Several preprocessing methods are available for the analysis of Affymetrix Genechips arrays. The most popular algorithms analyze the measured fluorescence intensities with statistical methods. Here we focus on a novel algorithm, AffyILM, available from Bioconductor, which relies on inputs from hybridization thermodynamics and uses an extended Langmuir isotherm model to compute transcript concentrations. These concentrations are then employed in the statistical analysis. We compared the performance of AffyILM and other traditional methods both in the old and in the newest generation of GeneChips.Tissue mixture and Latin Square datasets (provided by Affymetrix) were used to assess the performances of the differential expression analysis depending on the preprocessing strategy. A correlation analysis conducted on the tissue mixture data reveals that the median-polish algorithm allows to best summarize AffyILM concentrations computed at the probe-level. Those correlation results are equivalent to the best correlations observed using popular preprocessing methods relying on intensity values. The performances of each tested preprocessing algorithm were quantified using the Latin Square HG-U133A dataset, thanks to the comparison of differential analysis results with the list of spiked genes. The figures of merit generated illustrates that the performances associated to AffyILM(medianpolish), inferred from the present statistical analysis, are comparable to the best performing strategies previously reported.Converting probe intensities to estimates of target concentrations prior to the statistical analysis, AffyILM(medianpolish) is one of the best performing strategy currently available. Using hybridization theory, probe-level estimates of target concentrations should be identically distributed. In the future, a probe-level multivariate analysis of the concentrations should be compared to the univariate analysis of probe-set summarized expression data. Those studies allowed to compare samples between healthy and pathologic tissues or cell-types, to monitor the effects of several drugs, and to describe sets of genes based on their implication in several biological processes -9. As se binding ,11. The  binding ,11. MM p binding . Note thWhen comparing several samples, algorithms need to take discrepancies between arrays into account, such as a slight difference in the amount of hybridized material . The study of probe intensities thus traditionally implies a normalization step and/or the design of an appropriate statistical model. From a statistical point of view, several probes targeting the same transcript would ideally be jointly analyzed, using a multifactorial procedure - like the ANOVA-2 procedure - to be able to compare the expression of a transcript between two conditions , and several samples (replicates). However, the probe-specific signal are not identically distributed, so that the iid requirement of ANOVA-2 procedures is not met. Discrepancies between PM probes targeting the same sequence have been reported by several authors. Depending on probe-specific sequences, several processes have been reported to explain the important biases observed in PM signals ,14. FirsThe aim of this paper is to provide a general test of performance of some preprocessing methods for Genechips, focusing in particular on affyILM, an algorithm recently made available as a Bioconductor package and developed by us. This algorithm is based on physical modelling of the hybridization process and uses a generalized Langmuir isotherm  to estimPreprocessing microarray data is commonly performed on a four-step basis: background correction, pm/mm correction, normalization and summarization. Several algorithms have been reported to treat each of those steps, and this field of research has evolved in a combinatorial way, to define the best strategy . To imprOur aim is to provide a preprocessing algorithm based on physical chemistry. We used the extended Langmuir model, which is discussed in Ref. , to compThe estimation of non specific binding implies platform-generation-specific features. The use of the Langmuir Isotherm to estimate concentrations is presented here, first ignoring this background-correction step, so that interpretation of the results does not depend on a difference between algorithms used with regard to the specificities related to each generation of array. As a consequence, the variability of probe-specific concentrations may be somewhat over-estimated . For this reason, the individual analysis reported here has been performed using both the Student t-test and variants of this test designed to stabilize the variance, at the probe-set level, using shrunken estimates of variability (regularized t-test and window t-test) ,40.To test the performance of affyILM, we selected the Affymetrix Tissue Mixture Study (available on Affymetrix's Website) . This stDifferential expression analysis was performed between samples reported in Table Methods.The results of the analysis are reported in Tables The first three columns illustrate the correlations obtained when biological noise is added in equal amount in both samples. The following four columns illustrate the correlations computed when the analysis is performed between one sample (Brain or Heart) and the mixtures with 75% and 25% of each sample, respectively. The last six columns refer to the correlations measured on the comparisons between one sample (Brain or Heart), and 3 mixtures with 50% of each sample. The analysis shows that, whatever the differential expression analysis strategy, the best performances are obtained when the probe-level data is summarized using the medianpolish algorithm, followed by the 1-step Tukey-biweight algorithm. In addition, whatever the summarization method, the best results are obtained when the data is analyzed with variance-stabilizing methods (Regularized t-test and Window t-test), as compared to the classic Student t-test. As expected, the correlation decreases with increasing amounts of biological noise . affyILM concentrations analyzed with or without the scaling step leads to similar results, and the observed correlation is higher using scaled data for some comparisons, lower for the others. The same conclusions can be formulated for both generation of arrays, as shown by comparing Table Table Using Table Tables As expected, a decrease in correlation is observed for increasing amounts of biological noise. However, the comparisons between mixes and Brain/Heart samples reveals an unexpected behavior: 50/50 mixes  leads to higher correlation values when compared with Brain sample (mix9) than the correlation values obtained by comparison with Heart sample (mix1). One explanation for this effect could be that the 50/50 mixes are enriched in Heart sample, thus the difference between the mixes and Heart samples (mix1) may be lower than expected, and higher when compared to Brain samples (mix9). This effect can also be observed with 75% - 25% mixes (mix4 and mix 6) when compared to Brain and Heart samples (compare columns m1m6 with m4m9 or m1m4 with m6m9). As a consequence, we suspect that either the concentration of Heart samples was under-estimated, or the concentration of Brain samples was over-estimated, prior to the design of the mixes. Alternatively, this effect could be due to a difference in the quality of Heart and Brain samples, with a higher level of biological noise in the Brain sample than in the Heart sample .et al. recently reported that the medianpolish procedure induce inter-array correlation, and introduced tRMA, where the use of rows and columns is inverted with regards to the medianpolish used in RMA and GCRMA (transposed medianpolish). This study also showed that the magnitude of the artifact associated with the medianpolish increases when the number of replicates is small, and is affected by an odd or even number of replicates [In the correlation study reported here, we tested affyILM in combination with the summarization steps used by other methods, to provide a fair comparison. The medianpolish summarization is associated to the best correlation coefficients, whichever preprocessing strategy is used. Giorgi plicates . In addiCorrelation results on the differential expression analysis are not sufficient to discriminate those three methods. To best characterize the performance of the differential expression tests, we used the well-known latin-square HGU-133 spike-in dataset, which offers the opportunity to compare the most significant probesets with the precise knowledge of the true list of spiked RNA's. Each pairwise differential expression analysis has been performed, leading to 91 distinct comparisons (see Methods) . The resAs demonstrated in several papers, variants of the Student t-test designed to stabilize the variance estimates outperforms the classic Student t-test, whichever preprocessing strategy is used ,40,45-47Figure The AffyComp assessment of preprocessing methods allow to compare the performances of preprocessing methods by monitoring several descriptive statistics. Although affyILM misses an appropriate background correction algorithm, we submitted affyILM(medianpolish) to the AffyComp III assessment. The results of the assessment will serve as a basis for the evaluation of affyILM future developments. The aim of this paper was to assess the performances of affyILM with regards to differential expression. However, we provide the reports of Affycomp using affyILM(medianpolish) in the additional files The aim of this paper was to perform a thorough performance analysis of affyILM, a Bioconductor package designed to preprocess Affymetrix GeneChip expression data. This model relies on the thermodynamics of hybridization and avoids complex statistical transformation as normalization steps used by other methods. To avoid biases due to the variability of the amount of hybridized material, the concentrations are scaled with an array-specific factor (selected to get a slope of 1 between pairwise array comparisons). To avoid biases due to the need for platform-specific background estimation algorithms, the background correction step has been ignored in our study. The study reported here adresses two main goals: evaluating the performances of affyILM with respect to differential expression analysis, and selecting the best summarizing strategy to avoid outliers-associated bias.Our correlation study on mixtures between two biological tissue samples first highlights that the medianpolish summarization leads to the best results in conjunction with the extended Langmuir Isotherm, followed by 1-step Tukey-Biweight algorithm and MBEI, as seen from the data shown in Tables et al. data [According to the statistical tests performed in this paper the accuracy of affyILM is similar to the best performing preprocessing algorithms . The advantages of affyILM is that it is entirely based on physical principles and does not make use of excessive parameters fitting. It runs equally well on a single experiment and it does not make use of heavy normalization, apart from global rescaling of the concentration levels. In addition, it provides to each measured expression level an error estimate , which ial. data , obtaineet al. on intensity values and proved to be efficient [In the future, our efforts will be shared on two objectives. First, we will try to further improve the strategy by including a background-correction step. In our current implementation of affyILM, this step is not performed, causing a variable over-estimation of the concentration. Second, we will try to simplify the analysis by testing an appropriate weighted multivariate analysis strategy from probe concentrations, instead of summarizing it. Transcript concentrations are estimated from each probe, to get rid of a dependance between the intensity and the sequence-specific hybridization free energies. As estimated target concentrations are analysed in place of probe intensities, all probes targetting specificaly the same transcript should thus provide the same information and share the same biological variability. Multivariate analysis procedures are typically used to analyse such data. This strategy should be more powerful, as a multivariate analysis uses more values in the test than an univariate analysis of summarized values. This strategy was previously used by Barrera fficient . HoweverWe first selected the tissue mixture study dataset provided by Affymetrix in order to characterize the correlation results of the differential expression analysis between brain and heart samples, and several mixtures of the two samples, as described in Table To best characterize the performances of the selected preprocessing/analysis strategies, we selected the latin-square HG-U133A spike-in dataset. The design of the latin-square experiment relies on the definition of 14 sets of 3 probesets, leading to 42 probesets spiked with known concentrations of RNA. Using those RNAs, 14 triplicated hybridizations were performed with increasing concentrations . Each set of 3 probesets is spiked with a specific concentration. The latin-square experiment leads to 91 possible pairwise comparisons between triplicate experiments . The BioThe raw data provided by Affymetrix was preprocessed using the R programming environment and some Bioconductor packages ,52. The Differential expression analysis was performed using PEGASE, an R package written by Berger et al. in order to use several methods and to compare the results . ProbeseFor each available pairwise comparison in the Tissue Mixture study, the lists of p-values generated by PEGASE were used to compute a correlation score using two strategies.In the first strategy, we first defined the Mix1 vs Mix9 (Brain VS Heart) comparison as the reference list of p-values, for each type of array and for each analysis strategy. Pearson's correlation coefficient was then computed between the log10 of the reference p-values and the log10 of the p-values associated to any other pairwise comparison between mixtures. This procedure was repeated for each tested combination of preprocessing and differential expression analysis methodologies.The aim of the second strategy is to compare results from HG-U133Plus2 and Human Gene 1.0 ST v1 arrays. First, we retrieved the mapping table between the probesets designed in the two generations of arrays, available in the support documentation of the supplier. We selected the best-match mapping table, and used it to subset the list of p-values obtained from both types of array . PearsonDatasets section above). The differential expression analysis was performed with PEGASE  and 91 lists of p-values were generated for each method. To quantify the performances of the analysis in one step, the 91 lists of p-values were concatenated in a single list, for each combination of preprocessing/analysis methods. In addition, known concentrations of spiked RNA's were used to compute 91 lists of fold-change values (FC). The other probesets defined on the array are not expected to vary between samples and were associated to a fold-change value equal to 1. The 91 lists of expected fold-change were then converted into 91 binary lists , and concatenated in a single binary list. For each combination of preprocessing and differential expression analysis methodologies, the final binary list of spiked probesets and the total list of p-values were used with PEGASE to compute the sensitivity ), the false discovery rate (FDR = 1-precision = FP/(FP+TP)), and 1-specificity (= FP/(TN+FP)) for increasing thresholds.The performance evaluation of the Latin-square data was done using the PEGASE R package . As 14 sFB scripted the procedures and ran the analysis of the data. Both authors contributed to the analysis, interpretation and redaction of the paper. All authors read and approved the final manuscript.HG-U133Plus2-medianpolish-comp. HG-U133Plus2-medianpolish-comp.xls summarizes the performances of affyILM with the transposed medianpolish on the HG-U133 Plus 2 arrays (Tissue mixture correlation study).Click here for fileHugene10st-medianpolish-comp. Hugene10st-medianpolish-comp.xls summarizes the performances of affyILM with the transposed medianpolish on the Hugene 1.0 ST arrays (Tissue mixture correlation study).Click here for fileHG-U133Plus2-VS-Hugene10st-medianpolish-comp. HG-U133Plus2-VS-Hugene10st-medianpolish-comp.xls summarizes the performances of affyILM with the transposed medianpolish using cross-platform comparisons between HG-U133Plus 2 and Hugene 1.0 ST arrays. (Tissue mixture correlation study).Click here for fileAffycomp-LS95-report. affycomp-LS95-report.pdf provides the report of the affycomp III evaluation on the latin square HG-U95 experiment.Click here for fileAffycomp-LS133-report. affycomp-LS133-report.pdf provides the report of the affycomp III evaluation on the latin square HG-U133 experiment.Click here for fileAffycomp-LS95-scores. affycomp-LS95-scores.xls reports the scores assessed by affycomp III evaluation of selected methods, on the latin square HG-U95 experiment.Click here for fileAffycomp-LS133-scores. affycomp-LS133-scores.xls reports the scores assessed by affycomp III evaluation of selected methods, on the latin square HG-U133 experiment.Click here for file


We seek to incorporate paired structure into analysis.RNA-Seq technology measures the transcript abundance by generating sequence reads and counting their frequencies across different biological conditions. To identify differentially expressed genes between two conditions, it is important to consider the experimental design as well as the distributional property of the data. In many RNA-Seq studies, the expression data are obtained as multiple pairs, We present a Bayesian hierarchical mixture model for RNA-Seq data to separately account for the variability within and between individuals from a paired data structure. The method assumes a Poisson distribution for the data mixed with a gamma distribution to account variability between pairs. The effect of differential expression is modeled by two-component mixture model. The performance of this approach is examined by simulated and real data.In this setting, our proposed model provides higher sensitivity than existing methods to detect differential expression. Application to real RNA-Seq data demonstrates the usefulness of this method for detecting expression alteration for genes with low average expression levels or shorter transcript length. Gene expression profiles are routinely collected to identify differentially expressed genes and pathways across various individuals and cellular states. Sequencing-based technologies offer more accurate quantification of expression levels compared to other technologies. Early sequence-based expression measured transcript abundance by counting short segments, known as tags, generated from the 3’ end of a transcript. Tag-based methods include the Serial Analysis of Gene Expression , Cap AnSequence-based approaches quantify gene expression as a ‘digital’ count and require modeling suitable for a count random variable. The Poisson distribution has been central in modelling expression data -12 and cMany practical RNA sequencing studies collect data with a paired structure, where the global expression profiles are measured before and after a treatment is applied to the same individual. Appropriate modeling of such data requires taking this design structure as well as the distributional property of the data into account. The Poisson model has been used to test the effect of drugs when the observation occurs as paired data, such as predrug and postdrug counts . Lee 2828 considIn this paper, we propose a Bayesian hierarchical approach to modeling paired count data that separately accounts for the within and between individual variability from a paired data structure. Our work adopts the Poisson-Gamma mixture model  and utilThe rest of this manuscript is organized as follows. Data Section introduces the biological problem and data that motivated this study. Methods Section presents our parametric model and the Bayesian method to identify genes with differential expression levels. The performance of the proposed model is examined by Simulations. Two sets of simulation studies are conducted: (1) those based on the model assumption to investigate the accuracy of the proposed method on parameter estimation, and (2) those based on mimicking the motivating data set to examine the robustness of the proposed method. Finally, the proposed method is applied to real data with detailed discussion of the results and comparisons with other methods.Qian et al.  designed an RNA-Seq experiment to study human West Nile virus (WNV) infection. One objective of this study was to identify altered genes/transcripts from viral infection of primary human macrophages in comparison to uninfected samples. This study naturally has a paired design structure. A total of 10 healthy donors were recruited according to the guidelines of the human research protection program of Yale University and cells were isolated from fresh heparinized blood samples for infection with WNV  as described previously . PolyA+ Ygi1,Ygi2), for gene g = 1, …, G and individual i = 1, …, n, where Ygi1 is the observed baseline expression level and Ygi2 is the observed level after treatment. The sizes of the libraries are denoted as Ni1 and Ni2, respectively. Let λgi denote the true baseline expression relative to the library size. Then, Ygi1 can be modeled as a Poisson random variable with mean λgiNi1. Let χg denote the expression level fold change after treatment so the true expression level is χgλgiNi2, then Ygi2 can be modeled as a Poisson random variable with mean χgλgiNi2. Our goal is to test whether there is any treatment effect, i.e., χg ≠ 1, where We now describe our Bayesian hierarchical mixture model to identify differentially expressed genes/transcripts from paired RNA-seq data. As noted above, such data arise naturally from experiments measuring the biological change from treatments. We start with an overdispersed count model . The obsλgi, across individuals with shape parameter αg and rate βg;It has been shown that the variability among technical replicates for RNA-Seq data can be captured by the Poisson distribution . Howeveri.e., the λgi’s can be integrated out (see Appendix).This model allows us to obtain a simpler form of the predictive density, zg, with zg = 0 corresponding to no change and zg = 1 otherwise. We assume that zg has a probability of Π0 for equal expression, i.e., zg = 0, and a probability of Π1 = 1 - Π0 for differential expression. Given a state, 0 or 1, the log-scaled fold change is assumed to follow a normal distribution. Under equal expression, the log-fold change is assumed to arise from a normal distribution centered at zero and variance % of transcripts showing increased expression by more than 4 fold after the infection whereas 4.3% showing reduction by more than 4 folds. To accommodate this asymmetry, we assume the log-fold change for non-null genes arises from a normal distribution with mean μ1, which may be different from 0, and variance Assuming independence between the baseline expression and treatment effect, we use a two-component mixture model to characterize the fold change distribution, where the expression change state of each gene is defined by a latent variable i.e., Pr(zg = 1|data). Genes can then be inferred to DE  or EE  according to these probabilities.Collecting all the components discussed so far, the model can be summarized in Figure To complete our model description, we need to specify prior assumptions for the unknown model parameters, Π0, Π1)∼ Dirichlet, i.e., Π0 ∼ Uniform.1.  characterizing the baseline expression distribution (λgi). These parameters are separately updated using the Metropolis-Hastings algorithm. For the latent state zg and expression level change χg, the state zg is first proposed and then χg is sampled given the state. Lewin et al. [χg, zg) are described in the Appendix. Mixing proportions  and hyper-parameters for the mixture distribution (μ1) are sampled from their conditional posterior distributions which can be derived in closed forms.In this section, we describe the Gibbs sampling algorithm  that we n et al.  discusseThe MCMC algorithm generates random samples from the joint posterior distribution of all model parameters. These samples are then used to infer the status of differential expression. One way to select a set of interesting genes is to rank genes using estimated posterior-mean fold changeT is the number of iterations used for inference after the burn-in period and t of the Gibbs sampling algorithm. Another way to select DE genes is to consider the latent variable, zg. During the MCMC iteration, the expression state is sampled along with the fold change estimates. These MCMC samples can be used to approximate the posterior probability of differential expression by counting the proportion of sampled states being differentially expressed:where pthres) : pg > pthres. For example, one choice would be pthres = 0.5. The false discovery rate can be estimated from these posterior probabilities [The Bayes’ rule assigns a gene’s expression status according to the largest posterior probability. An alternative is to classify a gene if the posterior probability of being non-null is greater than a threshold , the log-scaled effect is sampled from a normal distribution with a mean 0 and a standard deviation (σ0) 0.1, whereas the log-effects are sampled from a normal distribution with mean (μ1) of 1.5 and standard deviation (σ1) of 0.5 for the non-null genes. For the simulation studies, the true library sizes are used for the parameter estimation.The first part of the simulation was conducted to examine the performance of the proposed approach when the data are generated under the model assumptions. For 10,000 genes and 10 individuals, we simulate expression counts both before and after treatment according to Equation 1. Library sizes are sampled uniformly from 7 to 18 millions and relative expected baseline expression % of true DE genes with an FDR of approximately 1%. Figure Results in Table λgi, i = 1, …, N, Equation 1) is computed proportional to the total counts in each sample.In the second part of the simulation, we assume that the expression abundance is measured for 5,000 genes simultaneously before and after a given treatment. The number of individuals is set to be 10 for the relatively larger sample case (cases 1 and 4), 5 for the medium (cases 2 and 5), and 3 for the relatively smaller sample case (cases 3 and 6). The size of each library is randomly sampled from 1.8 to 3 million to have simulated count distribution compatible with the real data distribution. The infected set of the RNA-seq data  was used as the expected baseline count data to mimic the observed mean-specific dispersion. First, we sample 5,000 gene indices with replacement to get the expected baseline expression. Expression counts from the selected indices are summarized by a matrix where rows from this data matrix correspond to the selected genes in the original data matrix and columns correspond to individuals. Then, the relative expression (zg = 0) and their log-fold changes, log(χg), are sampled from a normal distribution with a mean of 0 and a variance of 4 × 10-4. For the rest of non-null genes, we considered the following two scenarios. An empirical set-up  utilizes nominal fold change from the uninfected data set. Cases 4, 5, and 6 consider a theoretical setup, where the log-scaled fold change is drawn from a normal distribution with a mean of zero and a variance of 1. We further filter out non-null genes whose true fold changes are less than 1.4.Among 5,000 genes, the first 4,000 are assumed to have no change (Each case was repeated 100 times. We compare the performance of our approach with DESeq (version 1.8.3)  and edgepg > pthres and compare the estimated false discovery rate with the true value  and the size of 5 (case 8). Averages of the parameter estimates μ1 and pthres = 0.5), 2,352 transcripts are classified into DE after the West Nile virus infection. The estimated FDR is 16.2% from Equation 4. Figure In this section, we apply our method to the motivating data set described in the Data Section. Initial values of the model parameters are calculated directly from the data. The MCMC sampling is run 4,000 iterations after discarding the first 8,000 iterations. On average, computational time was around 5 minutes per every 100 iterations. The number of total iterations and burn-in period are determined by monitoring trace plots of MCMC samples . 2,352 DE transcripts inferred from our approach are mapped to 1,518 DAVID IDs for functional annotation clustering. Cluster 1 (DAVID enrichment score: 11.39) represents cellular response to the WNV infection. Specifically, pathways in cluster 10 (score: 2.72) are related to the activation of the macrophage after the virus infection. Molecular functions of these transcripts are characterized by their cytokine production (GO:0001817) in cluster 3. Cluster 8 (score: 2.89) consists of transcripts that are involved in apoptosis (GO:0042981) and the regulation of programmed cell death (GO:0043067). The induction of apoptosis by WNV is essential in the regulation of pro-inflammatory responses, and has been previously reported in cell lines and neuronal cell types [Pathway-level analysis is one effective way to summarize biological relevance of differentially expressed genes. We perform gene enrichment analysis using DAVID  allows extra variance among count expression values . The varzg and χg isThe joint density of θ be a vector of all model parameters, Let λgi follow.Here, some details on the integral over Therefore,λgi’s), the posterior density of unknown parameters is proportional to the product of likelihood and prior density.After integrating over the expected gene- and individual-specific relative baseline expression , where σβ is set to be 1. The acceptance ratio is calculated asUpdate θ-βg is the vector of parameters except βg. For the evaluation of the acceptance probability, updated value of αg in the Step 1 will be used.Similarly, χg, zg) by utilizing generalized Metropolis-Hastings. Lewin et al. [χg and zg have to be jointly estimated since the supporting space of χg depends on the choice of zg. For example, χg is a point mass at one if zg = 0. To estimate a pair of , they proposed the state zg first and then updated χg|zg. By utilizing this approach, we adopt the following steps to sample .Update  Generate LogNormal if LogNormal. The mean and variance of the log-normal proposal distribution are computed from the observed counts. First, we collect individuals whose pre- and post-treatment counts are non-zero for each gene, separately. Then, Mg is computed as a median of Vg, however, this estimate often gives an extreme value. In data analysis, we trim the estimates at 25th and 75th percentiles when the sample size is 10. For small sample case, the median of Vg’s is used as the proposal variance.(Step 3-2) Then, Alternative descriptioni.e., we use the independence chain Metropolis-Hastings. The proposal distribution is given byDefine min{1, r} where r is one of followings:The acceptance probabilty is LN0 is a probability density function for log-normal distribution with mean zero and variance LN1 is a log-normal density centered at where μ1, χg. Since it has a closed form for the posterior density conditional on all other parameters, we can directly sample those parameters.Update where Π0, Π1). We assume a Dirichilet prior for the mixture probabilities. Using Gibbs sampling scheme, these weight parameters are updated from Dir(1 + ♯(zg = 0), 1 + ♯(zg = s1)).Update the mixing proportions (The authors declare that they have no competing interests.LMC developed and implemented the proposed model, performed statistical analysis, and drafted the manuscript. JPF participated in model development and helped manuscript preparation. WZ processed the WNV data and participated in data analysis. FQ, VB, and RRM performed WNV experiment. HZ designed and coordinated the study and helped draft the manuscript. All authors read and approved the final manuscript.


For many prospective clinical trials, this material has been collected allowing for a prospective-retrospective study design which represents a successful strategy to define clinical utility for candidate markers. Gene expression data can be obtained even from FFPE specimens with the broadly used Affymetrix HG-U133 Plus 2.0 microarray platform. Nevertheless, important major discrepancies remain in expression data obtained from FFPE compared to fresh-frozen samples, prompting the need for appropriate data processing which could help to obtain more consistent results in downstream analyses. In a publicly available dataset of matched frozen and FFPE expression data, the performances of different normalization methods and specifically designed Chip Description Files (CDFs) were compared. The use of an alternative CDFs together with fRMA normalization significantly improved frozen-FFPE sample correlations, frozen-FFPE probeset correlations and agreement of differential analysis between different tumor subtypes. The relevance of our optimized data processing was assessed and validated using two independent datasets. In this study we demonstrated that an appropriate data processing can significantly improve the reliability of gene expression data derived from FFPE tissues using the standard Affymetrix platform. Tools for the implementation of our data processing algorithm are made publicly available at  In a study on diffuse large B-cell lymphoma (DLBCL), Williams et al. Many pre-analytical factors can affect the quality of FFPE-derived expression data, including sample collection and storage procedures and RNA extraction or amplification methods, so that an accurate quality pre-assessment evaluation is needed Several methods to summarize and normalize expression data were developed for the Affymetrix platforms, with MAS5 and RMA Expression profiles from FFPE samples are expected to have a lower signal to noise ratio, and an appropriate processing could be crucial to derive a reliable measure of gene expression. At this time, it is not known which processing approach should be used to produce the best results. Indeed, of 15 publications reporting Affymetrix expression data generated from FFPE samples, 4 used MAS5, 6 used RMA and 5 used other or unspecified procedures. None has reported the use of alternative CDFs.We thus set out to compare the performance of three different summarization and normalization methods, MAS5, RMA and fRMA used in combination with the standard Affymetrix CDF or two different alternative CDFs. The first CDF included all the probes unambiguously mapping RefSeq transcripts, while the second was defined similarly to the first one but contains, for each probeset, only the probes nearest to 3′-end as these probes could be the most informative and reliable in FFPE data because of RNA fragmentation. All these processing pipelines were applied to the Williams dataset RefSeq_all, for the Affymetrix chips of the HG-U133 series, where all the probes unambiguously mapping RefSeq transcripts were retained and merged to create a new single set of probes for each gene. As result, genes which were represented by multiple probe sets in the original chip design resulted in a new single probeset. A total of 16,991 probesets were generated and about half of them (45.3%) contain more than the 11 probes present in standard Affymetrix probesets . Using these criteria it was possible to define 8,263 probesets, in which the reliability of each probe was likely increased, although the number of probes measuring each gene was reduced.To verify our hypothesis, after probe re-annotation described before, we computed the distance from the probe to the 3′-end of the transcript. The correlation between frozen and FFPE data turned out to be a decreasing function of such distance, reaching a plateau at around 250–300 bp that corresponds with the average size of aDNA obtained after amplification . Thus weThree different normalization algorithms were considered in the subsequent analysis: i) MAS5, ii) RMA RefSeq_all CDF and the RefSeq_dist CDF). From the data processed with the standard CDF, we also extrapolated the subset of probesets mapping on genes targeted in the RefSeq_all and RefSeq_dist CDFs, in order to undertake a fair comparison. Moreover, we applied the method proposed by Li and colleagues To identify the best performing procedure to process FFPE-derived Affymetrix data, we compared the matched frozen and FFPE GEPs of the Williams dataset RefSeq_dist CDF  with the number of probes included in the probeset. The simple filtering of the standard probesets using the method by Li et al. RefSeq_all CDF.First we evaluated, for each pair of samples, the correlation between frozen- and FFPE-derived expression values over all probesets  and, for each probeset, the correlation between frozen- and FFPE-derived expression values over all samples . As not all genes are expected to be expressed or to vary significantly in a specific tissue type, the second analysis was performed only for the 50% most variant probesets . Wilcoxodist CDF . On the RefSeq_all CDF (R = 0.76), corresponding also to the highest percentage of commonly DE probesets  and increased positive predictive value (69.1%). When using the RefSeq_dist CDF, besides the highest sample correlations reported in RefSeq_all and RefSeq_dist CDFs, the same genes evaluated using only the 5 probes nearest to 3′-end gave on average higher signals  in keeping with what observed in the degradation plots  and the selection of the most reliable probes (i.e. using the RefSeq_dist CDF), the first approach seemed to be globally advantageous.In the second step we took advantage of the presence of both molecular subgroups of DLBCL in the dataset (ABC and GCB) by performing a class comparison analysis for all processing pipelines, separately for frozen- and FFPE-derived data . We compon plots . Neverthrelation  nor in trelation . TherefoTo evaluate the robustness of our results we generated partial datasets by removing one sample at a time, and we evaluated how PPV and sensitivity varied when removing one array (we thank one of the reviewers for suggesting this check). This showed that the effect of array removing is much smaller than the difference between pipelines. For example, when removing in turn each of the 45 classified samples we obtained from MAS5 with standard CDF an average PPV of 0.524 (standard deviation 0.024), while for fRMA with the RefSeq_all CDF we obtained 0.694 (0.025). Similar results apply to the sensitivity.RefSeq_all) was graphically represented in The impact of the normalization method (MAS5 vs fRMA) and type of CDF  positive and negative tumors was performed in the GSE5460 frozen dataset and probesets with P<1e-10 were selected. Genes targeted by such probesets, identified using a very stringent P-value threshold and a large dataset of GEPs from frozen tissues can be reasonably considered as true ER related genes. As reported in P-values computed in the INT FFPE dataset for these “gold standard” probesets significantly shifted towards lower values when using fRMA instead of MAS5 in combination with the standard CDF , with a percentage of probesets having P<0.01 rising from 22.6% to 29.2%. At the same time, an improvement seems to happen also in frozen data as the total number of DE probesets increased from 1635 to 2179 out of 54675, corresponding to the 3.0% and 4.0% respectively. The use of the RefSeq_all CDF with fRMA further shifted the P-value distribution  and 34.5% of the “gold standard” probesets had P<0.01 in FFPE data. Overall these results also suggest that despite using an optimized processing algorithm, many genes will not be detected as DE when using GEPs derived from FFPE material. This observation should be carefully considered when data generated from frozen-material has to be validated in data derived from FFPE.Through the analysis described in P<1e-4 were defined as DE. Their P-value distribution in the frozen dataset were similar when using MAS5 or fRMA in combination with the standard CDF . However, the number of probesets identified as DE in the FFPE dataset were higher for fRMA compared to MAS5, 362 (0.7%) and 218 (0.4%) respectively. The use of the RefSeq_all CDF further increased the proportion of DE probesets (up to 0.9%) and the P-value distribution in frozen data shifted towards lower values , with 98.1% of probesets having P<0.01 in frozen data.Using the same datasets, we also employed FFPE-derived data to identify the genes DE between tumor subtypes and then evaluated the proportion of these genes which can be confirmed as DE in frozen derived GEPs according to different processing methods. To this aim we performed the analysis as described in dard CDF , with a In the previous analysis no correction for multiple testing was applied; however similar results were obtained by selecting as DE probesets in FFPE data those with a Benjamini-Hochberg adjusted p<0.01 .RefSeq_all CDF compared to the standard CDF  and CDF are also available. Moreover, sample R code was included. Updated CDFs (and related fRMA parameters) using new RefSeq versions will be periodically released.Globally the use of an alternative CDF in combination with the fRMA algorithm seems to be advantageous in many situations. The parameters required by fRMA have to be re-estimated if using an alternative CDF and this is time consuming and a computationally demanding task. To make available an immediately applicable bioinformatic tool, the software and data files needed to implement the pipelines using an alternative CDF are available at: Obtaining reliable gene expression data from fragmented RNA derived from FFPE specimens is challenging, with many pre-analytical and analytical steps which can affect the quality of the results Our methodology was specifically developed for the Affymetrix chips of the HG-U133 series. While microarrays in general, and the HG-U133 series in particular, can be considered an obsolete way of conducting gene expression profiling experiments, the availability of an impressive corpus of data obtained with this platform on many different tumors makes this choice still appealing by making comparisons with previous results straightforward. In fact these chips are still used in current projects RefSeq_all CDF as the more effective processing approach. The advantage of using this optimized processing could be even more valuable in the identification of the tiny differences expected in biomarker discovery for more demanding prognostic and predictive clinical questions in the modern era of personalized medicine. Indeed, our algorithm has been successfully applied to GEPs derived from a large series of FFPE tumor samples from patients enrolled in the ECTO randomized clinical Phase III trial By assessing the performance of different processing approaches and comparing distinct molecular groups in both lymphoma and breast cancer (ABC vs GCB or ER+ vs ER−), we identified the use of fRMA as normalization method in combination with the All datasets used in this study contained data from the Affymetrix HG-U133 Plus 2.0 microarray platform and are available on GEO repository GSE19246GSE5460GSE38554 (INT dataset) – contains expression data from 44 FFPE primary breast cancer samples taken for routine diagnostic purposes in our Institution between 1997 and 2002. The patients signed an informed consent and this study was approved by the Institutional Review Board and independent ethic committee of Fondazione IRCCS Istituto Nazionale dei Tumori (INT). Thirty samples were from ER+ and 14 from ER− tumors. Presence of lymphocytes infiltration (LI) was quantified by an expert pathologist. Tumors having 5% or less LI (n = 22) were compared with those having 10% or more LI (n = 22). RNA was amplified with the Nugen WT-Ovation FFPE System. A quality control was performed at each level, from sample representativeness to expression profile. Methodological details will be described in an independent manuscript submitted for publication.altcdfenvs Bioconductor package  RefSeq_all CDF), otherwise were not further considered. For the RefSeq_dist CDF the five probes closest to the 3′-end and in any case mapping within 300 bp from the 3′-end were used.Alternative CDFs were generated as previously described affy Bioconductor package (version 1.32.1) frmaTools Bioconductor package (version 1.6.0) The hgu133plus2.db Bioconductor package (version 2.6.3) and redefined probesets were annotated using the org.Hs.eg.db Bioconductor package (version 2.6.4)Standard probesets were annotated using the Pearson's correlation was used to compute samples, probeset and fold change correlation analysis in the GSE19246 dataset.Student's t-test was used to assess probesets differential expression. Probesets with p<1e-4 were defined as DE if not otherwise specified.Differences in p-value distributions were tested for significance using the Wilcoxon-Mann-Whitney test.Enrichment analysis was performed using GSEA (v. 2.0) Figure S1RefSeq_all CDF. (B) RNA degradation plot for the frozen (left) and FFPE (right) data in the Williams dataset (A) Number of probes in each probeset in the (TIF)Click here for additional data file.Figure S2Frozen-FFPE correlation as a function of the distance of the probes from 3′-end. (A) Frozen-FFPE correlation for the 56 matched samples of the GSE19246 dataset increases when only probes nearer to the 3′-end are selected. (B) Frozen-FFPE pair plot of probe-level log2 intensities for a representative sample. Probes with a 3′-distance <100 bp are highlighted in red.(TIF)Click here for additional data file.Figure S3RefSeq_all and RefSeq_dist CDFs and fRMA normalized data.Average distribution of signals in the FFPE GSE19246 dataset (n = 56) for the 8263 common genes using (TIF)Click here for additional data file.Figure S4RefSeq_all CDF (right).Evaluation of the positive predictive value of FFPE data after applying different processing pipelines in two breast cancer datasets. (A) Flow chart of the analysis. (B) Distribution of p-values in the GSE5460 frozen dataset for probesets DE (FDR<1%) in the INT FFPE dataset between ER+ and ER− tumors. The analysis was performed on data processed using MAS5 and the standard CDF (left), fRMA and the standard CDF (center) or fRMA and the (TIF)Click here for additional data file.Table S1Wilcoxon matched pairs test of frozen-FFPE sample correlations using different processing pipelines.(XLSX)Click here for additional data file.Table S2Mann-Whitney test of frozen-FFPE probesets correlations using different processing pipelines.(XLSX)Click here for additional data file.Table S3Main features of the datasets analyzed.(XLSX)Click here for additional data file.


Breast cancer outcome can be predicted using models derived from gene expression data or clinical data. Only a few studies have created a single prediction model using both gene expression and clinical data. These studies often remain inconclusive regarding an obtained improvement in prediction performance. We rigorously compare three different integration strategies  as well as classifiers employing no integration (only one data type) using five classifiers of varying complexity. We perform our analysis on a set of 295 breast cancer samples, for which gene expression data and an extensive set of clinical parameters are available as well as four breast cancer datasets containing 521 samples that we used as independent validation.mOn the 295 samples, a nearest mean classifier employing a logical OR operation (late integration) on clinical and expression classifiers significantly outperforms all other classifiers. Moreover, regardless of the integration strategy, the nearest mean classifier achieves the best performance. All five classifiers achieve their best performance when integrating clinical and expression data. Repeating the experiments using the 521 samples from the four independent validation datasets also indicated a significant performance improvement when integrating clinical and gene expression data. Whether integration also improves performances on other datasets (e.g. other tumor types) has not been investigated, but seems worthwhile pursuing. Our work suggests that future models for predicting breast cancer outcome should exploit both data types by employing a late OR or intermediate integration strategy based on nearest mean classifiers. These predictors have been derived from gene expression data, such as the 70-gene  to ensure approximately equal spread for all features.et al.et al.et al.et al.et al.Reyal We employed five classifiers with varying degrees of complexity, some of which have been used before to integrate clinical and expression data. We shortly discuss each classifier see :A Nearest Mean Classifier (NMC), with the cosine correlation as distance measure. This linear classifier has previously been applied on expression data, and was shown to outperform more complex classifiers A Simple Bayes Classifier (SBC) , which is based on the assumption that the features are independent. This simplifies the computation of the class conditional densities significantly. In spite of this simplification, it has been shown that this classifier performs remarkably well A 3-Nearest-Neighbor classifier (3NN) , employing the cosine correlation as distance measure, and majority voting to assign a sample to a class. Since there is a class imbalance, the majority vote is adjusted with the class priors. This classifier is capable of constructing non-linear decision boundaries. Moreover, it is frequently applied to microarray data, see e.g. Dudoit et al.A Support Vector Machine (SVM) , using a cosine correlation kernel , i.e. a kernel function which computes the cosine correlation between two input objects. This classifier is appropriate for small sample size problems, and has previously been used to integrate expression and clinical data A Tree classifier (Tree) , which allows for highly non-linear decision boundaries. Gini’s diversity index was used as splitting criterion. In order to regularize the tree classifier, we employed two variants. The first variant (Tree1), optimizes the tree depth but selects a subset of features from all features. The second variant (Tree2) is not pruned, but selects features from the subset of up to 200 most predictive features as provided by the feature selection procedure.etal.We excluded the Bayesian approach introduced by Gevaert etal.To evaluate the performance of the classifiers, and determine the optimal number of features (tree depth for the Tree and the HybridTree classifiers (see Section ‘Integration strategies’)), we applied a double loop cross validation protocol  into five parts (different splits for each repeat).For each fold, four parts are used for the inner loop (training set), the fifth part is used in the outer loop for validation .On the training set, a 10-fold cross validation is performed to estimate the optimal number of features , is not an appropriate comparative measure. Therefore, classification errors were calculated by using the average False Positive False Negative ratio, defined as:The entire protocol was run 60 times . To find the optimal number of features, we constructed learning curves in the inner loop for up to 200 features . In all experiments, we used the exact same repeats and folds. As a result, we were able to compare the performance results in the outer loop on a pair-wise basis, using a one-sided, paired t-test.Kaplan-Meier curves were constructed by using the predictions that were made in the outer loop. Consequently, in each repeat, every sample has once been part of the test set in the outer loop. Thus, for each sample we have a fully unbiased prediction of the binary label. After completing the 60 repeats, we have 60 unbiased predictions of each sample. Next, we take the mean of those 60 predictions, and assign a sample to the poor group if the average is below As an alternative performance criterion, we also considered the AUC (Area Under the Curve) of the ROC (Receiver Operator Characteristic) curve instead of In the inner loop of the cross validation procedure, we used a feature filtering approach. To rank the features, we employed a t-test for the continuous features and the chi-squared test for discrete features. The combined set of features are then ranked based on the p-values of the associated tests.et al.Following Gevaert Classifiers are indicated by their abbreviation, followed by the type of integration used. For example, ‘NMC; None E’ is the nearest mean classifier (NMC) without integration (None), trained on expression data (E).For the early integration strategy we concatenated the E and C datasets, and thereby created a single dataset, EC, with For all classifiers (except the intermediate Tree classifier), we first determine the optimal sets of features from each data type separately (in the inner loop). In all subsequent steps, we used these sets of features and all training samples. We define For the NMC classifier, we compute the centroids of the poor and good class . This classifier splits the samples into two groups, each associated with a node in the tree. In these and all subsequent nodes, we branch further using a NMC trained on E and the samples at the relevant node. The procedure was stopped when a particular branch was pure (only poor or only good samples), or contained fewer than ten samples. This approach will be referred to as HybridTree (C). We also included the complementary setup, which starts with a NMC trained on E, and uses NMC classifiers trained on C in the subsequent nodes (HybridTree (E)).For the two HybridTree variants, we optimized the tree depth in the cross validation procedure (inner loop), while we fixed the number of features used in each classifier to the top 100 features when trained on E, and the top ten features when trained on C. These features were selected using all training samples  in a particular branch of the tree, using the same feature selection methods as described above in the Section ‘Feature selection’.The mixing parameter Classifiers trained using the intermediate integration strategy are indicated with the suffix ‘Intermediate’, e.g. ‘NMC; Intermediate’ for the NMC variant.For late integration we train a classifier on E and C separately. After that, we apply a logical function on the binary classifier outputs . We considered a logical AND function, for example for the NMC classifier::The lowest error is achieved using the NMC classifier with late OR integration strategy  classifier is 1.1. At this tree depth, the HybridTree (C) is practically equivalent to the NMC using clinical data. On the other hand, the HybridTree (E) has an optimal tree depth of 1.8. This suggests that a second level of NMCs using clinical features might be beneficial on top of the expression NMC. However, both HybridTree classifiers are significantly outperformed by the NMC classifiers without any integration (The HybridTree (C) setup is very similar to training an expression based classifier within clinical subgroups. Our analysis indicates that, there is little to be gained by such a strategy. The intermediate and late integration strategies using a NMC are better options.A major selling point of existing gene expression based classifiers is their superior performance compared to the existing clinical models. However, we observe a small performance advantage for the NMC trained on C compared with the NMC trained on E : OriginaThe NMC with late OR strategy performs the best, and therefore we trained a final classifier on all samples of the Vijver dataset. The number of features was chosen by averaging the number of features that was found to be optimal in the inner loops, resulting in 87 and 9, for the expression and clinical features, respectively , giving a total of 4525 gene sets with at least five genes. We used the hypergeometric test to asses the significance of the overlap, followed by a Bonferroni correction. A heatmap of the enrichment is shown in The nine clinical variables that were selected are shown in In order to see whether the clinical features pick up a signal different from the expression features, we inspected their correlation. et al.The SCUBE2 gene from the smaller Subgroup C is part of the ‘Estrogen genes’ in the signature from Paik The matrix variable is not correlated with any of the 87 genes, nor with the other eight clinical variables. Next, we tested whether any of the genes is associated with the matrix clinical variable, by means of a t-test. After Bonferroni correction, none of the genes have a significant p-value . However, from a previously gathered collection of breast cancer datasets In the DLCV procedure, we optimized the number of features by minimizing the eFPFN error. As an alternative, we repeated the experiments aiming to maximize the AUC, which reflects the performance across the entire ROC curve rather than a single operating point . We repeated the experiments using the NMC classifier, as that classifier achieved the best performance in the eFPFN experiments. All DLCV settings were kept the same . For all classifiers tested, we found evidence to support the hypothesis that integration of expression and clinical data leads to better predictors. We hypothesize that this is the result of two effects. First of all, both individual classifiers pick up a noisy proliferation associated signal, and their redundancy leads to a better prediction. Secondly, the clinical set of features has some additional information, for example the ‘Matrix formation’ variable, which is not captured by the expression. This complementarity of features results in a synergetic effect on the classification performance.The late OR integration is the strategy that most often leads to the best performance improvement on the Vijver dataset. Using the late OR strategy, samples for which the individual classifiers are discordant are assigned to the poor outcome group. As a result, the identified good group becomes smaller but also purer. We hypothesize that this is also why the performance increases, the two data types are primarily synergetic in finding a pure group of good cases. A similar effect was seen when combining the classifier outputs of existing gene expression signatures Using the eFPFN as criterion shows that the Late OR strategy is the best on the Vijver data, and the intermediate strategy on the independent data (the Late OR is second best). When using the AUC as criterion, the Late OR strategy performs the best on the Vijver data, and the late AND strategy on the independent data (the Late OR is second best). These differences in the best integration strategy may be due to 1) potential differences in composition of the samples between the cohorts, 2) the use of different microarray platforms, 3) differences in clinical data that is available (much more extensive for the Vijver dataset), and 4) differences in annotation (such as differences in grading between pathologists). Some or all of these effects will play a role in which classifier/integration strategy performs the best. Remarkably, in all cases best performances are achieved by integrating the two data types, showing strong evidence of their synergy.In the intermediate and late integration strategies, the optimal sets of features are selected on each data type separately and not in the context of the final integrated classifier, which might be sub-optimal. We did not explore alternative feature selection procedures, which take this complementarity into account, due to the additional computational complexity.The nearest mean classifier significantly outperforms all other classifiers. Thus, our results support earlier indications that a relatively simple classifier, is least hampered by the small sample size problems. On top of that, we conclude that this is the case regardless of the choice of integration strategy. We would like to stress that these claims can only be made for the breast cancer data sets examined in this study.et al.Gevaert et al.et al.Daemen ‘Hormone related’ and ‘Proliferation’ features are selected by both the E and C classifiers indicating the importance of these processes in predicting breast cancer outcome. Matrix formation was selected on the Vijver dataset but was not available on other validation datasets. Scoring additional histo-pathological features on tumor specimens may yield further improvement in breast cancer outcome prediction and is therefore worth pursuing.Table S1Overview and details of the clinical variables used for the Vijver dataset.(XLSX)Click here for additional data file.


In this paper we would carry out inference on isoform expression under different normalization techniques, since it has been recently shown that one of the most prominent sources of variation in differential call using mRNA-Seq data is the normalization method used. The statistical framework is developed for multiple isoforms and easily extends to reads mapping to multiple genes. This could be achieved by slight conceptual modifications in definitions of what we consider as a gene and what as an exon. Additionally proposed framework can be extended by appropriate modeling of the design matrix to infer about yet unknown novel transcripts. However such attempts should be made judiciously since the input date used in the proposed model does not use reads from splice junctions.mRNA-Seq is a precise and highly reproducible technique for measurement of transcripts levels and yields sequence information of a transcriptome at a single nucleotide base-level thus enabling us to determine splice junctions and alternative splicing events with high confidence. Often analysis of mRNA-Seq data does not attempt to quantify the expressions at isoform level. In this paper our objective would be use the mRNA-Seq data to infer expression at isoform level, where splicing patterns of a gene is assumed to be known. A Bayesian latent variable based modeling framework is proposed here, where the parameterization enables us to infer at various levels. For example, expression variability of an isoform across different conditions; the model parameterization also allows us to carry out two-sample comparisons, e.g., using a Bayesian  Sequencing technology has advanced at a rapid rate in the past decade. The advent of massive parallel sequencing technologies, such as Illumina Genome Analyzer/Solexa, has revolutionized the genome-wide transcriptome studies leading to multiple applications. One such application is known as mRNA-Seq technology that provides a far more precise measurement of levels of transcripts and their isoforms than microarrays  represent the signal and background, whereas those coming from non-transcribed regions (“introns” or other inter-genic regions) can be assumed to be only background. Often the density of reads falling in the non-transcribed region would be of the order 10Apart from being more reliable than the more popular microarrays, there are some very appealing advantages of this technique. For example, it actually produces sequence information of a transcriptome at a single nucleotide base-level. As a result we are able to determine splice junctions and alternative splicing events with high confidence. This technique has been used to investigate alternative splicing in several organisms, e.g., mammals . Depending on the data these errors may not pose any significant problem  these typically do not reflect expression of a single transcript but is often shared by several transcripts. Majority of these would be splice variants; however there are other possibilities as well, which we will address later.Reads not only from exon regions but also from splice junctions (span two exons) could be available, but they too suffer from similar limitation of being shared by multiple isoforms. In case a junction is unique to a transcript then the reads from splice junction may be used as indicative of the expression. Otherwise in a complex structure of multiple exon sharing between different transcripts, the reads mapping to splice junctions would have to be modeled additionally if they are to be used for inferring expression of the isoforms.As has been pointed out by Zheng and Chen  comparisIn the following sections we present review of relevant literature on expression estimation, followed by the description of the proposed Bayesian latent variable model and its application to a real data set.mRNA-Seq technique provides read count for genomic segments, known as exons. These can then be utilized in various manner depending on the question of interest, more often than not, these are summarized at gene level. However we prefer to quantify them at the level of disjoint exons or parts thereof. The motivation is as followed by Jiang and Wong , whereinSince number of reads for any genomic region would naturally depend on the length of that region it is a common practice to normalize it using the length information. Quite often it is represented as reads per kilobase per million (RPKM) mapped reads . Each sample would produce different total read counts depending on sequencing depths. Thus, as described above, the common approach is to adjust individual expression counts for each sample by the total count for that sample: e.g., RPKM as described above or a hypergeometric model  due to change in analysis techniques in previous step of data analysis. Quite often a moderate change in algorithm for normalization can dramatically alter biological conclusions  of collection of all genes (or parts thereof). If gp is the probability of each read being mapped to a gene g then since n is large and gp is small, approximately gn ∼ Poisson(λg) with λg = gnp. It has been shown that more than 95% counts can be modeled well by this Poisson model a as reflected in sample i plus an offset (log id) and possibly other technical effects (þig). If no technical replicates are carried out, as is often the case, a(i) will be simply i.This model was recently proposed by Bullard et al. . Thereint-test, moderated t-test, to identify significant expression changes. Note that the arcsine-root transformation is suggested for variance stabilization of the per-gene read proportions within each sample . On the other hand although Fisher’s exact test does not make any assumptions on the sample size; it only adjusts for global experimental effects, unlike the likelihood ratio statistics adjust for general experimental effects as well as sample covariates. t-statistics on the other hand is severely affected by zero count in even one sample and is unable to detect differential expression in some of the obvious cases.For the GLM, three types of methods for differential expression inference have been proposed, viz. Fisher’s exact test statistic, likelihood ratio statistics based on a GLM, and It has been noted by several groups that longer genes contribute more to mapped sequence reads than shorter genes with similar expression. More importantly this may not be removed by scaling with length like RPKM . There was a sharp drop at the last bin, which could be due to the fact that this bin contains exceptionally large exons, however there is always a physical limitation of number of reads coming from these exons, thus bringing down the RPKMs.1, λ2 by L folds. Then the resulting t-statistics would be the following:The effect of length bias has been noted on differential expression call also  level expression of a gene and these can then be used to assess overall expression of a particular gene. The data used here for the purpose of illustration has been limited to uniquely mapped reads, however as has been mentioned earlier, by introducing an extended concept of (pseudo-)gene and (pseudo-)exon we can accommodate reads mapping to multiple locations as well. Thus this model can borrow information across different genomic locations belonging to same or different genes. For other methods to adjust for reads mapping to multiple genes see Li et al. , FaulkneThe model presented here requires known structure of the splicing patterns of a gene. Although with some advanced modeling we are able to infer when the exiting knowledge of transcription variation is in question (thus leading to randomized-design matrix). Also by extending the design matrix would enable us to infer about yet unknown novel transcripts.Additional advantage of the proposed method is that it is developed for multiple samples comparison unlike Zheng and Chen  and alsoThis technique has twofold advantages over existing methods, at the level of model identifiability and also at the level of pairwise testing. Firstly, when genome level expressions of genes (and exons in this case) are explored the majority of them are not expected to express at every situation. Thus to represent the underlying biology realistically requires the distribution of the expression parameters to be able to take values very close to zero as well as large values. This often poses computational problems and one way to overcome this is to use the “spike-n-slab” type of model  as a linear combination of expressions of the isoforms of that gene which share this particular exon. Thus,gily: normalized reads for the i-th exon in the g-th gene for the l-th sample, gklI: latent indicator variable, which is one if the k-th isoform of the g-th gene is expressed in the l-th sample and it is zero otherwise, βgkl: latent variable measuring expression of the k-th isoform of the g-th gene is expressed in the l-th sample, gikX: the zero-one matrix indicating whether exon i is known to form part of the k-th isoform of the g-th gene, εgil: residual error term for the i-th exon of the g-th gene in the l-th sample, g: ranges from 1 to G, the number of genes covered in the data (7737 genes from chromosome-1 of the Arabidopsis data), i: ranges over the number of exons for the g-th gene in the data, these exons could be biologically whole exons or disjoint parts thereof, (for the current data it ranges from 1 to 73), k: takes values 1 to the known number of isoforms for gene g , l: represents different samples (for the data used for illustration there are five distinct treatment conditions with one sample each and a control sample to contrast with are available).For each exon After careful exploration we chose multivariate Normal distribution for the errors; however for individual error a Gamma model might have been more effective in overcoming some biases in the data. Our choice of distribution was for the ease of computation.m exons. Since the gene is known to have only one transcript thus if this transcript it expressed in a sample then all of its constituent exons will be expressed and should be expressed in similar amount. Thus any variation in the measurements gily for i = 1, …, m would be purely noise in the measurement of expression of the gene at specific sample level. Thus our error modeling is clearly intuitive for single isoform genes which is majority of genes for this particular data (since 6510 genes of the 7737 genes have single isoform in this particular data). Now let’s consider the situation of a gene with multiple known isoforms. There, if a residual error is high that could not only indicate noise in measurement but also incomplete knowledge in all possible isoform formation of that gene, that is we could very well be missing a few isoforms and thus are unable to explain the observed expression measurement for some exons. Thus an assumption of gene x sample level variation would be realistic for such genes also.In regard to the choice of error variance, our model assumes a sample × gene parameterization. Consider a gene with single isoform with g-th gene for the l-th sample as: gm is the number of known exons for gene g; gX: is the known exon-isoform indicator matrix, dimension gm × gs; gs is the number of known isoforms for gene g;This helps us in defining the likelihood of the data and to complete the hierarchical structure of the Bayesian model we restrict to known conjugate distributions as priors. In standard notation we define our model for the vector of expression of all exons pertaining to gl ∼ Gamma with mean α1/α2 and variance α1/(α2)2;τk-th isoform of the g-th gene in the l-th sample;gklI ∼ Bernoulli(p), is the latent indicators variable indicating whether the k-th isoform of the g-th gene is expressed in the l-th sample or not.gkl, gkI, τgl to infer about these parameters and their functions of interest. Multiple choices of hyper-parameters Using Markov-Chain-Monte Carlo samples for the parameters βWe implemented our model in the WinBUGS software  contains zero.Moreover two-sample comparisons can be carried out with the help of Bayesian t-test might suffer from inflated standard error estimate of a gene/isoform is not expressed in one of the two conditions. In our modeling framework we easily overcome this issue by utilizing the latent expression indicator variable. If the two latent variables indicate with high degree of confidence that an isoform is expressed in one condition and not in the other, then irrespective of expression amount it can be safely declared differentially expressed. This is a known knowledge in biology, that in order to play a significant role in a biological process a transcript may not have to be expressed in high degree but differently with high confidence.As has been reported by Bullard et al.  classicaNote that these latent indicator variables also serve the purpose of variable selection and regularization against over-fitting.Arabidopsis thaliana by Filichkin et al.  sample, RNA-Seq libraries were prepared and sequenced individually. The five conditions are Cold Stress (CS), Drought Stress (DS), heat stress (HS), High-light Stress (LS), and Salt Stress (SS).For illustration purposes we used the RNA-Seq data on n et al. . High-thn et al.  were carArabidopsis genome were downloaded from TAIR9 database release available at http://www.arabidopsis.org. In house programs were made to extract isoform level information. Bowtie program was used to align the reads to genome and isoforms. We used 30-bases with up to 2-bases mismatch and unique match options to align the reads. The results presented in the subsequent sections will be based on data from Arabidopsis chromosome-1 only for limitation of space.The dataset was downloaded from NCBI GEO website (accession ID = SRP000935). Pooled data contains approximately 271 million. The gene information and other necessary resources of For technologies like RNA-Seq, sequencing bias toward 3′ end is well-known. However for our data this effect is visible only moderately  could also be a possibility; however it requires relevant biological information which is not available in our case. Thus we proceed with comparing results based on two different types of normalization, global correction and percentile normalization.The normalizations continue to have effects on isoform level expressions. In Figure Arabidopsis, based on present knowledge, nearly 84% of the genes (on chromosome-1) are single isoform genes. However 69.4% of these genes have more than one exon.Note that in our method of defining expression (at gene or isoform level) we utilize expression at exon-level. For this particular data, 74.2% of the genes (and 78.7% of isoforms) consisted of multiple exons, ranging from 2 to 73 exons for a single transcript. Amongst all isoforms only 12.9% consisted of 50% or more long exons, 28.5% have 50% or more short exons, and remaining had varied lengths of exons. We used 5-th and 95-th percentiles from the exon-length distribution to define short and long exons respectively. Thus in differential calling it is unlikely to have a systematic bias toward any length for these transcripts. However due to RPKM bias toward length the standard error will be affected by the underlying variation in length, weakening our power of detection. Another point to note is that for Highly expressed isoforms and low/no-expression isoforms for each stress condition and for control sample were identified. A pairwise check for commonality of these when compared to other conditions were carried out Table . We defit-like statistic was computed for each isoform in each such comparison. We consider a decision rule based on the mean of this statistic and compare it with an appropriate t-critical value based on the number of exons for that isoform. Note that this rule can only be used for isoforms with two or more exons.We present differential expression behavior under different stress conditions when compared with expressions in the control sample . A Bayesian t-statistics and define those as up or down regulated if the 95% PPI of the t-statistic is in the upper or lower 10 percentile of all (mean) t-statistics thus calculated .Alternately we use the PPI of the ed Table . This meIt is apparent from the results presented so far that the isoform expressions vary under different stress conditions as expected. However many of the genes are not single isoform genes thus we need to explore further whether the observed variability is only at the gene level across conditions or whether alternately spliced transcripts behave differently under different conditions.Using overall variability parameters we estimate that approximately 4.06% of isoforms with globally normalized data and 2.74% isoforms with quantile normalized data exhibit varied expression under different stress conditions. To infer these we observe that the variability parameters estimated follow approximately Gamma distributions Figure .Of the total 7737 genes analyzed, 1227 genes have multiple isoforms. Of which 75 genes have at least one isoform not variable  and another moderately variable . More interestingly 195 genes have at least one highly variable isoform (with variability above than the 90-th percentile) and another in the lower half. Thus for same gene not all isoforms behave in similar manner across all sample conditions. The above findings are based on globally normalized data and similar summary under quantile normalization are respectively 57 and 175 genes.We compared our findings with two existing methods, namely modeling the exon-expression data with GLMs and secondly by using splice junction data only to infer isoform expression using Bayesian models.For GLM we used a model similar to one proposed by Bullard et al. . HoweverThe Bayesian modeling framework proposed for exon data can be readily used for splice junction data too. Note that splice junctions would be typically short in length and as discussed earlier mRNA-Seq technology produces number of reads biased toward longer genomic regions. This is expected to cause the reads to have inflated amount zero read counts and underrepresentation the true expression from these regions. Our preliminary exploration of the splice junction data confirmed this hypothesis. We further compared the distributional behavior of the tag counts from the splice junctions to that based on reads from exons and found them to be comparable to those from exons of similar lengths.R2) were presented in the figures to provide an assessment of linear association between the two sets of estimates.For further analysis of the splice junction data, it was first normalized using a similar percentile normalization technique described earlier and then modeled using the proposed Bayesian modeling framework. Figure R2 measure reflects this low degree of linearity between the two estimates. The expression estimates are affected also but the degree of linearity is much improved (with a reasonably high R2), although still continues to under-estimate. We also explored the inherent variability in splice junction data and found it to be higher compared to exon-based-data. This can be assessed easily by comparing measurements on exons and junctions from genes with single transcript only (results not shown).As was noted from the raw data itself, the splice junction data underestimates transcript presence and thus the estimated probabilities based on junction data are much lower than those obtained using exon data. This relation is curvilinear in nature and possibly is “S-shaped” as has been observed elsewhere, e.g., for microarrays. The We have presented a Bayesian framework based on mRNA-Seq data to infer expression at isoform level. One of the main advantages of our model is that it has been developed for multiple conditions, however the parameterization enables us to infer at various levels. Although complex experimental scenarios are not uncommon, as can be seen from the real data sued here for illustration, a lot of the focus on methodological development for mRNA-Seq data continues to focus on differential expression , at transcript level, comparison across samples, comparison between samples, etc.We have utilized latent indicator variable for expression apart from additional parameters to quantify such expression. This differs significantly from existing approaches, where latent variables are used for differential call. Our method has twofold advantages over existing methods. First advantage is at the level of model identifiability, which is well-known for this type of spike-n-slab models. These variables also serve the purpose of variable selection and regularization against over-fitting.t-statistic, however can be captured here using the latent expression indicators. This is a known in biology, that in order to play a significant role in a biological process a transcript may not have to be expressed in high degree but differently with high confidence. Thus if for an isoform the latent expression variables indicate with high confidence expression in one condition and not expressed in another the corresponding isoform can be declared differential, without the help of a t-statistics.Secondly, our method has an advantage at the level of pairwise testing. If an isoform is not expressed in one of the samples then this would typically un-stabilize a formal We would like to reiterate that focus of this paper has been in developing modeling and inference procedure for expression measurement. Thus several other relevant aspect of mRNA-Seq data has not been addressed. Some of these are, how to use splice junction reads, what to do with multi-reads, how to make better use of unmapped reads. From current literature we see that a considerable effort is being put on these issues [Top-Hat and Cufflink by Trapnell et al. , FX by HOur aim has been to make the readers aware that, firstly there should be a modeling setup that allows complex experimental data going beyond differential expression to be analyzed, secondly even for simplest of inference, like expression of a single transcript gene; there could be significant effect of normalization procedure. We believe the proposed model and inference setup here addresses these adequately.Arabidopsis and for many genes multiple splice variants were found to be active under different conditions.For the particular data used for illustration here, we noted that there could be significant effect of normalization, if not for all, at least in part of the data. For this data an in-depth presentation of the differential and variable expression could not be provided here. However it was known that alternate splicing plays a very important role in functioning of The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


We propose a method for improving the quality of signal from DNA microarrays by using several scans at varying scanner sen-sitivities. A Bayesian latent intensity model is introduced for the analysis of such data. The method improves the accuracy at which expressions can be measured in all ranges and extends the dynamic range of measured gene expression at the high end. Our method is generic and can be applied to data from any organism, for imaging with any scanner that allows varying the laser power, and for extraction with any image analysis software. Results from a self-self hybridization data set illustrate an improved precision in the estimation of the expression of genes compared to what can be achieved by applying standard methods and using only a single scan. DNA microarray technology is used to study simultaneously the expression profile of a large number of distinct genes . SeveralOne of the objectives of microarray experiments is to identify a subset of genes that are differentially expressed be-tween the samples of interest. The relative intensity between the samples at a spot  is extracted by applying suitable image processing methods to the images produced by scanning the microarray slides on which the two samples have been hybridized. Errors occurring during image acquisition affect all further analyses and, therefore, the process of generation of these digital images is crucial. Photomultiplier tube (PMT), laser power (LP), and analog to digital converter (ADC), are the main components of an acquisition device, the scanner, which controls the for-mation of digital images. Each spot on the hybridized slide has fluorescent molecules corresponding to the two labeled samples and they emit photons upon excitation by a laser. The photons are converted into electrons by the PMT and the amount of current that eventually flows is directly proportional to the amount of incident light at the photocathode, unless saturation occurs . SaturatA single scanner setting will not be optimal for both weakly and highly expressed genes. The choice of the parameters (of a scanner) involves a trade-off between spots with a low intensity and spots that are saturated to some degree. Thus it seems reasonable to consider multiple scanning of the same microarray at different scanner sensitivities and estimate spot intensities from the combined data.Not much work has been done so far on improving the data quality by using multiple scans and by adjusting for pixel censoring. Dudley et al.  increaseOur approach towards improving quality of intensity measurements is based on first producing three images with different scanner sensitivities, and obtaining three different sets of expression values. We then apply a novel Bayesian latent intensity model, in which these different sets of expression values are used to estimate suitably calibrated true expressions of genes. The resulting estimates, treated in the form of respective (posterior) distributions, can be used in a higher-level analysis for identifying differentially expressed genes. The proposed approach is applicable to standard microarray methodology and to cDNA arrays. The method, however, cannot be applied to Affymetrix gene chips as the current Affymetrix technology does not allow multiple scanning. The method is generic and can be applied to data from any organism, imaging with any scanner that allows scanning at different laser powers, and extraction with any image analysis software.In this study, we used cDNA microarrays containing 16 000 individual fragments printed in duplicate . Our approach was tested on two experiments. The first experiment was designed to examine the effects of RhoG on HeLa cells by comparing expression profile of RhoG expressing cells versus control cells. This experiment was performed on two arrays  using an appropriate setting for samples labeled with Cy3 and Cy5. The line scan function of the scanner was used to equalize the intensities from Cy3 and Cy5 channels. A setting with the highest laser power was used to make the first scan scan-1). Under this setting, because of high laser power, saturation occurs for spots with high RNA abundance, but the spots with low RNA abundance get captured accurately. This setting was chosen so that the background corrected intensity (foreground-background) from the spots with low RNA abundance was at least 200. Subsequent scans were performed with a lower laser power (reducing it by 10 units in each subsequent scan) for both channels but keeping the same PMT as in the first setting. With this lower laser power the number of spots with a saturated intensity decreases, whereas the number of spots with a low intensity (or below the threshold of 200 units) increases. Repeated scanning does not significantly damage fluorescence (data not shown), nor does lowering laser power affect the balance between the channels. Figure . Under thttp://www.axon.com/GN _ GenePix4000.html). The automatic spot finding algorithm of GenePix was used to find spot boundaries and to calculate spot intensities. Spot fore-ground and background intensities for both channels were derived and background corrected intensities above 200 from all three scans were used for our study.Digital images were processed using GenePix Pro version 3.0 software  scale by Here we describe the model (on logarithmic (base e) scale) used for estimating a suitably calibrated "true underlying expression of a gene." We assume that each gene has an underlying signal, which cannot be measured directly. We call this underlying signal the where http://www.hamamatsu.com). If there were no measurement errors, we could write the observed intensity Let where Strictly speaking, right censoring at o et al.  providedTo complete specification of the model, we assume errors Several authors suggested Bayesian methods for analyzing microarray data –16. UndeOur primary interest is in estimating the true underlying latent intensities A priori, the parameters Step 1.Specify initial values of Step 2.Sample the latent intensities Step 3.Sample Step 4.Sample Step 5.Sample augmented Step 6.Repeat step 2 to step 5 till sufficient samples are gen-erated.The model was formulated in BUGS language and pa-rameter estimation was performed using WinBUGS . WinBUGSThe approach described in this paper was tested on two real data sets described in Section 2.1 For the first experiment, samples were hybridized on two arrays To estimate   within an array due to the print-tip effect and across arrays due to the array effect 19, the cThe estimated posterior medians of the latent intensities  for data from Cy3 dye, along with the measurements from scan-1  for 530 spots are displayed in Figure Figure We validated the fit of the model by plotting the re-siduals arising from each of the three scans as displayed in Figure A different way of illustrating the performance of our method can be provided by using simulated data (from the same model). For each data set generated by our model, and for each gene, we obtain the posterior distribution of the "true" expression level (known from the simulation), and can thereby quantify the degree of uncertainty in the estimation of that value . This is illustrated in Figure Finally, to also consider simulations where the data had been generated by a different model, we generated 100 datasets from model (2) of Khondoker et al.  by usingIn our work the correction for the two dyes was done separately, as the labeling efficiencies and fluorescent properties of the two dyes are different. The existence of systematic differences between the two dyes has been documented in the literature, and they have been treated separately by 2021 whil20Here our focus has been on the systematic bias in the intensity measurements caused by intrinsic scanner noise at the lower end and pixel censoring at the upper end. These two problems cannot be handled under a single scanner setting. Moreover, guidelines are not available for choosing optimal scanner settings to address both of these issues. Therefore, it seems reasonable to do several scans on every array, some at relatively lower sensitivities (ensuring no censoring at the upper end) and others at higher sensitivity levels (to capture weakly expressed genes), and ultimately combine the information to get improved gene expression measurements at all ranges. More scans can easily be accommodated in the model but there are practical limitations like degradation of the dye and the time required for scanning. Keeping these points in mind, three scans seem to be a good compromise.The proposed method has advantages at three levels. First, modeling under the Bayesian framework allows for missing data estimation by sampling randomly from the corresponding posterior predictive distribution. Second, it allows for joint estimation of a large number of model parameters and latent variables. Usually for analyzing microarray data, the statistical methods are applied in a sequential manner with the output of each step in the analysis serving as the input for the next. Under the sequential approach, the uncertainties in the conclusions from any earlier step make the subsequent steps dependent on the particular choice of the method and the resulting point estimate that is then used. In our model, such uncertainties are accounted for in a systematic manner as we work with distributions of all the unknown parameters, including the latent expression of the genes being considered. A third aspect of our method is that it opens up the possibility of extending the current model to accommodate features of normalization and identification of differentially expressed genes in an integrated model, which first improves the overall signal and then identifies differentially expressed genes by using such improved signals. Realization of the integrated model is in principle a straightforward modification to the model proposed here, by adding further layers to the present hierarchical model. Such additional layers would then account for between-array variations, within-array variations, and dye swap, and allow for comparing and combing data from multiple arrays. We are currently working towards such an integrated model.See Algorithm 1.Algorithm 1: Code written in BUGS language.modelcut1<- 6.29cut2<- 7.29cut3<- 8.29cut4<- 9.29cut5<- 10.29for(i in 1 : N) T[i]<- muYe1[i] class[i]<- 1 + step(logye1[i] - cut1) + step(logye1[i] - cut2) + step(logye1[i] - cut3) + step(logye1[i] - cut4) + step(logye1[i] - cut5)muYe2[i]<- A[i]+B[i]+C[i]A[i]<-  Ilogye2[i] ~ dnorm Ilogye3[i] ~ dnorm Ifor(j in 1 : nClass)tau1[j] sigma1[j]tau2[j] sigma2[j]tau3[j] sigma3[j]b[j] ~ dunifd[j] ~ duniffor(i in 1 : N)residual1[i]residual2[i]residual3[i]where N is the number of genes, logye1, logye2, logye3 are the measurements from the three scans on logarithmic scale,I, I, I were used to specify the lower bound for the censored measurementsfrom the three scans.