Transcriptomics meta-analysis aims at re-using existing data to derive novel biological hypotheses, and is motivated by the public availability of a large number of independent studies. Current methods are based on breaking down studies into multiple comparisons between phenotypes (e.g. disease vs. healthy), based on the studies' experimental designs, followed by computing the overlap between the resulting differential expression signatures. While useful, in this methodology each study yields multiple independent phenotype comparisons, and connections are established not between studies, but rather between subsets of the studies corresponding to phenotype comparisons. We propose a rank-based statistical meta-analysis framework that establishes global connections between transcriptomics studies without breaking down studies into sets of phenotype comparisons. By using a rank product method, our framework extracts global features from each study, corresponding to genes that are consistently among the most expressed or differentially expressed genes in that study. Those features are then statistically modelled via a term-frequency inverse-document frequency (TF-IDF) model, which is then used for connecting studies. Our framework is fast and parameter-free; when applied to large collections of Homo sapiens and Streptococcus pneumoniae transcriptomics studies, it performs better than similarity-based approaches in retrieving related studies, using a Medical Subject Headings gold standard. Finally, we highlight via case studies how the framework can be used to derive novel biological hypotheses regarding related studies and the genes that drive those connections. Our proposed statistical framework shows that it is possible to perform a meta-analysis of transcriptomics studies with arbitrary experimental designs by deriving global expression features rather than decomposing studies into multiple phenotype comparisons.
Citation: Caldas J, Vinga S (2014) Global Meta-Analysis of Transcriptomics Studies. PLoS ONE 9(2): e89318. https://doi.org/10.1371/journal.pone.0089318
Editor: Tanja Zeller, Medical University Hamburg, University Heart Center, Germany
Received: September 24, 2013; Accepted: January 18, 2014; Published: February 26, 2014
Copyright: © 2014 Caldas, Vinga. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was supported by national funds through Fundação para a Ciêancia e a Tecnologia (FCT, Portugal) under contracts PestOE/EEI/LA0021/2011; through IDMEC, under LAETA (PestOE/EME/LA0022); and projects PneumoSyS (PTDC/SAUMII/100964/2008), InteleGen (PTDC/DTPFTO/1747/2012), and BacHBerry (FP7KBBE20137 singlestage, Grant Agreement no 613793). SV acknowledges support by Program Investigador FCT (IF/00653/2012) from FCT, co-funded by the European Social Fund (ESF) through the Operational Program Human Potential(POPH). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Meta-analysis consists of aggregating the outcome of multiple studies in order to derive robust and reproducible results . In DNA microarray transcriptomics, the availability of large-scale public databases such as ArrayExpress has encouraged the development of meta-analysis methods . The meta-analysis paradigm has been successfully used in a variety of applications, including oncogenomics , drug repurposing , disease diagnosis , and mapping of tissue and condition-specific expression signatures . Additionally, web-based tools have been developed for facilitating the exploration of large collections of transcriptomics studies –. For recent reviews of the field, see e.g.  or .
The challenges involved in performing meta-analysis stem from the intrinsic complexity of biological phenotypes, as well as from the observed heterogeneity between independent studies, namely the use of multiple microarray platforms, biological samples, and experimental procedures. In order to minimize the impact of those factors, meta-analysis methods typically focus on examining differential expression signatures across studies. Figure 1a illustrates this approach. This consists of first breaking down each study into a set of comparisons between phenotypes and then deriving a differential expression signature from each phenotype comparison. Connections between phenotype comparisons are then established based on the similarity between the corresponding differential expression signatures. Potential similarity measures include for instance correlation-based methods or probabilistic relevance measures ,.
Two studies from a collection of independent studies are shown. One of the studies includes experimental annotations about gender (Male or Female) and disease status (Healthy or Disease), while the other study includes experimental annotations indicating whether each sample comes from a Control or a Treatment. In the differential expression approach each study is broken down into a set of comparisons between phenotypes, with the first study yielding two comparisons and the second study yielding a single comparison; genes are ordered according to a differential expression measure, e.g., log-ratios, which are used as a basis for computing the similarities between phenotype comparisons. In the proposed approach, one first decides if the analysis is based on absolute expression or differential expression. Then, in the case that one is interested in a differential expression analysis, the expression in every non-control sample (e.g. Treatment or Disease) is computed relative to the corresponding control sample. Afterwards, the rank product method is used to compute global, study-wide features corresponding to genes that possess a consistently high expression or differential expression in a given study. These global features are statistically modelled and used as a basis for deriving similarities between studies. The connections are therefore established not between subsets of studies, but rather directly between studies.
Meta-analysis approaches based on decomposing studies into comparisons between phenotypes, while successful, are critically hampered by the lack of extensive experimental and clinical annotations about the samples in each study. They also do not infer global connections between studies, rather detecting similarities between subsets of the studies corresponding to specific phenotype comparisons (cf. Fig.1a). While this latter aspect is not necessarily a disadvantage, an important methodological open question in transcriptomics meta-analysis is whether it is possible to aggregate and summarize all of the expression data within each study, regardless of the study's specific experimental design, with the aim of directly establishing global connections between independent studies. To the best of our knowledge, no general methods have been proposed with this purpose in mind.
While gene or pathway-oriented statistical tests  have been frequently used in the context of differential expression-based meta-analysis frameworks, they rely on decomposing each study into a set of comparisons between phenotypes. On the other hand, standard similarity measures such as Spearman correlation may be combined with linkage criteria to establish an overall similarity measure between studies. For instance, the global similarity between two studies may be computed as the mean Spearman correlation between microarrays from the two studies. However, this approach merely aggregates similarity measures between study subsets; our aim is rather to devise a method for globally encoding each study with features that represent the study's relevant expression signatures, allowing studies to be globally connected on the basis of those features. Additionally, the global features can be used to guide the interpretation of the inferred connections, which helps to formulate posterior biological hypotheses.
We propose a statistical meta-analysis framework for establishing global connections between transcriptomics studies, which does not require breaking down the studies into sets of phenotype comparisons. Intuitively, our approach detects the genes within each study that consistently possess high absolute or differential expression (for one-channel arrays) or expression ratio (for two-channel arrays) values across the arrays in that study. If the aim is to analyze absolute expression values in one-channel arrays, our approach does not make use of each study's experimental annotation. On the other hand, if the aim is to analyze differential expression values in one-channel arrays, our approach simply requires an indication of which samples in the study are used as a control. Connections between studies are then inferred and interpreted on the basis of shared relevant genes, via a vector space model. Figure 1b summarizes the flowchart of the proposed framework.
Our framework partly relies on using the non-parametric Rank Product method  to aggregate gene expression data from all samples in any given study. The rank product method has been previously shown to be a useful statistic for aggregating differential expression fold-change measures across independent control-vs-treatment studies . In the present paper, we apply the rank product method in a vastly different manner. Instead of restricting ourselves to simple control-vs-treatment studies, we consider studies with arbitrary experimental designs. Also, we do not use the rank product method to directly aggregate data from independent studies; rather, we use the rank product method to obtain a measure of consistent expression for every gene within each study, thus deriving an encoding for every study which is then used as a basis for matching independent studies according to their similarity. In effect, in our setting it is not possible or meaningful to apply the rank product method as described by Hong and Breitling , because we do not have an a priori list of related studies with equivalent experimental designs; we instead have a large, heterogeneous collection of studies with varying experimental designs that we want to mine for interesting connections.
We apply our framework to large, heterogeneous collections of transcriptomics studies from human and Streptococcus pneumoniae. We perform an analysis both on absolute and differential expression data, and also provide a strategy for harmonizing data from multiple platforms and S. pneumoniae strains. We propose a quantitative validation strategy that assesses the quality of the inferred connections by verifying if the connected studies share Medical Subject Headings (MeSH) terms . Using this strategy, we show that our method outperforms standard correlation-based measures in terms of connecting studies that are effectively related. Finally, we provide illustrative case studies of applying our method to both study collections.
Results and Discussion
In this section we provide an analysis of our proposed framework. Figure 2 displays a detailed methodology flowchart. We assess our framework in two ways: First, we measure the ability of the framework to detect connections between studies that are effectively related, using MeSH terms assigned to each study as a gold standard; second, we provide multiple case studies that show how the framework can be used as an exploratory tool to detect interesting connections between transcriptomics studies and generate novel biological hypotheses.
For succinctness, we illustrate the steps as applied to the Streptococcus pneumoniae two-channel array data collection. In stage (A), we download data from three souces: RefSeq, for bacterial genomes from multiple S. pneumoniae strains; ArrayExpress, for two-channel microarray transcriptomics studies along with the corresponding experimental annotations; PubMed, for the MeSH annotations associated with each study's corresponding publication. Stage (B) consists of multiple preprocessing and modeling steps. We start by mapping orthologous genes from different strains to the same so-called metagene. For each transcriptomics study, we rank metagenes in each sample according to their absolute log-ratio. Then, for each study and metagene we take the product of its ranks across the study's samples, derive a corresponding -value, and binarize -values accounting for multiple hypothesis testing. This yields a metagenes studies binary matrix that indicates for every metagene-study pair if the metagene is significant in the corresponding study. The last step in stage (B) is to convert the binary matrix into a weighted matrix via TF-IDF modeling. This consists simply of replacing ones in the binary matrix by a weight that is indicative of the corresponding metagene's information content. In stage (C), we apply the cosine similarity measure to connect studies on the basis of their TF-IDF vector-space encoding. We then assess the performance of the framework by quantifying the extent to which related studies are found to be similar, using MeSH terms as a gold standard. We also inspect the similarity matrix to detect interesting case studies that provide novel biological hypotheses.
The results and accompanying R software are available from http://kdbio.inesc-id.pt/~svinga/meta/.
We applied the MeSH test setting outlined in the Methods section to compare our framework to alternative approaches in three contexts: one-channel human microarrays with absolute expression values, one-channel human microarrays with differential expression values, and Streptococcus pneumoniae two-channel arrays with differential expression values.
We tested four alternative versions of our framework. In each version, either the binary or discrete rank product significance matrix is used; also, we either apply the TF-IDF model before computing cosine similarities between studies, or skip the TF-IDF step and directly compute cosine similarities on the rank product matrix . As additional competing methods, we considered correlation-based approaches that, unlike our framework, do not extract any global features from the studies. Instead, these approaches simply estimate the similarity between studies as a combination of the similarity values between microarrays of the compared studies. We chose the Spearman rank correlation coefficient as the similarity measure between microarrays from different studies. We then estimated the similarity between two studies as the maximum, mean, or median of the Spearman correlation between microarrays from the two studies. Our choice of similarity measure is based on the fact that the Spearman correlation coefficient is a well-performing robust nonparametric estimator of statistical dependence . Additionally, it has been previously shown to perform well in the transcriptomics meta-analysis setting ,.
Regarding the actual testing procedure, in essence we measured each method's ability to connect studies that are effectively related, using PubMed MeSH annotations as a gold standard. Given a study designated as the query, we sort the remaining studies according to their relevance to the query study. Then, for each of the query study's MeSH terms, we quantify how top retrieved studies tend to include that same MeSH term, using a standard information retrieval performance measure known as Average Precision (AP). Applying the aforementioned test setting yields a set of AP performance scores for every competing method, with every study yielding an AP score for each of its assigned MeSH terms. Throughout this section, we apply a one-sided paired Wilcoxon signed-rank test  to evaluate if the AP scores in a given method are significantly higher than the corresponding AP scores in another method. In our context, the one-sided Wilcoxon signed-rank test specifies the null hypothesis that the median difference between paired AP scores from the two methods is zero, while the alternative hypothesis specifies that the median difference is greater than zero.
The first question we addressed was whether the -value threshold used in computing the binary significance matrix had an impact on the framework's performance. Figure 3 displays the mean and standard error of AP scores when varying the -value threshold. It can be seen that the performance peaks at for the human data sets and at for the S. pneumoniae data set, which indicates that standard -value thresholds may be safely chosen. Additionally, it can be seen that the framework's performance when the TF-IDF step is not performed typically lags behind. The exception is for the S. pneumoniae data set, where the “no TF-IDF” framework appears to perform slightly better than the “TF-IDF” framework, particularly at the peak performance point . However, the one-sided paired Wilcoxon signed-rank test indicates that this difference is not significant (). On the contrary, the signed-rank test on the human data set (absolute or differential expression), applied to the data at the peak performance point , indicates that the “TF-IDF” framework is significantly better than the “no TF-IDF” framework (). In the following method comparisons, when considering the binary version of our framework, we take for the human data and for the S. pneumoniae data, in order to avoid displaying an excessive number of performance values for multiple methods.
Mean and standard error of the AP scores when a -value threshold is used. For each data set, we display the performance for two alternatives of our framework, namely with or without the TF-IDF step. Notice that, for every -value threshold (x-axis), the two framework alternatives are displayed side-by-side.
Then we proceeded to assess the performance differences between our framework variants and the Spearman competing methods. Figure 4 displays the mean and standard error of the AP scores for both our framework and the Spearman correlation-based methods. It can be seen that our framework attains higher scores in all data sets. Finally, is can be seen that on the human data sets, the discrete variants attain a better performance, while in the S. pneumoniae data set the binary variant performs the best.
Mean and standard error of the AP scores for four variants of our framework, as well as for three Spearman correlation-based methods. Regarding the x-axis labels, “binary” indicates the binary significance matrix variant of our framework while “discrete” indicates the discrete significance matrix variant; “bin + IDF” and “disc + IDF” indicate those two same variants, but also performing the TF-IDF modeling step prior to establishing connections between studies; finally, the “max-SP”, “mean-SP”, and “median-SP” labels refer to the maximum, mean, and median statistic summarization approaches in the competing Spearman correlation methods.
Taken together, these results indicate that our method's feature-based, global encoding is an adequate basis for connecting studies, improving on correlation-based approaches that are known to perform well in the meta-analysis setting ,. Additionally, usage of the TF-IDF weighting scheme improves upon the connectivity performance of our proposed framework, for both the binary and discrete rank product estimation approaches.
In this section, we describe case studies using our proposed method with a -value threshold of .
Homo sapiens study collection.
Table 1 displays query examples, the first two considering absolute expression and the second two considering differential expression. The table also include the corresponding top-three most similar studies and the three protein-coding genes with the highest IDF score that are significant in both the query and the top-three most similar studies. The justification for this heuristic is to focus on genes that are significant in a low number of studies in the collection (i.e. that possess a high IDF score); the event of these genes being significant in both the query and the top-three most similar studies is statistically more significant than the same event for genes with a low IDF score. For succinctness of analysis only the three top studies are shown. Note that in order to maximize the interpretability of the results, we display the three protein-coding shared genes with the highest IDF scores. In some case studies, the shared probesets with the highest IDF scores do not match to known protein-coding genes. In such cases, we do not present those probesets in the corresponding results table, as interpreting why such probesets are shared by independent studies requires further probeset-mapping work that falls outside the scope of this paper. However, our web-based tool shows the full extent of the results, including probesets that do not match to known protein-coding genes.
In the first case study, the query study analyses the expression of pancreatic cell clusters derived from the embryonic stem cell T3 cell line. All of the top three studies are mapped to the MeSH term “Embryonic Stem Cells”. The first shared significant gene is CTSL2, a cathepsin family member; it has recently been proposed that Cathepsin L family members play a role in differentiation via histone proteolysis . The second shared gene VWDE codes for the von Willebrand factor (VWF) D and EGF domain-containing protein; while no direct role in stem cell differentiation has been proposed for VWDE, EGF has been shown to promote proliferation of mouse embryonic stem cells in mouse , while VWF has been shown to regulate adhesion of mesenchymal stem cells to endothelial cells . Finally, ZFP42 is a known marker for pluripotency in embryonic stem cells .
In the second case study, both the query study and the top-three most relevant studies involve expression profiling of muscle tissue. Concerning the three protein-coding genes with the highest IDF score, BEST3 is expressed in renal and muscle tissues . On the other hand, MYLK4 is a partly characterized member of the Myosin Light Chain Kinases (MLCKs) protein family, known to have muscle-specific expression . Finally, we did not find evidence for constitutive expression of MIB1 in muscle tissue, which leaves open the question as to why it is relevant to the association between the three muscle tissue studies. This case study again highlights the ability of the proposed framework to connect independent studies based on tissue-specific expression.
In the third case study, both the query and the retrieved studies concern transcription profiling in hepatocytes. While NR1I3 is a regulator of multiple hepatic genes , we did not find a hepatocyte-related role for WDR72 or IDO2, which suggests these genes may have yet unknown liver-related roles.
In the fourth case study, the framework connects a prostate cancer study with two other cancer studies and one hepatocyte-related study. Concerning the top-three shared genes, HINT1 is a tumor-suppressor gene in gastric cancer, which suggests it may have a yet-unknown role in prostate cancer . As for DGKH, it is known to be associated with bipolar disorder , leaving open the question of a potential role in prostate cancer. Finally, we did not find a relevant role for VPS13B in the query or retrieved studies. Interestingly, when considering only the query and the top retrieved study, the shared protein-coding gene with the highest IDF score is the transmembrane protease, serine 2 (TMPRSS2) gene, known to be differentially expressed in prostate cancer .
Finally, we note that when applying the previously described median Spearman correlation method to compute the top-three studies for each query, we were not able to obtain the results here described. Concretely, for the stem cell case study, the retrieved studies were about ulcerative colitis, Parkinson's disease and double-stranded RNA recognition; for the muscle tissue case study, while the top retrieved study is E-GEOD-35659 (i.e. the same study as retrieved by our framework), the other two studies are about renal transplantation and pulmonary lymphoma; for the hepatocyte case study, only the study E-GEOD-24187 is retrieved in the top-three studies, the others being about keratinocytes and pancreatic cancer; finally, for the prostate cancer case study, the retrieved studies concern stem cells, interstitial lung disease, and B-cell differentiation, therefore seeming less relevant to the query study than the retrieval results provided by our framework. Additionally, in all case studies the average number of MeSH terms shared between the query and the top-three studies is lower for the median Spearman correlation method. This implies that our framework's improved performance ultimately yields results that are biologically more meaningful than when applying correlation-based approaches.
Streptococcus pneumoniae study collection.
Here, we describe two case studies from the S. pneumoniae two-channel microarray study collection related to the MeSH terms “Zinc” and “Virulence”. Table 2 displays each query study, along with the top three most similar studies. In each of these two case studies, we found that the third most similar study does not share the same MeSH term as the query. Therefore, we restricted our analysis to the top-two most similar studies. In general, since the S. pneumoniae study collection includes only 21 studies, it is expected that only the very top most similar studies are effectively related to the query.
Regarding the zinc case study, both the query and the top-two studies are annotated with the MeSH term “Zinc”. The study samples correspond either to an adhesin competence repressor (adcR) knockout strain vs. wildtype or to a zinc pulse. Zinc is known to influence the expression of multiple S. pneumoniae genes ,, while adcR is a zinc-sensing transcription factor involved in multiple processes including virulence and antibiotic stress response . We computed the genes that are significant in all three studies, obtaining a group of nine genes: adh, adhP, adcA/B/C/R, lmb, and phtD/E. Most of these genes have been reported as direct transcriptional targets of adcR in one of the analyzed publications . Our framework therefore confirmed that a group of adcR transcriptional targets is significantly expressed in multiple zinc-related studies. This shows how our meta-analysis approach can be used as an in silico computational validation strategy.
Regarding the virulence case study, both the query and the top two studies share the same “Virulence” MeSH annotation. The genes that are significant in all three studies are the transcription factor mutR and two members of a putative bacteriocin system (SP_0142/0143). Interestingly, while large differences in the bacterial virulence phenotype of mouse models were observed in all three studies, no major virulence role has been assigned to any of these genes. It is therefore an open question whether these genes possess a relevant role in the S. pneumoniae virulence phenotype. Potential follow-up studies may involve performing transcription and virulence assays of S. pneumoniae response to knockouts of mutR, SP_0142 and/or SP_0143.
As in the human case studies, the overlap between our results and the results obtained with the median Spearman correlation method are low — only one study from the virulence case study is also retrieved by the correlation-based method. Additionally, the mean number of MeSH terms shared between the query and the top studies is lower in both case studies for the median Spearman correlation method.
In the present work we have proposed a framework for performing meta-analysis of transcriptomics studies. Our main contribution is in providing a solution to the open methodological question of whether it is feasible to perform meta-analysis on a global, study-wide level (establishing direct connections between studies rather than between study subsets), by learning study-wide expression signatures that provide a basis for interpreting the connections and deriving novel biological hypotheses.
Using a MeSH-based test setting, we have shown that our framework improves upon the performance of correlation-based measures that estimate the similarity between studies as a combination of the similarities between the corresponding microarrays (this latter approach does not learn any global study features, therefore hindering the subsequent analysis). Finally, via a series of case studies, we showed that our global meta-analysis framework yields biologically meaningful results, in particular suggesting a follow-up study on the potential virulence role of the Streptococcus pneumoniae genes mutR, SP_0142, and SP_0143.
Our proposed framework has certain desirable properties: It is fast, since both the rank product and the TF-IDF methods are easily parallelizable and run in a few minutes on a single CPU; it is parameter-free, since apart from an optional, standard -value significance threshold, the user is not required to specify any parameter settings. Importantly, the rank product method is threshold-free, i.e., it does not require the previous specification of a rank threshold that classifies genes in each study sample as “high-ranking” or “low-ranking”. Finally, our log-score interpretation of the rank product method suggests that this method is particularly suited to the high-throughput setting, as log-ranks yield a damping effect that effectively makes large ranks equivalent.
Our proposed test setting was based on the MeSH annotations of the paper associated with each study. However, other ontological tools may be used for evaluation purposes. For instance, the recently developed Experimental Factor Ontology (EFO)  maps experimental design variables to standardized terms. The EFO may be used for instance to measure the degree to which similar studies share the same experimental annotations.
One important consideration is how our framework and other recent proposals for gene expression meta-analysis map to “classical” meta-analysis frameworks. In classical meta-analysis, one starts with a set of studies that are known to be related, and methods are proposed for aggregating the results of said studies. Here, the aim is different: There is instead a large, disorganized collection of studies and methods are proposed for suggesting which studies are related. Naturally, the detected connections may correspond to studies that are known to be related and which could be obtained using standard text-driven methods (e.g. studies about the same disease). However, the detected connections may also correspond to unexpected, novel connections, which are not supported by the textual annotations assigned to each study, and which may be used as a basis for establishing and testing novel biological hypotheses. Once related studies are identified by our framework, it is straightforward to derive a consensus from the studies, by simply computing the genes which are the most significant in the majority of them.
Finally, the integration of additional data types into our framework is also an open challenge for future work, which is becoming increasingly relevant due the emergence of large-scale transcriptomics projects which aggregate data from complementary technologies . Additionally, statistical meta-analysis methodologies will have to adapt to emerging next-generation sequencing technologies . While our framework takes as input pre-processed gene expression data, therefore not being directly dependent on the underlying technology used to generate the data, applying our framework to next-gen data falls outside the scope of our paper and is presently difficult due to the yet small number of available studies.
Materials and Methods
Microarray Data Source
We accessed the ArrayExpress database  to download transcriptomics studies from the one-channel Affymetrix GeneChip Human Genome U133 Plus 2.0 and from the species Streptococcus pneumoniae. We chose this particular Affymetrix platform because it is the one with the highest number of human studies in ArrayExpress. We also chose S. pneumoniae for analysis due to our own expertise and to demonstrate the applicability of our method to two-channel microarrays. For S. pneumoniae studies, we focussed our analysis on two-channel microarray studies, which correspond to the vast majority of available studies. We discarded studies that did not contain processed data, which were not associated with published articles indexed in PubMed, or which were a subset of other studies.
For human studies, we restricted our analysis to studies with processed data files under 16 MB, corresponding to about eighty percent of the total number of studies. This threshold was established in order to accelerate the analysis by avoiding the download and parsing of excessively large files.
We considered microarray studies whose processed expression files contain the standard column names ID_REF or Reporter_Identifier for identifying probesets and the column names VALUE or AFFYMETRIX_VALUE for identifying processed expression values. Since S. pneumoniae studies correspond to multiple array platforms, we considered only studies whose microarray platform file contains the standard columns Reporter Name (probe identifiers) and ORF (open reading frame). The column-name requirements allow for a fully automated processing pipeline.
For human studies, we performed the subsequent analysis directly on probesets, while for S. pneumoniae studies we first mapped probes to ORFs using each study's corresponding array design file, summarizing the expression of probes that map to the same gene by computing their median expression. We assumed two strategies for missing value replacement, depending on whether the human study collection analysis is based on absolute or differential expression. For absolute expression, we replaced missing values within a given study's expression data with the minimum absolute expression value in that study; for differential expression, we replaced missing values for a given gene with its mean observed expression. The rationale for these two strategies is to assign the lowest ranks to genes whose expression is not observed.
After pre-processing, our approach yields a total of 289 human studies corresponding to 4368 microarray samples and 21 Streptococcus pneumoniae studies corresponding to 129 microarray samples.
Homo sapiens Differential Expression
For the human study collection, we performed two independent analyses, one based on absolute expression, the other based on differential expression. In the absolute expression analysis, we did not make use of each study's experimental annotations. In the differential expression analysis, we downloaded each study's experimental design annotation files from ArrayExpress. In those files, each array in each study is assigned to a number of so-called experimental factor values which indicate the experimental annotation for that array, e.g., Disease State = Cardiomyopathy or Gender = Male. We collected all the experimental factor value annotations for all arrays in all studies and manually decided which of those annotations correspond to typical experimental controls (e.g., DiseaseState = Normal, Treatment = Control, Time = 0h). The full list of control annotations is available from Text S1 in File S1. Then, for each study, we selected a subset of arrays corresponding to the study's control. If any arrays in the study are annotated only with experimental control labels, they are selected as the control and averaged. If no such arrays exist, then the control is defined as the average of all arrays in the study. Finally, we compute the log-ratio for each probeset's expression in each of the non-control arrays relative to the corresponding control.
Streptococcus pneumoniae Ortholog Mapping
In order to reconcile S. pneumoniae studies from multiple strains, we downloaded reference sequences for strains TIGR4 (NC_003028.3), D39 (NC_008533.1), and R6 (NC_003098.1) from the RefSeq database . We assessed the homology of coding sequences between every pair of strains by running the Nucleotide Basic Local Alignment Tool (BLASTN; ). We obtained orthologous gene groups by identifying groups of three genes, one per strain, which are all reciprocal BLASTN best-hits to one another. This approach yields a total of 1621 so-called S. pneumoniae metagenes.
We downloaded the entire MeSH tree from the MeSH web site and kept terms from the top-level categories Anatomy, Diseases, Chemicals and Drugs, Biological Sciences, and Persons. For every study corresponding to a PubMed-indexed paper, we downloaded its associated PubMed MeSH annotations, discarded qualifiers (e.g., Breast Neoplasms/genetics and Breast Neoplasms/metabolism are treated as equivalent annotations), and kept only the terms that belong to any of the aforementioned MeSH categories. The rationale for only considering a subset of MeSH categories is to discard categories that are not directly about biological findings or the samples and biological/clinical conditions under study (e.g. the Information Science category, which describes the computational methodology followed in each paper, is not taken into account).
We obtained study rank data by sorting the genes in each study sample according to their absolute expression (in the case of one-channel absolute expression analysis) or absolute log-ratio (in the case of two-channel arrays or one-channel differential expression analysis). Then we applied the Rank Product method  to compute the relevance of each gene in each study. Succinctly, the rank product assigns a score to each gene by computing the product of the gene's ranks across samples in a given study, or equivalently by computing the sum of the log-ranks,(1)(2)where indexes genes, indexes samples in a given study, is the total number of samples in a given study, and is the rank of the -th gene in the -th sample of a given study. The log-function above dampens the distinction between large ranks. We provide an additional discussion of this effect in Text S2 in File S1.
We used a Gamma distribution approximation method to compute -values, which is based on the null hypothesis that ranks are uniformly distributed . Text S2 in File S1 provides the details of the approximate method derivation. More recently, a method has been proposed for computing exact -values . Unfortunately, the running time for this method does not scale well enough for our large-scale purposes (Text S2 in File S1).
After obtaining -values, we tested two alternatives. First, we computed the corresponding false-discovery rate -values using the qvalue R package , and considered genes to be significant at a standard cut-off value of . As an alternative, instead of computing a binary significance, we round the value to the nearest integer. This latter alternative yields sparse discrete rather than sparse binary data. Additionally, this latter alternative does not require setting a significance threshold, thus making our framework entirely parameter-free.
The final output of the above approach is either a binary significance matrix that indicates for every gene-study pair whether gene is significant in study ,(3)or a discrete matrix where for each gene-study pair , we have , where is the -value of gene in study . In subsequent sections, we consider a gene to be active in a study when .
Term Frequency–Inverse Document Frequency
In order to detect connections between studies, we model the rank product matrix using the Term Frequency-Inverse Document Frequency (TF-IDF) vector space model ,. The TF-IDF model is commonly used in the natural language processing field; here, each study may be conceptually seen as a “document” and each gene as a “word”.
The IDF score is higher for genes that are active in a lower number of studies, and conversely lower for genes that are active in a greater number of studies. The idea is to model the information content of the event of a gene being active in a given study. Each study is then encoded as an array , where . As a technical detail, if a gene is inactive in all studies, then we simply discard it from the data instead of computing its IDF score. This speeds-up the computations and avoids the problem of having infinite IDF scores.
Finally, the similarity between two studies and is computed via the standard cosine similarity coefficient which measures the cosine of the angle between the corresponding pair of vectors in the TF-IDF vector space,(5)where is the dot product operator. Genes that possess a lower IDF score contribute less to the dot product between two studies. Conversely, genes that are seldom active in the rank product matrix and which therefore possess a higher IDF score make a larger contribution to the dot product between two studies. In other words, two studies are similar when they both activate genes that possess a high information content.
Connectivity Performance Evaluation
To assess if the model connects studies that are effectively related, we quantified the relation between study similarity in terms of (5) and study similarity in terms of shared MeSH terms assigned to the studies' PubMed-indexed papers.
For each study (hereafter designated as the query study), we consider each of its assigned MeSH terms in turn. We assume that studies possessing that same MeSH term are relevant to the query study, while the remaining studies are irrelevant. First, we sort all studies according to their similarity to the query study as per (5). Then, we take the similarity-sorted study list and compute the precision at each rank in the list,(6)(7)
This measure is known as Average Precision (AP) and is a standard performance measure in Information Retrieval. It can be geometrically interpreted as approximating the area under the precision-recall curve .
The above procedure yields for every study (considered as the query) and each of its MeSH terms a performance measure between zero and one, that quantifies how the studies that are most similar to the query tend to possess that same MeSH term. Figure 5 illustrates the described performance evaluation strategy.
Illustration of the proposed validation strategy. Each study in turn is considered as the query study, with the remaining studies being ordered according to their similarity with the query study. The query study has three fictitious MeSH terms: A, B, and C. The brown circles indicate studies that also possess those terms. The Average Precision (AP) performance measure is higher when the most similar studies also possess the given MeSH term, or conversely lower when studies mapped to the MeSH term are among the least similar to the query study. Notice that the number of AP performance scores per query study equals the number of its MeSH terms.
We thank Ana Rute Neves and Sandra Carvalho for valuable comments.
Conceived and designed the experiments: JC SV. Performed the experiments: JC. Analyzed the data: JC. Wrote the paper: JC SV.
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