. Type 3: Compound symmetry covariance matrix with different variance parameter for each data set bhil has only one component hilb and its variance is given by4. Type 4: One common compound symmetry covariance matrix with the same variance parameter for all data sets Type 2 assumes the covariance matrix of gene expressions within each data set is unstructured like Type 1 but it is the same over the data sets, which is a simplified form of Type 1. Type 3 assumes each covariance matrix within the data set is compound symmetric and differs over the data sets. Type 4 is simplified version of Type 3 assuming the same covariance matrix over the data sets.Yhil is given byFor all types of covariance structure, the variance of Yhil = Var(bhil) + Iσ2.Yhil becomes one. The LMe allows only a scalar random effect. That is, bhil has only one component hiklb. For example, Type 1 assumesFor the non-paired observation, the dimension of Tlβ = 0 or not. LMe models also suffer from the multiple testing problem. We apply the FDR adjustment method proposed by Benjamini et al.[LMe model parameters can be estimated via maximum likelihood estimation. The DEGs can be identified by testing whether bhil has the covariance structure of Types 1 to 4. These four models are denoted by M1, M2, M3, and M4, respectively. The last LMe model M5 assumes no random effects and is expected to provide similar results to the two-stage ANOVA model.We applied the integrated analysis using LMe models, two-stage ANOVA model, and meta-analysis to liver cancer data. The LMe model is given in Equation 3. We fit this LMe model by assuming that Table Now, we focus on comparing the results. For simplicity, we consider LMe model M3 only for summarizing the LMe models. Figure The number of common genes selected by all three methods was only 16. Among them 9 genes are known and Table The number of genes identified only by M3 was 183 in the Figure C6 is a component of the complement system, which plays an important role as a humoral effector system during inflammation and infection, and consists of more than 25 components, including regulatory proteins. C6 was shown to late-acting complement proteins that participate in the assembly of the membrane attack complex, which causes cell lysis by the formation of pores in the cell membrane of certain microorganisms. . C9 was β/ALK1/Smad1 target gene in HSCs and represents a critical mediator of transdifferentiation that might be involved in hepatic fibrogenesis. Transforming growth factor (TGF)-β is critically involved in the activation of hepatic stellate cells (HSCs) that occurs during the process of liver damage, for example, by alcohol, hepatotoxic viruses, or aflatoxins [Gab1 was reported to be related with hepatic insulin action. Deletion of Gab1 in the liver leads to enhanced glucose tolerance and improved hepatic insulin action. It was also shown that association of Gab1 adaptor protein and Shp2 tyrosine phosphatase is a critical event at the early phase of liver regeneration ,28. Id1 latoxins ,30. NTRKlatoxins . PSG1 walatoxins . PSMG walatoxins .In order to evaluate the proposed methods, we simulated the two sets of microarray data and then performed the integrated analysis by using the proposed LMe method as well as other methods. For simplicity, we assume the log-transformed ratio of two intensities are normally distributed. To mimic the liver cancer microarray data, we assume that a pair of microarrays are obtained from the same patient. The first microarray data set consists of 60 microarrays from 30 patients and the second data set consists of another 60 microarrays from 30 patients. Suppose that two microarrays from the same patient are from different groups, say from tumor and control tissues. The main objective of the analysis is to identify the DEGs between two groups.We assume the number of genes in each microarray is 30 among which the six genes (20%) are truly differentially expressed: three genes are over-expressed and the other three genes are under-expressed in the tumor tissue. The simulation model is given byDlβ represents a fixed effect of the difference between two data sets and Tlβ represents a fixed effect for difference of expression levels between tumor and control tissues. The values of Tlβs are 1.5 for l = 1, ⋯, 3, and -1.5 for l = 4, ⋯, 6, respectively, and zero for l = 7, …, 30. The values of Dlβ are randomly determined by generating random variables from the standard normal distribution. Errors are also generated from the normal distribution with mean 0 and variance σ2 = 0.52.where hiklb we assume three types of covariance matrix corresponding to Types 1, 2, and 3 defined in Section Types of Covariance Structure. For Type 1, the covariance matrix bil=T is given byFor the random effect σ11 = 1, σ12 = 2, σ21 = 1.5, and σ22 = 2.5. In addition, the correlation parameter between tumor and control tissues are set as 0, 0.2, and 0.4. For Type 2, two variance parameters are set as σ1 = 2.5 and σ2 = 1, and the correlation parameters are set as 0, 0.2, and 0.4 as Type 1. Finally, for Type 3, two variance parameters are set as σ1 = 2.5 and σ2 = 1. For the detailed information of the covariance structure, see Table We set values of parameters as bil has the covariance structure of Types 1 to 4. These four models are denoted by M1, M2, M3, and M4, respectively. The last LMe model M5 is the one assuming no random effects, which is expected to provide similar results to the two-stage ANOVA model.For the simulated data sets, we perform the analyses using the meta-analysis, the two-stage ANOVA model and five LMe models. We fit this LMe model by assuming that q was 0.05. Genes having ordered q values smaller than 0.05 were identified as DEGs. Note that there are 6 true significant genes and 24 null genes. The empirical FDR values were computed as the number of false significant genes from 24 null genes divided by the total number of significant genes. The empirical power was computed as the number of significant genes among the 6 true genes divided by 6.Table ρ was zero, powers and FDRs showed very consistent results for all methods, although the variances of tumor tissue and control tissue are assumed to be different. This means all methods perform similarly when the correlation between tumor and control tissues does not exist.When Table ρ. For meta-analysis, two-stage ANOVA, and M5, the powers decrease as ρ increases. On the other hand, the powers of LMe models M1 to M4 increase. These tendencies illustrate that meta-analysis and two-stage ANOVA do not handle correlations efficiently as LMe models do.It is interesting to note that the performance of each method depends on the value of ρ is close to zero. Thus, M1 is not appropriate to use when there is no correlation between tumor and control tissues.FDRs of LMe models, M2, M3, and M4 are slightly larger than 0.05. However, the FDR of M1 is much larger than 0.05, especially when ρ. In summary, meta-analysis, ANOVA model analysis, and M5 provided similar results in powers and FDRs. On the other hand, other LMe models provided quite different results. Among the five LMe models, M1 and M5 provided distinct results from the other three LMe models. The powers of LMe models M1 to M4 are larger than meta-analysis, ANOVA, and M5. Although M1 has the largest power, it also shows the largest FDR.Table ρ was not considered in this case, the correlation between tumor tissue and control tissue of same patient was assumed by the shared random parameter hilb. The results of simulated data under Type 3 are quite different from those obtained from Types 1 and 2. That is, all LMe models, M1, M2, M3, and M4 show extremely good performance. The powers are all 1 and FDRs are well-controlled around 0.05. LMe models work very well for this high correlation case. On the other hand, meta-analysis, ANOVA, and M5 performed worse. Among these, meta-analysis showed a slightly better performance. It is probably due to the fact that the meta-analysis allows different variances between two data sets, while others do not.Finally, Table The LMe model is much more flexible than meta-analysis. One of the main limitations of meta-analysis is that it cannot handle the sample-specific covariates appropriately. Effect-size is simply the standardized mean difference between tumor tissue and control tissue . Meta-anWhen there are no random effects, the LMe models become equivalent to the ANOVA models. The heterogeneity among data sets is only represented by the fixed effects. When heterogeneity among data sets is small, the ANOVA model can easily handle the variability among the data sets. However, when data sets have high variability and contain the correlated data, the addition of only fixed effects may not be satisfactory. In this case, the LMe model is more appropriate to analyze data sets, because it can model the heterogeneous variance and correlation structure more appropriately. The proposed LMe model is capable of handling heterogeneous covariance structures by allowing for various random effects.When the data set contains paired and non-paired microarrays simultaneously, both meta-analysis and ANOVA model approaches cannot handle them appropriately. For example, the meta-analysis and the ANOVA analysis treated paired microarrays as independent microarrays. On the other hand, the proposed LMes can handle appropriately the correlation between the paired microarrays.Finally, note that the proposed LMe model is valid when the normality assumption holds. We do not expect this assumption to hold for real microarray data. However, we expect the assumption is decreased when sufficiently large number of microarrays were combined. In future studies, we will develop permutation tests for the LMe models which do not require any distributional assumption.We proposed the LMe model for the integrated analysis of microarray data to identify DEGs in the presence of many controlling variables. We analyzed the liver cancer microarray data set and simulated microarray data to evaluate the performance of the integration methods. LMe models except M1 maintained FDRs approximately. Powers of LMe models except M5 tended to be much larger than meta-analysis and two-stage ANOVA model analysis. These tendencies illustrated that meta-analysis and two-stage ANOVA do not handle correlations efficiently as LMe models do.The authors declare that they have no competing interests.Sung Gon Yi performed the statistical analysis and drafted the manuscript. Taesung Park conceived of the statistical method for analysis and helped to draft the manuscript. All authors read and approved the final manuscript.


Counts have classically been assumed to follow a Poisson distribution in which the variance is equal to the mean. The Negative Binomial distribution which allows for over-dispersion, i.e., for the variance to be greater than the mean, is commonly used to model count data as well.In mRNA-Seq data from 25 subjects, we found technical variation to generally follow a Poisson distribution as has been reported previously and biological variability was over-dispersed relative to the Poisson model. The mean-variance relationship across all genes was quadratic, in keeping with a Negative Binomial (NB) distribution. Over-dispersed Poisson and NB distributional assumptions demonstrated marked improvements in goodness-of-fit (GOF) over the standard Poisson model assumptions, but with evidence of over-fitting in some genes. Modeling of experimental effects improved GOF for high variance genes but increased the over-fitting problem.These conclusions will guide development of analytical strategies for accurate modeling of variance structure in these data and sample size determination which in turn will aid in the identification of true biological signals that inform our understanding of biological systems. Next generation sequencing is a tool that is revolutionizing scientific research with its unprecedented depth of coverage, accuracy, precision, and the ability to link gene expressions with phenotype. The Illumina Genome Analyzer (GA), originally by Solexa, enables interrogation of mRNA expression via the mRNA Sequencing protocol. There are several reports on quality assessments of next generation sequencing and comparisons with microarray gene expression ,2. BioloFirst we describe some distributional background. The Poisson distribution is commonly assumed when modeling count data. This distribution considers each individual piece of mRNA to be a random draw from a large collection of pieces of mRNA with some probability vector describing the relative proportion across all possible mRNA pieces. A piece could refer to a particular exon or gene according to the researcher’s interest. The Poisson distribution appears to describe well the variation observed between two technical replicates of the same specimen, i.e., two aliquots of the same library allocated to two lanes on a flow cell -5. The mBiological replication adds another level of variability to the observed data. Biological variability is that due to inter-individual differences between human or animal subjects, for example, which cause the probability vector describing the distribution of mRNA strands to differ between subjects. Thus, when count data are observed in multiple biological replicates, the observed variance is a sum of both the technical and biological variability pieces. This results in the observed variance being larger than expected under the Poisson distribution. That is, the variance is larger than the mean. This scenario is termed “over-dispersion” .2[In the simplest case, variance increases as a linear function of the mean, i.e., the variance is a constant multiplied by the mean, Var(y) = kμ. We denote this as the over-dispersed (OD) Poisson throughout and model parameters can be estimated via quasi-likelihood methods. A more sophisticated model assumes the within-specimen  variation follows a Poisson distribution and the between-specimen mean values follow a gamma distribution. This gives rise to the negative binomial (NB) distribution in which the variance increases as a quadratic function of the mean, i.e., Var(y) = μ + φμ2.2 with and without normalization and blocking factors. We believe this work will be useful to others in analyzing and interpreting similar data.Our goal in the present work was to characterize the mean-variance relationship in mRNA Seq data in order to guide the choice of distributional assumptions. We first evaluated technical variability in gene-level counts to ensure consistency with what others have reported. Next, we evaluated the variance structure between biological replicates within a treatment group, considering the functions Var(y) = μ, kμ, and μ + φμTwenty five study subjects representing the extremes of the humoral immune responses to rubella vaccine (12 high antibody responders with a median titer of 145 IU/mL and 13 low responders with a median titer of 10 IU/mL) were selected from a large population-based, age-stratified random sample of 738 healthy children and young adults (age 11 to 19 years), from Olmsted County, Minnesota. Clinical and demographic characteristics of the population based sample have been previously reported [Subjects’ PBMC  were thawed and stimulated (or left unstimulated) with live rubella virus . Total RNA was extracted from stabilized cells using RNeasy Plus mini kit . RNA concentration and quality were assessed by Nano Chip kit analysis on an Agilent 2100 Bioanalyzer . Fifty samples from 25 subjects were completed for culture, RNA extraction and RNA quality control with adequate concentration and purity (lack of DNA contamination), as well as good RNA integrity and lack of RNA degradation.Libraries were prepared using the mRNA-Seq Sample Prep Kit  following the manufacturer’s instructions. Briefly, polyadenylated RNA was isolated from 1 μg of total RNA using two rounds of hybridization to oligo-dT magnetic beads. The mRNA samples were chemically fragmented, reverse transcribed and converted into double stranded cDNA. Unique Illumina adaptors were ligated to the DNA fragments after end repair (to produce blunt ends) and A-base tailing. Fragments of approximately 200 bp were gel purified and amplified by PCR. The libraries were validated and quantified on an Agilent 2100 Bioanalyzer  using DNA 1000 Chip kits. Sequencing was carried out on the Genome Analyzer GAIIx . Samples were sequenced as single end reads using Illumina’s Single Read Cluster Generation kit (v2) and 51 Cycle SBS Sequencing Kit (v3) following the manufacturer’s instructions.The first five flow cells were processed using Sequencing Control Studio (SCS) v 2.01 and the last eight flow cells were processed with SCS v 2.4 which allowed for higher cluster densities and higher pass filter rates. The images from the sequencing cycles were processed using the Illumina Pipeline Software v1.5. Specifically, images were converted to signal intensities using Illumina Pipeline’s FireCrest program. Base calling from intensity values was performed, and the quality scores for every base were calculated using the Bustard program. Illumina’s alignment tool, ELAND, was used to align the sequence reads to genome build 36 and exon junction databases. Illumina’s CASAVA tool version 1.0 was used to summarize the alignment results using only reads that mapped to a unique genome location and CASAVA results were imported into Genome Studio to generate the count tables for genes, exons, and exon-junctions. Sequencing pass/fail quality was determined by cluster densities, percent of clusters passing filters, percent of reads aligning to the reference, and percent error rate of the alignment.Specimens were randomly allocated to flow cells and lanes as follows Figure A. First,μ. The OD Poisson assumes the variance increases as a linear function of the mean, kμ, where k is a constant and μ is the true mean. The NB distribution assumes the variance increases as a quadratic function of the mean as μ + φμ2, where φ is a constant.The endpoint used for analysis was total reads or counts per gene; for the analysis of technical variation this is counts per lane while for biological variation this is counts summed over two technical replicate lanes. We evaluated the suitability of the Poisson, OD Poisson, and NB assumptions for modeling biological variability. The Poisson distribution assumes variance is equal to the mean i indexes n samples, y is the observed count, n-p degrees of freedom, where n is the sample size and p is the number of model parameters. While GOF statistics are a rather crude measure of how well a model fits, the magnitude of changes observed here are informative. We verified that the asymptotic assumptions were reasonable with the present sample size in simulated NB data  was assessed via quantile-quantile (QQ) plots of per-gene Pearson statistics eviously . Here, ip = 1 model degree of freedom.The generalized linear model (GLM) framework was used to fit per-gene models to test for differential expression between high and low response groups using the log link function . The mosth percentile count per lane-pair as a normalization constant [p = 13), lane-pair (p = 4) or library preparation batch (p = 6) as blocking factors. These blocking factors are potential sources of systematic non-biological variation in the experiment. There may be global shifts in counts due to flow cell, lane position on the flow cell such as middle versus edge, or PCR batch effects. Lastly, per-gene, local and global variance parameter estimation strategies were evaluated.Model fits were evaluated with no normalization, with total count per lane-pair, or with 75constant . In addiφ. Per-gene estimates were estimated within the glm.nb function call in the MASS package on a per-gene basis. Global and local (moderated) estimates of φ were computed with the edgeR package [All statistical computing was performed in R . The glm package -16 in R. package  and is s package . The deghttp://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?token=nxahvuioqmkwwzg&acc=GSE29022.Convergence rates were excellent for all models, with the worst case being non-convergence for four genes when a blocking factor was included in the model. The data have been deposited in the Gene Expression Omnibus and are available  via the following link: All 25 study subjects were female Caucasians to minimize variation. Median rubella-specific antibody response in the 12 high response subjects was 145 IU/ml  and in the 13 low response subjects was 10 IU/ml  .Figure At least one count was observed for 17,337 genes. Total counts per lane ranged from 3.7 million to 10.7 million Figure A. The wiWe assessed technical variation as the variation between the same specimen pipetted onto two lanes of a flow cell. Technical reproducibility in these data was good as demonstrated by scatter and minus versus average (MVA) plots  of approximately 2 and extending to approximately 4.5 on the horizontal axis  that the relationship, i.e. the precise multiplier 0 Figure C, G. To 0 Figure D, H. Eig5 Figure B. Note ts Figure B, we foun Figure A. SecondAs in Bullard et al. , we founth percentile offset was included, there was no clear relationship between flow cell effect estimates and run order , had only a minor impact on the distributions (data not shown). The GOF statistics for genes averaging less than 5 counts per subject were distributed throughout the range of GOF statistics  or largest  GOF statistics when using NB distributional assumptions with local variance estimate and no blocking factorsWe set out to evaluate technical, biological, and experimental variation in gene expression measured by mRNA-Seq counts from n = 25 subjects. Technical variation in these data were in keeping with Poisson distributional assumptions in general as has been reported by some -5, while2, the square root of φ corresponds to the subject-to-subject CV of the Gamma distributed Poisson mean parameters. The CV corresponding to the global estimate of φ for the data presented herein is 36%. We have observed a CV of approximately 9% for technical variation in genetically similar rats and 22% for biological replicates in genetically similar rats (data not shown). This is in keeping with the expectation that biological variation is larger than technical variation, and human variation is larger than genetically inbred animal model variation.Over-dispersion, i.e., variance larger than the mean, is a common phenomenon in observed count data . Others There are several potential sources of experimental variation in these studies including PCR library preparation batch, flow cell, lane, and for large studies, machine and software upgrades. Some effects can be addressed through normalization while others must be modeled directly. We found that normalization strategy had little impact on GOF statistics. Bullard et al.  reportedBullard et al. found experimental variation due to library PCR preparation batch to be greater than that due to flow cell . We founEstimation of the over-dispersion parameter has been the subject of much research; see for example the summary in . While tOur study had several strengths and limitations. We reported on technical and biological variation in mRNA-Seq data from a relatively large sample set and provide valuable insight into biological variation that will be useful to many researchers. The data herein were from true human biological replicates rather than contrived cell line replicates. We expect that the conclusion of a quadratic mean-variance relationship for biological replication will extend to other experimental settings. However, the precise estimates of over-dispersion are expected to be study-specific; it is plausible they would be smaller in inbred mouse models, smaller yet in cell lines. The present study was not designed to assess bias in estimating gene expression, fold-changes or sensitivity and specificity of fold-change detection. While the modeling strategy utilized does not account for the degrees of freedom used in estimating the dispersion parameter, thousands of data points are used in this estimation, so the estimate should be very stable and precise . UnfortuWe found that the within-gene variance structure is over-dispersed relative to the Poisson distribution. As a result, hypothesis tests based on Poisson distributional assumptions will be too liberal (reject more often than they should) and power estimates based on these assumptions will be over-estimated for most genes, i.e., sample sizes will be too small for the estimated power. Local estimates -16 of thThe authors wish to declare that GAP is the chair of a data safety monitoring board for Merck for non-rubella novel vaccines in clinical trials.ALO helped design the sequencing study, conceived the statistical questions, directed the statistical work and wrote the manuscript. BMB helped refine the study questions, performed all computing and participated in critical interpretation of the data. DEG helped design the sequencing study, helped direct the statistical computing, helped refine the study questions and participated in critical interpretation of the data. GAP helped design the sequencing study. TMT participated in critical interpretation of the data. All authors read and approved the final manuscript.Figure S1. Evaluation of asymptotic GOF distributional assumptions. QQ plot of GOF statistics from simulated null  NB data. Data for genes were simulated with mean equal to the mean vector in the unstimulated data presented herein, dispersion parameter equal to the edgeR estimated moderated dispersion parameter values. GOF statistics were calculated for each gene as described in the methods, here using the sample mean and true dispersion parameter. Sample sizes of A) n = 1000 and B) n = 23 were simulated in order to understand whether the asymptotic chi square distribution was appropriate. The theoretical distributions are chi square with A) 999 degrees of freedom and B) 22 degrees of freedom. From the right hand tails we see that the observed distribution does not have values quite as extreme as those in the theoretical distribution. However, the observed distributions are very close to the theoretical distributions as demonstrated by most points lying on the identity line. We conclude that the chi-square distribution is approximately correct for the data presented herein. Additional fileFigure S2 – Technical reproducibility and functional form of bias. Counts were scaled by total lane counts. A) Representative scatter plot of technical replicate 1 versus technical replicate 2 for one subject. Spearman correlation was 0.9941 for this pair. Axes are on the log base 2 scale. B) MVA plot for the same pair of technical replicates. The vertical axis is difference between the counts in the two replicates on the log2 scale and the horizontal axis is the average of the two counts on the log2 scale; there is one point for each gene observed in at least one replicate. The shading indicates density of points in that area with darker shading representing higher density. If two replicates yielded identical results, all points would lie on the y = 0 horizontal line (indicated on the plots for reference). A locally weighted moving average smoother is indicated to demonstrate the average bias as a function of average count. Additional fileFigure S3 – Individual QQ plots assessing distribution of technical replicates. QQ plots for all 24 subjects for whom data was received assuming Poisson variation in pairs of technical replicates. Vertical axes indicate observed quantiles and horizontal axes indicate theoretical quantiles.Click here for fileR function to plot variance as a function of the mean.Click here for fileR function to create QQ plots of Pearson GOF statistics assuming the NB distribution.Click here for file


DNA microarray data are used to identify genes which could be considered prognostic markers. However, due to the limited sample size of each study, the signatures are unstable in terms of the composing genes and may be limited in terms of performances. It is therefore of great interest to integrate different studies, thus increasing sample size.In the past, several studies explored the issue of microarray data merging, but the arrival of new techniques and a focus on SVM based classification needed further investigation. We used distant metastasis prediction based on SVM attribute selection and classification to three breast cancer data sets.The results showed that breast cancer classification does not benefit from data merging, confirming the results found by other studies with different techniques. DNA microarray technology and expression profiles are the most suitable tools to investigate gene activity with respect to the progress of disease. Furthermore, they are useful for molecular classification of tumor types , for revHowever, the sample size of each study is usually too small with respect to the number of the genes in analysis to allow an accurate statistical evaluation. Therefore, some authors used to analyze different data coming from different experiments with the goal of increasing sample size and thus increasing the power of the study.This could be done in two ways: by meta-analysis ,7, whichTypically, the first transformation applied to expression data, referred to as normalization and summarization, removes non-biological variability between arrays  and extrHowever, the transformation procedure cannot reduce completely the systematic differences from different data sets. When combining data sets from different experiments, non-biological experimental variation or ''batch effects'' are carried over and therefore it is inappropriate to combine data sets without adjusting for batch effects ,12.The goal of this paper is to compare the performance of various data merging methods. Our strategy for biological comparison is to use microarray data with known phenotypes associated with specific gene sets (pathways).In literature, several techniques have recently been proposed for adjusting data for batch effects ,14. ManyWe used three breast cancer microarray data sets from three different studies in which all the samples came from lymph-node-negative patients who had not received adjuvant systemic treatment. We performed three pre-processing methods: Robust Multi-Chip Average , frozen For microarray data classification the methodologies involving feature selection and classification applied to SVM are proposed in a previous study .Variation attributable to batch effects before and after batch adjustment were identified using principal variation component analysis (PVCA) . The sucSubsequently, the three microarray datasets, processed in different ways, were examined for specific patterns of pathway deregulation with respect to clinical disease outcome. For this reason we used the most popular gene-set analysis method, Gene Set Enrichment Analysis (GSEA) .We directly merged the three microarray data sets, using the 22283 probe sets on Affymetrix HG-U133A microarray, to form an integrated data set in seven ways: RMA, Quantile/MBEI, RMA - ComBat, Quantile/MBEI-ComBat, RMA - Z-Score and Quantile/MBEI - Z-Score, frozenRMA. The integrated data set consisted of 111 samples with distant metastases and 394 samples free of distant metastases, randomly divided into training and testing sets but respecting the proportions of the complete dataset. We evaluated the classification performance using precision and recall of class 1 because of its clinical significance. Table Batch effects are present in microarray experiments when data are combined from different studies. To assess the quantity of batch effect and to compare the data merging methods Combat, ZScore and fRMA, we performed a novel hybrid approach known as principal variance component analysis.Principal Variance Component Analysis (PVCA) integrates two methods: principal components analysis (PCA) finds low dimensional linear combinations of data with maximal variability and variance components analysis (VCA) attributes and partitions variability into known sources via a classical random effects model.The first step is to obtain the covariance/correlation matrix of the microarray expression data matrix. Secondly, PCA is applied to the correlation matrix and once the number of principal components is determined, a variance component model is fitted separately to each of these principal components. The variation in each principal component is weighted by its eigenvalue from PCA, and the resulting value represents the overall variation explained by that component.The PVCA revealed that batch effects explained 22.4% of the overall variation in the RMA data Figure  and 32,3After applying ComBat Figure  and Z-ScTo assess the removal of microarray bias effect across data sets, Principal Component Analysis (PCA) was applied to the data sets after the application of data merging methods. The aim was to reveal intermixing of samples from different datasets before and after adjustment. The results of these approaches Figure  demonstrAgain, fRMA seemed to be unable to adjust the combination among the three datasets.The results of hierarchical clustering analyses of class 1 before and after batch adjustments are presented in Figure After batch adjustment of the RMA dataset Figure  and the The GSE1121 samples clustered together more sharply than the GSE2990 and the Foekens samples which created overlapping clusters.Normalized Mutual Information (NMI)  between As previously described, two separated methods, SAM and RFE, were used to identify differentially expressed probes and to show the validation of RFE as feature selection in the training step of the classification.SAM resulted in 204, 289, 166, 197, 257, 197 and 210 differentially expressed genes for the RMA, CB-RMA, ZS-RMA, MBEI, CB-MBEI, ZS-MBEI and fRMA respectively.Table A total of 50 common probes were found from SAM and RFE comparison. Most probes were successfully identify by RMA-Combat. None was found by fRMA.These results were analyzed by fisher's exact test to examine the significance of overlapping between the two gene selection algorithms. After correction for multiple testing by the Benjamini-Hochberg standard false discovery rate correction, we found that it could not be excluded that the overlappings were derived by chance for all but the fRMA dataset, where the test was positive for the "less" alternative. This result indicates that the frozen RMA normalization hindered RFE from finding biologically relevant genes, although SAM reported a number of genes comparable to the other normalization methods. With the "greater" alternative, every merging technique showed a pvalue >> 0.05, showing that the number of overlapping genes between FRE and SAM is never greater than expected by chance.We explored the performance of various pre-processing and data merging techniques by using biological pathway-based analysis and determining whether a group of differentially expressed genes is enriched for a particular set.Here, we utilized a powerful analytical method called Gene Set Enrichment Analysis (GSEA) focusing on several biological pathways: EGF, Stathmin, HER2, BRCA1,Homologous Recombination, which are associated with breast cancer progression.The use of different methods of data merging and preprocessing can lead to a problem of poor congruency among datasets. To compare the ability of the different methods we performed GSEA algorithm showing the heat map, enrichment scores and corresponding p-values .All probe sets were pre-ranked using SNR  with respect to their correlation with distant metastasis-free survival.The signal to noise ratio (SNR) detects the expression patterns with a maximal difference in mean expression between two groups and minimal variation of expression within each group.The order probe set list was used as the GSEA input for pathway analysis.In a heat map, expression values are represented as colors, where the range of colors  shows the range of expression values . The light blue and dark blue bars reflect genes that are positively associated with DMFS , indicating a higher expression in tumors without metastatic capability. The red bars reflect genes that are negatively associated with DMFS, indicative of higher expression in tumors with metastatic capability. The heat map of data sets that are pre-processed by robust multi-array average (RMA) and MBEI and merged by fRMA are presented in Figures Considering the expression level of the genes reported in each considered pathway, it can be observed that applying ComBat after RMA Figure  or MBEI The heat map of RMA and MBEI data identified two over-regulated gene sets, EGF and Stathmin Pathway, indicative of higher expression in tumors with metastatic capability and three up-regulated gene sets, Homologous Recombination, BRCA1 and HER2 pathway, indicating a higher expression in tumors without metastasis.Gene Set Enrichment Analysis computes an enrichment score (ES) for a given gene set which reflects the degree to which a gene set is over-represented at the extremes of the entire ranked list of genes.A positive ES suggests gene set enrichment at the top of ranked list; a negative ES suggests gene set enrichment at the bottom of the ranked list.The nominal p-value estimates the statistical significance of the enrichment score for a single gene set.We found Tables , 4 that Overall, GSEA with RMA normalization identified two gene sets, Homologous Recombination and BRCA1 pathway, as statistically significant at p<0.05 whereas GSEA with MBEI normalization detected Homologous Recombination and EGF pathway with the same p-value.For all gene sets, p-values obtained by RMA normalization were generally smaller than the p-values of corresponding gene sets obtained by MBEI normalization.With Combat data, GSEA identified, although with higher significance, the same gene sets derived from RMA or MBEI data alone.Comparison of different data merging techniques confirmed that ZScore shows more variation than MBEI or RMA data alone.fRMA revealed different gene sets regulated with a higher p-value than ZScore and Combat. A comparative representation of the different evaluation and verification methods is presented in Figure In this study we have presented the results of the classification of breast cancer microarray data, with respect to the event of distant metastasis free survival in terms of recall and precision. The results show very low classification performances. This is explained in part by heterogeneity of the data in terms of tumor grade, tumor size, histopathological tumor type and progesterone and estrogen receptor that might negatively influence the prediction. In the past, different classifiers were built for patients showing different values for these features with successful results .The F-2 scores in Figure Z-score performed better than Combat with both summarization techniques and the worst results were achieved by fRMA.The LDO validation is representative of a clinical application where batches of patients are analyzed after the classifier has been built on previous batches. In this context of practical interest the merged datasets show some advantages compared to non-merged datasets.Figure The difference between Stratified Percentage Fold and weighted LDOCV average is very sharp in the MBEI pre-processed datasets showing that this method gets greater benefits from the merging algorithms. The comparison within the RMA processed datasets shows that the non-merged dataset has even higher performances than the ComBat and Z-score merged ones in stratified percentage folding.However, the merging procedure achieved some results, as shown by the PVCA and Clustering analysis, where both z-score and Combat datasets behaved better than non- merged ones. Combat and z-score did not show sharp differences with these techniques. When comparing the differences in the SVM versus PVCA/Clustering results, we can conclude that the merging algorithms are an effective tool, but should be handled with care when it comes to the next algorithm in the workflow pipeline.fRMA showed performances comparable to non-merged datasets also in the PVCA/Clustering case and our findings exclude it from being a good data merging algorithm even when compared with the simplest strategy of z-scoring.A comparative study of performances of Recursive Feature Elimination (RFE) with SAM has been given as an additional evaluation tool for the validation of RFE as feature selection.Also in this case we found an exception: SAM did not suffer from the fRMA normalization and reported a number of differentially expressed genes compared to the other techniques. Again in this case Combat outperformed z-score with a number of genes almost double.In the same step of gene selection, RFE showed results markedly different from SAM, and the number of common genes, equal to zero, is not derived from chance: fRMA hindered RFE from finding biologically relevant genes.The biological meanings of gene expression have been also analyzed in terms of enrichment analysis.Our objectives tested predefined gene sets for their association with breast cancer progression, assuming that gene expression changes can be identified at the level of co regulated gene sets rather than individual genes.The application of gene set analysis by GSEA was also useful in finding common biological pathway changes and in comparing different preprocessing and data merging methods.GSEA detected three gene sets, Homologous Recombination, BRCA1 and HER2 pathway, as significantly up-regulated versus two gene sets, EGF and Stathmin Pathway, which were over-regulated; although in many cases the same gene sets were identified as significant by various programs, in a direct comparison across MBEI and RMA normalization using breast cancer datasets, the p-values of RMA were lower than the respective p values obtained by MBEI Table , indicatAgain, fRMA found gene sets with lower significance than the others and Combat outperformed z-score, although the latter showed better results in terms of classification performances. In terms of pathway enrichment, the results of Combat merging are comparable to those of non-merged datasets.Overall, this study confirms the previous studies that did not show benefits of survival prediction with merged datasets as compared to individual data sets using linear methods . It alsoFurthermore, the analysis of gene expression level in specific pathways confirmed the better performance of ComBat with respect to Z-Score, and focusing on PVCA, fRMA was inaccurate in removing the batch effect from the data. This is evident when observing the graphical representation of data after PCAnalysis, hierarchical clustering and PVCA.The present study showed the difficulty of merging data from different datasets, even if they come from the same type of chip, due to the low accuracy even when using different approaches. This suggests that because of the low recall and precision of all methods, data merging does not seem to be the elective approach to combine samples in array analysis. Thus a better way to improve accurate signature from microarray datasets is to apply a meta-analysis rather than merging all raw data or developing algorithms that can leverage the effect of data merging, since we have demonstrated that it is algorithm-dependent.We applied pre-processing and data merging techniques to three breast cancer data sets: GSE11121, GSE2990 (Gene Expression Omnibus) and a dataset used by Foekens et al. in , containThree pre-processing methods were applied to microarray data to compute expression values from input CEL files: Robust Multi-array Average (RMA), Quantile normalization - Model-Based Expression Index (MBEI) and frozenRMA. This last method estimates batch effect directly from probe intensities. The other methods were integrated in an independent manner with two data merging techniques: 1) ComBat 2) Z-score. All computations were done using the free statistical software package R and DNA-Chip Analyzer (dChip).Processing Affymetrix expression arrays usually consists of three steps: background adjustment, normalization and summarization and, in this study, the data sets were processed in three ways Table .Before proceeding to the next analysis, it is necessary to detect and remove the batch effects. Here, the term "batch effect" refers to experimental variations of datasets generated by different labs.An Empirical Bayes method, called Combating Batch Effects when Combining Batches of Gene Expression Microarray Data (ComBat) and Z-Score were used to adjust the systematic difference of differently normalized data generated by the three different labs. The algorithm of Johnson et al. was implemented into the software package ComBat, which includes two empirical Bayes frameworks, one with parametric and one with non-parametric approach. With this algorithm, location and scale model parameters are specifically estimated by pooling information across genes in each batch to adjust for the batch effect parameter estimates toward the overall mean of the batch estimates.Each data set was alternatively standardized using a simple z-score transformation method and combined for analysis. In contrast to classic pre-processing and data merging techniques, we applied another pre-processing algorithm, Frozen Robust Multiarray Analysis (fRMA) which allowed us to analyze microarray in batches and then combine the data for analysis. fRMA without further adjustment for batch effects is similar to RMA when the data are analyzed as a single batch.This procedure led to seven differently-merged datasets: RMA without merging (RMA), RMA data merged by Combat (CB-RMA) and by z-score (ZS-RMA), MBEI without merging (MBEI), MBEI data merged by Combat (CB-MBEI) and by z-score (ZS-MBEI) and fRMA data (fRMA).After these steps, the above procedures were analyzed to extract a gene signature, in order to associate it with distant-metastasis-free survival (dmfs) discretized into two values . The datasets were unbalanced towards class 0, but from a clinical stand point, the cost of false negatives is higher than false positives: patients that should receive treatment may be neglected and not receive treatment. For this reason, the class 0 set were down-sampled until half spread.The training step applies a SVM based Recursive Feature Elimination (RFE) method ,32 for tThe models were validated using Leave-One-Out Cross Validation (LOOCV), Leave-Dataset-Out Cross Validation (LDOCV), Percentage Fold and Stratified Percentage Fold. The Leave-One-Out (or LOO) is a simple cross-validation. Each learning set is created by using all the samples except one, the test set being the sample left out.Leave-one-out cross validation is used in the field of machine learning to determine how accurately a learning algorithm will be able to predict data that it was not trained on. It creates all the possible training/test sets by using a single observation from the original sample as the testing data, and the remaining observations as the training data. LDOCV is very similar to LOOCV but it considers the single dataset rather than samples. Percentage Fold randomly divides the merged data set into training and testing sets, 66% and 34% respectively; the Stratified Percentage Fold splits each dataset by preserving the same percentage for training and testing sets.In this study we utilized PVCA to compute non biological experimental variation or "batch effects" carried over when we combined the three data sets from different experiments. The approach utilizes two data analysis methods: first, principal component analysis (PCA) is used to efficiently reduce data dimension while maintaining the majority of the variability in the data, and variance component analysis (VCA) fits a mixed linear model using factors of interest as random (or batch) effects and other variables (or covariates) to estimate and partition the total variability.Average linkage hierarchical cluster analysis was carried out using Mev software with a modified Pearson correlation as a similarity metric. The clustering on each dataset was performed using all the genes in the platform.The genes that exhibited little variation in their profile and which were not of interest were removed from data for the subsequent pathway analysis. Filtered datasets were also analyzed for statistically significant genes using the Significance Analysis of Microarray (SAM) algorithm . SAM is A comparative study of performances of Recursive Feature Elimination (RFE) with SAM was carried out as an additional evaluation tool.For further validation of different data merging and processing technique comparison, we analyzed specific pathways associated with breast cancer progression: EGF, Stathmin, HER2, BRCA1 and Homologous Recombination. The pathway database was compiled from the Kyoto Encyclopedia of Genes and Genomes (KEGG) and Biocarta. The GSEA algorithm, an established method in pathway enrichment analysis, was used. Enrichment analysis is an automated statistical technique to analyze and interpret large gene lists using a priori knowledge. The strength of gene regulation information is an important component of cancer classifiers, which have been proven to be able to leverage such information . A data The genes can be ordered in a rank list, according to their differential expression between the classes, and the goal of GSEA algorithm is to determine whether the members of specific pathways are randomly distributed throughout the ranked list or primarily found at the top or bottom. If a statistically significant number of genes from a specific pathway is present in the gene list, it may indicate that the biological pathway plays a role in the biological condition under study.The authors declare that they have no competing interests.VB, PP, MA and CC carried out the data merging and classification, clustering and SAM. VB, MA and CC carried out the PVCA, PCA and enrichment analysis. VB, ST, AP and PP conceived of the study and participated in its design and coordination. VB, PP, MA, CC and ST drafted the manuscript and then all the authors read and approved the final manuscript.


High-density oligonucleotide microarray is an appropriate technology for genomic analysis, and is particulary useful in the generation of transcriptional maps, ChIP-on-chip studies and re-sequencing of the genome.Transcriptome analysis of tiling microarray data facilitates the discovery of novel transcripts and the assessment of differential expression in diverse experimental conditions. Although new technologies such as next-generation sequencing have appeared, microarrays might still be useful for the study of small genomes or for the analysis of genomic regions with custom microarrays due to their lower price and good accuracy in expression quantification.Saccharomyces cerevisiae dataset and it has been compared with two well-known algorithms: pseudo-median sliding window (PMSW) and the structural change model (SCM). As a proof-of-principle, we applied the ZCL algorithm to the analysis of the custom tiling microarray hybridization results of a S. aureus mutant deficient in the sigma B transcription factor. The challenge was to identify those transcripts whose expression decreases in the absence of sigma B.Here, we propose a novel wavelet-based method, named ZCL (zero-crossing lines), for the combined denoising and segmentation of tiling signals. The denoising is performed with the classical SUREshrink method and the detection of transcriptionally active regions is based on the computation of the Continuous Wavelet Transform (CWT). In particular, the detection of the transitions is implemented as the thresholding of the zero-crossing lines. The algorithm described has been applied to the public S. aureus dataset have demonstrated the valuable utility of this novel device to the biological analysis of the S. aureus transcriptome.The proposed method archives the best performance in terms of positive predictive value (PPV) while its sensitivity is similar to the other algorithms used for the comparison. The computation time needed to process the transcriptional signals is low as compared with model-based methods and in the same range to those based on the use of filters. Automatic parameter selection has been incorporated and moreover, it can be easily adapted to a parallel implementation. We can conclude that the proposed method is well suited for the analysis of tiling signals, in which transcriptional activity is often hidden in the noise. Finally, the quantification and differential expression analysis of  The complete deciphering of the information contained in the genome would be helpful to improve our understanding of the biological processes occurring in living organisms. High-density oligonucleotide-based whole-genome microarray is an extensively used technology to detect the expression of all RNA species including protein coding RNAs and non-coding RNAs. It is particularly suitable for the analysis of whole small-sized genomes such as those corresponding to bacteria. For these organisms high resolution can be achieved with the microarrays currently provided by the manufactures.Applications of tiling array technology include the generation of transcriptional maps and annotations of genomes, the identification of transcription factor binding sites, the analysis of alternative splicing events, the analysis of methylation states, the discovery of genotyping and polymorphism, and the re-sequentation of genomes .The emerging high-throughput next generation DNA sequencing (NGS) technologies  have revThe analysis of a tiling microarray experiment starts with a two-step process that generates a discrete signal. First, the DNA or RNA samples are hybridized in the custom designed tiling array. Second, for each probe, the raw intensities are converted to a score . The resThe workflow shown in Figure Transcriptome analysis refers to the detection of segments where the noisy tiling signal is constant. The start and end points of these segments correspond to transcript start and end sites. Several approaches have been deployed in the segmentation of tiling signals: pseudo-median or Hodges-Lehmann estimator ,7, localSaccharomyces Cerevisiae dataset to validate our analytical approach. The novel identification algorithm was compared with two well-known methods: pseudo-median sliding window (PMSW) and structural change model (SCM). The absence of a biologically validated ground truth to evaluate the resulting segmentations prevent the use of specificity and sensitivity as performance metrics. Consequently, the evaluation has been made in terms of positive predictive value (PPV), sensitivity and computation time. We also evaluated the segmentation quality resulting from the combination of the TARs detected by several of the methods under study.Wavelet analysis using the Discrete Wavelet Transform (DWT)  has demoS. aureus strain deficient in the sigma B transcription factor. SigB has been shown to be involved in the stress response to different stimuli, the regulation of sarA, sarH1, and agr that control a wide array of virulence factors, biofilm formation, the ability of S. aureus to bind to various host-cell matrix proteins such as fibrinogen and fibronectin, and in the development of resistance to the antibiotics methicillin and teicoplanin [We also used this algorithm for the identification of the subset of transcripts whose expression decreases in a coplanin -26.We applied the segmentation methods to this high quality dataset and we have demonstrated its usefulness for the analysis of the tiling array derived transcriptome map. The results demonstrate that ZCL not only allows a rapid identification of the transcripst based on the segmentation procedure but also a more accurate estimation of the expression level of each transcript.R/Bioconductor[Rwave, wavethresh and wmtsa have been used for wavelet analysis. All the R functions described are available as Supplementary Material  have been implemented using the statistical language conductor. The CRAS. cerevisiae was developed. It contains 6.5 million probes and interrogates both strands of the full genomic sequence with 25-mer probes tiled at an average of 8 nucleotide intervals on each strand and 4 nucleotide tile offset between strands. The first-strand cDNA was synthesized using random primers from poly(A) and total RNA. A set of genomic DNA was also hybridized for normalization purposes [The dataset is described in . An oligpurposes . Their apurposes . All datStaphylococcus aureus custom tiling microarray (NA-Staph-b520729F) was designed in collaboration with Affymetrix . Specifically, the microarray (format 49-7875 with 11 μm features) contains a total of 522,406 probes, divided into two parts. The first part corresponds to the tiling array containing a total of 384,932 probes (25-mer), which are further divided into eight sets. The set used in our analysis covers both strands of the S. aureus NCTC 8325 genome . Each 25-mer probe was tiled each 14-nt across the whole genome, resulting in 11-nt overlaps and a 7-nt tile offset between strands. The microarray design has been deposited in the ArrayExpress Archive at EMBL-EBI (http://www.ebi.ac.uk/microarray-as/ae/), ArrayExpress accesion no. A-AFFY-165.The μg of RNAs extracted from bacterial strains grown until exponential phase (OD600nm = 0.8) were reverse transcribed using SuperScript II reverse transcriptase (Invitrogen Life Technologies). They were processed following the protocol of the Affymetrix GeneChip Expression Analysis Technical Manual (P/N 702232 Rev. 2) in the presence of 6 ng/ml Actinomycin D to avoid spurious second-strand cDNA synthesis during the reverse transcription reaction [lys, phe, thr, trp, dap genes were spiked into sample RNA as a control for the labeling and hybridization steps. cDNA was digested by DNase I (PIERCE) in 10X DNAse I buffer (USB-Affymetrix) and the size of digestion products was analyzed in the Agilent Bioanalyser 2100 using RNA Nano LabChips to ensure that the fragmentation resulted in a majority of products in the range of 50 to 200 base-pairs. The fragmented cDNA were then biotinylated using terminal deoxynucleotidyl transferase (Promega) and the GeneChip DNA labeling reagent (Affymetrix) following the manufacturer’s recommendations. Biotinylated cDNA (5 μg per array) were hybridized for 16 hours according to the Affymetrix protocol in a total volume of 200 μl per hybridization chamber. Following incubation, the arrays were washed and stained in the Fluidics station 450 (Affymetrix) using the protocol FS450_0005. The arrays were then scanned using the GeneChip scanner 3000 (Affymetrix). The intensity signals of each probe cell were computed by the GeneChip operating software (GCOS) and stored in cell intensity files (.CEL extension) before preprocessing and analysis. All microarray data described in this study have been deposited in the ArrayExpress Archive at EMBL-EBI (http://www.ebi.ac.uk/microarray-as/ae/), ArrayExpress accesion no. E-MEXP-2778.Before cDNA synthesis, RNA integrity from each sample was confirmed on Agilent RNA Nano LabChips (Agilent Technologies). 10 reaction . Sense RS. cerevisiae strain S288c  as provided in the package davidTiling of Bioconductor. Available data correspond to 3 replicates of poly(A), 2 replicates of total RNA and 3 replicates of genomic DNA. The CEL files were read and the normalized signals (poly(A) and total RNA) were obtained using Equation 4. The analysis steps  were performed on the poly(A) signal as it showed an improved hybridization quality [tilingArray package functions to obtain equally-spaced samples. Other resampling methods can be applied without loss of generality.The annotation of the PM probe sequences was obtained with the alignment to the genome sequence of  quality . Once thS. aureus microarray are provided in the ArrayExpress database (A-AFFY-165). The microarrays of the experiment correspond to three replicates of genomic DNA, three replicates of RNA of the 15981 wild-type strain, and three replicates of the sigB deletion. All the preprocessing steps were performed as previosly described for S. cerevisiae dataset.The annotation files for S. cerevisiae , a quantitative measure of its performance. In order to compare the results obtained with those from Huber et al.  based onThe SNR was computed as σcalculated as the average of the differences between 0.975 and 0.025 quantiles of the data within each of the control regions. Namely, with the noise standard deviation r counts over the different regions and QN refers to the standard normal distribution % with Donoho’s method and 30.63%with SUREShrink approach), especially when the SUREShrink denoising is applied. This could be due to the elimination of most part of the non-Gaussian noise component and the consequent reduction in the estimated variance. In the rest of the paper, the SUREShrink is the method applied for denoising. where the symbol ution N0,. Table 1S. cerevisiae is shown in Figure A descriptive example of the denoising and segmentation for segmentZCL  implements the whole segmentation procedure.The TAR start and end positions were defined as the transition locations for which the difference between the mean intensity of neighboring segments is greater than 10% of the dynamic range of the tiling signal. Moreover, the inspection of the intensity histogram of chromosome 1 forward strand was used to set the minimum normalized transcription level value to −2. The same parameters were adopted to process the other strands of the organism. The R function S. aureus signal of 15981 and sigB mutant were segmented using ZCL and fixing only the number of scales to 100. No denoising was applied prior to the segmentation. The figure represent a fragment of the signals from position 2.1 Mb to 2.3 Mb. In Additional file Another representative example of segmentation results is given in Figure Tilescope pipeline [The results from the ZCL segmentation were compared to those obtained with PSMW  and SCM pipeline  was impltilingArray package of Bioconductor computes a globally optimal set of parameters for segmentations of increasing number of segments.Huber’s method is based on the structural change model (SCM). The SCM model ,16 is usTP) divided by the total number of probes in the annotated regions : Sensitivity=TP/(TP + FN). The PPV is defined as the number of probes in the detected TARs that overlap with annotated regions (TP) divided by the total number of probes in the detected TARs : PPV=TP/(TP + FP). A sensitivity of 100% is not expected since in any given tissue or cell line at any given experimental condition, not all known genes will be expressed. Also, a PPV of 100% is not expected since an accurate and complete gene annotation is not available [Due to the lack of a biologically validated ground truth to evaluate the outputs, we compared the methods in terms of two metrics, sensitivity and positive predictive value (PPV) at probe-level. We define sensitivity as the number of probes in the detected TARs that overlap with annotated regions . From the annotated probes, 63.12% are detected by all methods, while only 11.85% of the probes are not detected by either of them. This means that 88.15% of the annotated probes are detected by at least one of the methods. The reverse strand contains 11866 annotated probes (17.90% of probes located in this strand), from which 19.74% are considered part of a TAR by all the methods and 28.35% are true negative probes. In this strand, 51.41% of the annotated probes are included in a TAR by any method while only 14.35% are never detected. In other words, 85.65% of the probes in the strand are detected by at least one algorithm. In light of this outcome, we considered it worthwhile to evaluate if the combination of results computed with the different methods would improve the performance of the segmentation.S. cerevisiae chromosome 1. As individual methods, ZCL gives the best PPV and the best sensitivity for the reverse strand. The best performing combination considering a compromise between PPV and sensitivity is given by the majority voting system.We evaluated the improvement in performance obtained by the combination of the different segmentations. We chose different strategies to define the sets (intersection of two or three methods and majority voting system). After a decision is taken on the candidates, TARs are constructed to create the transcriptional map. In Table S. cerevisiae analyses were executed in an Intel(R) Xeon(R) processor server  with 32 Gb installed memory running Red Hat Enterprise Linux AS release 4 and R 2.13.0. Computing times needed to process each chromosome strand with the described methods are shown in Figure S. aureus. Segmentation results for S. aureus are summarized in Table Comparative segmentation analysis using ZCL and PMSW and SCM algorithms was applied for the hybridization data obtained with a custom designed Affymetrix tiling array of affxparser, affy and limma of Bioconductor for CDF (chip definition file) generation, normalization and differential expression analysis.The most frequent transcriptional analysis is the detection of genes that have changed their expression in the conditions under study . As sigma B affects the expression of more than one hundred genes, we decided to test whether it is possible to use the intensity of all the probes included in each detected TAR with the ZCL segmentation procedure to calculate the expression level of the transcript in a particular environmental condition. In order to carry out this analysis using tiling microarrays we need to compress the intensity of all the probes included in each detected TAR into one value. Standard methods for microarray normalization can be applied, for example RMA (Robust Multichip Average) algorithm in the case of Affymetrix microarrays . This prS. aureus annotation, we found previously described alterations in several genes [σB-regulated genes, as the alkaline shock protein 23 (asp23) [lysP) [nuc) [aur) [α-hemolysin (hla) [We introduced a simple analytical tool to be used independently of the microarray platform to measure the gene expression level based on the median value of the TAR probe intensities. We calculated this value for each wild-type and sigmaB mutant sample. We applied a statistical analysis (t-test) to obtained the p-value associated with the expression change taking into account the biological variability of the samples. Considering well-defined TARs in the al genes . In Figu asp23) ,23 and l ,23 and ) [lysP) , althougP) [nuc) , the zinc) [aur) ,25 and tin (hla) ,26, the Caulobacter crescentus[Escherichia coli and [Listeria monocytogenes[Transcriptomics is a powerful technology for the study of gene structures and RNA-based regulation in any organism. Genome-wide transcriptome analysis of prokaryotes can be carried out with any of these two techniques: RNA-seq and genomic tiling arrays . High-rerescentus, Eschericoli and , Listericytogenes.S. cerevisiae. Our denoising results show an increase in the SNR of the filtered signal with respect to Huber’s method [In this paper, we propose a combined WT-based method for the denoising and segmentation of tiling signals. For illustrative and evaluative purposes, we applied the proposed analysis to the public s method . We beliOur segmentation algorithm (ZCL) calculates all the possible break points based on the zero-crossing lines of the second derivative of the Gaussian wavelet. The results show that our method achieves the best compromise between accuracy  and computation time. The R code provided can be used to apply our algorithm as well as to combine the resulting segmentation with other methods as PMSW and SCM.S. aureus genome, publicly available in the ArrayExpress database (accession number A-AFFY-165). This platform has been used for the comparison of the gene expression pattern of the S. aureus 15981 wild type and its isogenic sigB mutant. We selected this mutant because it is one of the most study staphylococcal regulatory factors and consequenctly it was a useful gold standard to compare the accuracy of our algorithms. The relevance of the segmentation results comes from the fact that a correct analysis of the tiling signals could improve the matching between the probes and the corresponding transcriptional units. In particular, it could help to more precisely localize the start and end transcription sites or even, include units that are not annotated in the current genome definition.We also designed a new tiling microarray for the analysis of nuc, aur, hla) and down-regulated  genes in sigB mutant were verified.Once the TARs are properly detected, differentially expressed transcripts can be identified by well-known methods (such as Linear Models for Microarray Data (LIMMA) ) with a In conclusion, we present a novel method for denoising and segmentation of tiling microarray signals based on wavelet multiresolution analysis that outperforms previous methods in terms of SNR, positive predictive value and computation time. The R code that implements the method is given as supplementary material and can be easily adapted to a parallel computing schema. Also, we have introduced the possibility of combining the results of ZCL with those obtained with other two well-known approaches (PMSW and SCM) for the segmentation of tiling signals.s(x)is defined as [The CWT of a continuous signal fined as ψ(x) is the mother wavelet, ψ∗((b−x)/a) is the complex conjugated, scaled and translated wavelet and CWT is the 2D matrix of wavelet coefficients. The continuous input signal s(x) interpolates the discrete input samples sk,k=1,…,nwhere n is the length of the signal.where ψ rescaled by a factor a. For an 1D input signal, the result is a 2D description of the signal with respect to the position b and scale a and shifted by b. The scale a is inversely proportional to the central frequency of the dilated wavelet ψa=ψ(x/a), which is typically a bandpass function; b represents the position location at which we analyze the signal. The larger the scale a, the wider the analyzing function ψa, and hence the smaller the corresponding analyzed frequency. The output value is maximized when the frequency of the signal matches that of the corresponding dilated wavelet. The CWT computation for arbitrary scales can be easily adapted to a parallel implementation with a linear computational complexity [The CWT can be interpreted as the correlation of the input signal with a position reversed version of mplexity .a=2i and time shifts b=2ik, Mallat’s fast wavelet algorithm  uses theerred to .sk at position k proportional to the transcription level in the reference genome [The analysis starts with background correction and quantile normalization as describe by the RMA algorithm . Next, we genome n is the number of RNA samples and m is the number of DNA samples.where a=2. This method is composed of three steps: (i) calculate the DWT of the tiling signal sk at scale a=2; (ii) threshold the wavelet coefficients; (iii) compute the inverse wavelet transform of the thresholded coefficients. A universal threshold, T, is proposed [One of the most established methods of wavelet-based denoising was proposed by Donoho and Johnstone  and it iproposed  to removn is the length of s, σis the noise level and MAD is the estimated median absolute deviation in the first scale. An important issue is the selection of a suitable wavelet function. As the signal can be roughly approximated to a zero-order polynomial, a boxcar-like function such as the Haar wavelet gives a reasonable level of correlation  with the target signal.where jth subband are {xi:i=1,…,n}, we consider a soft thresholding procedure and apply Stein’s result. The quantity Another well established method of wavelet shrinkage is SUREShrink . This isT is the threshold and xi∧t=min(xiT). This estimator can be used to select a threshold: is an unbiased estimate of risk, where n the law of large numbers will ensure that TSURE will be almost the optimal threshold [For a large dimension hreshold .An important issue in signal processing is to define an appropriate representation able to compress most of the signal information into few representative features. Sharp variations in amplitude  are among the most meaningful features of a signal. For that reason, many segmentation algorithms rely on their detection. Previous studies have detected the peaks in mass spectrometry data using either the ridge lines  or the za as It has been previously shown that the position of multiscale sharp transitions can be obtained from the zero-crossings of the signal convolved with the Laplacian of a Gaussian . We defiθa is a Gaussian function dilated by a factor a. Since the wavelet transform can be represented as where we derive that s(x) is proportional to the second derivative of s(x)smoothed by θa(x). The zero-crossings of CWT(ab) correspond to the inflection points of s∗θa. The identification of transcript start and end sites is achieved by computation of the redundant CWT over a wide scale range followed by zero-crossing line detection and length thresholding. The chosen mother wavelet is the second derivative of a Gaussian. The redundancy of the CWT yields enhanced information on the position-scale localization of the features of interest  [Hence, the wavelet transform of sitions) .An illustrative example is given in Figure The candidates start and end sites detected as described in the previous section, are filtered to remove incorrect assignments. The purpose of this procedure is to filter those transitions that do not correspond to variations in signal intensity. For the generation of TARs we considered the signal transitions in which variation in intensity is at least 10% of the dynamic range of the analyzed signal. We also eliminate from the list of detected TAR all the start and end points that are not correctly paired off. We use the sign of the zero-crossing lines to separate start and end points and we match each start site with its corresponding end site. Finally, we define the minimum normalized intensity threshold required for the segments to be considered as transcriptional active regions. This value is calculated as the median of the signal intensity distribution, but this threshold can also be user-defined. In order to improve the definition of TARs, we cluster together consecutive segments for which the mean normalized intensity value is over the threshold.The authors declare that they have no competing interests.VS and AMB conceived the idea, developed the methods and implemented the software. ATA and IL design the NA-Staph-b520729F microarray and MU and ATA carried out the processing and hybridization of samples. ATA, IL and VS made the biological interpretation of the results. All authors participated in writing and revising the manuscript.R code: Segmentation and visualization functions. Implemented functions in R language to perform PMSW and SCM segmentation and the proposed wavelet-based method for denoising and segmentation. In addition, functions are provided for proper visualization of data, integration of analysis results and evaluation of the obtained transcriptional maps.Click here for fileR code: Segmentation analysis of S. cerevisiae. R script for segmentation of the S. cerevisiae dataset and the generation of the figures included in the manuscript.Click here for fileR code: Segmentation analysis of S. aureus). R script for the segmentation of the S. aureus dataset and the generation of the figures included in the manuscript.Click here for fileFigure S1. Visualization of S. aureus tiling microarray signal along 200 kb of NCTC8325 genome. Each dot corresponds to a probe of the forward strand (top) and reverse strand (bottom) for NCTC8325 wild-type normalized signal. Superimposed pulse signal represents the segmentation obtained using PMSW method. The parameters of the analysis are described in the Results and discussion section of the manuscript.Click here for fileFigure S2. Visualization of S. aureus tiling microarray signal along 200 kb of NCTC8325 genome. Each dot corresponds to a probe of the forward strand (top) and reverse strand (bottom) for sigmaB mutant normalized signal. Superimposed pulse signal represents the segmentation obtained using PMSW method. The parameters of the analysis are described in the Results and discussion section of the manuscript.Click here for fileFigure S3. Visualization of S. aureus tiling microarray signal along 200 kb of NCTC8325 genome. Each dot corresponds to a probe of the forward strand (top) and reverse strand (bottom) for NCTC8325 wild-type normalized signal. Superimposed pulse signal represents the segmentation obtained using SCM method. The parameters of the analysis are described in the Results and discussion section of the manuscript.Click here for fileFigure S4. Visualization of S. aureus tiling microarray signal along 200 kb of NCTC8325 genome. Each dot corresponds to a probe of the forward strand (top) and reverse strand (bottom) for sigmaB mutant normalized signal. Superimposed pulse signal represents the segmentation obtained using SCM method. The parameters of the analysis are described in the Results and discussion section of the manuscript.Click here for file