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Mulcom: a multiple comparison statistical test for microarray data in Bioconductor
BMC Bioinformatics volume 12, Article number: 382 (2011)
Abstract
Background
Many microarray experiments search for genes with differential expression between a common "reference" group and multiple "test" groups. In such cases currently employed statistical approaches based on ttests or close derivatives have limited efficacy, mainly because estimation of the standard error is done on only two groups at a time. Alternative approaches based on ANOVA correctly capture withingroup variance from all the groups, but then do not confront single test groups with the reference. Ideally, a ttest better suited for this type of data would compare each test group with the reference, but use withingroup variance calculated from all the groups.
Results
We implemented an RBioconductor package named Mulcom, with a statistical test derived from the Dunnett's ttest, designed to compare multiple test groups individually against a common reference. Interestingly, the Dunnett's test uses for the denominator of each comparison a withingroup standard error aggregated from all the experimental groups. In addition to the basic Dunnett's t value, the package includes an optional minimal foldchange threshold, m. Due to the automated, permutationbased estimation of False Discovery Rate (FDR), the package also permits fast optimization of the test, to obtain the maximum number of significant genes at a given FDR value. When applied to a timecourse experiment profiled in parallel on two microarray platforms, and compared with two commonly used tests, Mulcom displayed better concordance of significant genes in the two array platforms (39% vs. 26% or 15%), and higher enrichment in functional annotation to categories related to the biology of the experiment (p value < 0.001 in 4 categories vs. 3).
Conclusions
The Mulcom package provides a powerful tool for the identification of differentially expressed genes when several experimental conditions are compared against a common reference. The results of the practical example presented here show that lists of differentially expressed genes generated by Mulcom are particularly consistent across microarray platforms and enriched in genes belonging to functionally significant groups.
Background
A frequent approach to analyse gene expression data involves the use of ttests, or their derivatives, to identify lists of genes with differential expression between two experimental groups [1]. Indeed, several microarray expression datasets encompass multiple experimental points to be compared with a common reference point such as timecourse designs or multiple different treatments versus a control condition. The analysis is then aimed at assessing for each gene in which experimental group the expression is significantly different from the control group.
A frequently chosen approach is to run a ttest for each comparison. However, when applied to this type of data, the ttest has two main problems: (i) it does not correct the result of each comparison for the total number of comparisons made and (ii) information about experimental variability (the standard error) is extracted only from the two groups actually compared. Consequently, in the instance of limited replicates, inaccurate estimation of standard error leads to high type I and type II errors in the analysis. For these two reasons, simple remedies like Bonferroni or other types of multiple testing correction of the threshold tvalue may avoid excessive false positives only at the cost of a significant reduction of the power. Alternatively, limitations of the ttest in this context have been addressed by implementing Bayesian modeling of the error [2] or by implementing sample permutationbased estimation of False Discovery Rate (FDR), like in the SAM approach [3, 4]. In particular, SAM compares the number of null hypothesis rejections in the dataset organized in the subgroups of interest against the median number of rejections on a series of randomly generated subgroups. These approaches however do not benefit, within each comparison, from information on withingroup variability available in the additional experimental groups.
As an alternative, ANOVAbased methods accumulate withingroup variability from all the groups. However, this strategy does not permit a pairwise comparison of each test group with the reference group [5]. Therefore, if a gene is differentially expressed in only one group versus the reference, this difference is diluted in the betweengroup variance calculated from all the groups.
The ideal approach would therefore be to estimate withingroup variance from all the groups and then to perform single pairwise comparisons. Towards this end, we designed the Mulcom test, a derivative of the Dunnett's ttest [6] adapted to microarray data analysis. The test, implemented as an RBioconductor package [7], includes an optional tuneable foldchange threshold (m) and Monte Carlo simulation performing sample permutations to assess FDR in each comparison. We also implemented a streamlined procedure for automated optimization of test parameters, to maximize the number of significant genes at a given FDR.
In the present work we provide a detailed description of the Mulcom algorithm and the results of comparative analyses between Mulcom and other widely used Bioconductor packages (SAM and Limma). Comparative analyses were run on a microarray dataset obtained on two different array platforms from the same set of samples.
Implementation
The Mulcom test was implemented using the statistical programming language R [8] with some functions wrapped from C++ to improve the performance of the script. The package is included in the opensource Bioconductor project [7].
The Mulcom package is designed to analyse ExpressionSet objects from the "Biobase" package as well as standard numeric matrices from the R environment. The Mulcom algorithm is based on the Dunnett's ttest [6], which estimates the withingroup variability across all the different groups to be compared with the common reference.
The Mulcom analysis takes place according to the following steps:
For each experimental group E, it compares the average signal E with that of the common reference group C to obtain the function.
It then applies all the experimental groups to calculate the withingroup Mean Square Error (MSE):
where s^{2} = square error, for each group i, including the reference group and a = degrees of freedom
Finally, the Mulcom t is calculated:
Where:
FC = fold change (difference), as calculated in (1)
m = minimal difference threshold (optional)
Nh = harmonic mean of sample replicates for the two conditions tested
t = tvalue of the test
MSE_{ wg } = mean square error within group, as calculated in (2)
To estimate the False Discovery Rate (FDR), steps (1) to (3) are repeated after random sample permutation for n times, to generate a distribution of the number of positive hits from n randomly assembled sample groups.
For each experimenttoreference comparison, the median number of positives in permuted sample groups is calculated, and FDR is estimated as $FDR=\frac{\overline{MRP}}{EP}$
Where:
MRP = Median Random Positives, i.e. the median number of null hypothesis rejections by the Mulcom test in all random sample permutations.
EP = Experimental Positives.
If no m fold change threshold is applied, users can manually define tvalue significance thresholds on the basis of Dunnett's test alpha tables, such as the one at http://davidmlane.com/hyperstat/table_Dunnett.html. The degrees of freedom are obtained by subtracting the number of groups (including the control) from the total number of subjects in all groups. If the alpha tables cannot be used the package implements a set of functions to choose the best combination of t and m, i.e. one giving the highest number of positives at a chosen FDR rate. Furthermore the package also assists the user in the identification of alternative combinations of t and m, which can be evaluated and chosen using the Mulcom Optimization Plot (Figure 1). The plot visualizes the number of significant genes for each combination of t and m within the respectively chosen ranges, limiting the display to those combinations having an FDR below a threshold of choice. Together with the optional m threshold value for foldchange, the FDR analysis based on Monte Carlo simulation is the main difference between the Mulcom test and the conventional Dunnett's ttest. Additional information on the use of Mulcom is provided with the package vignette http://bioconductor.org/help/biocviews/2.8/bioc/html/Mulcom.html.
Results and Discussion
A previous spreadsheetbased implementation of the Dunnett's ttest was successfully applied to gene expression studies comparing multiple independent points against a common reference [9, 10]. To evaluate the performance of the Mulcom test implemented as a Bioconductor package, we generated and analyzed transcriptomics data on a set of 10 RNA samples profiled with two independent microarray platforms (Affymetrix hgu133a and Illumina RS8 Human Beadchip). This enabled crossplatform concordance analysis of the results. The experiment explored gene expression changes induced in MDAMB435 human melanoma cells by 1, 6 or 24 hours of stimulation with Hepatocyte Growth Factor (HGF), known to trigger proliferation, motility and invasion [11]. The same cells were also transduced with IntegrinBeta4 (ITGB4) to stably upregulate its expression. Therefore the dataset encompassed both a timecourse experiment and one positive control condition, each repeated to generate biological duplicates. Data were normalized and filtered for significant detection as described in the Preprocessing section.
Mulcom analysis on Affymetrix data identified a total of 1556 significant probe sets (1249 genes), out of 10137 detected probe sets (8105 unique genes), at a threshold FDR below 5%. The same data were analyzed with Bioconductor implementations of two other widely used tests, Limma and SAM [2–4], each tuned to yield a comparable number of significant probe sets. SAM identified 1235 probe sets (1006 genes) with FDR below 1%, and Limma identified 1262 probe sets (956 genes) with pvalue below 0.05. The intersection between the three lists was of 871 probe sets, showing a notable but partial concordance (Figure 2). All Affymetrix probe sets were then mapped to the Illumina dataset by gene symbol, and the three tests were applied to this second dataset, maintaining the respective FDR or pvalue thresholds, to check crossplatform consistency. Interestingly, Mulcom displayed the highest fraction of validated genes (Table 1) and a similar number of significant genes in the two platforms.
To assess the functional significance of the genes identified by the three tests, we analysed them using Ingenuity Pathways Analysis (Ingenuity^{®} Systems, http://www.ingenuity.com. For each of the three tests, the list of significant genes defined in Affymetrix data was tested for enrichment in specific functional annotation keywords. Four keywords displayed an enrichment pvalue below 0.001 in at least one of the three lists: "gene expression", "cell cycle", "cell death" and "cellular movement". Interestingly, these categories altogether recapitulate the biological effects of HGF on epithelial and other adherent cells. As shown in Figure 3, the Mulcom list was significant in all four categories, and the most significant in three of them. We then repeated this analysis on lists generated by the three tests on the Illumina dataset. Overall, enrichments were lower, and therefore the significance threshold was lowered to p < 0.005, yielding nine keywords enriched for Mulcom, seven for Limma and three for SAM (data not shown).
To extend the significance of the results we performed the same comparison between Mulcom, Limma and SAM on an unrelated time course experiment (GSE19044) [12]. In this experiment, germ line cellderived pluripotent stem cells (GPSC) were induced to differentiate into hepatocytes and subsequently profiled at different stages. In order to identify differentially regulated genes between the reference time 0, and the different temporal stages, (namely day 2, day 7 day 21 and day 27) we applied the same settings for the statistical analysis as previously described (FDR < 0.01 or corrected pvalue < 0.01) on the data series GPSCA and GPSCB (two independent cell lines). Cross validation of the results highlighted that Mulcom test was the most efficient in identifying a high number of differentially regulated genes, which were systematically validated in the second experiment. The results are presented in Additional file 1, Figure S1.
Conclusions
Overall, these results show that, in a multiple comparison setting, the Mulcom package is particularly good at generating reliable lists of biologically informative genes. In our opinion, the main reasons for the good performance of Mulcom under these conditions are as follows: (i) Withingroup variability is estimated from all experimental groups even if only two of them are compared at a time. It is therefore more reliable when few replicates are available for each group; (ii) The optional foldchange threshold m avoids false positives due to aberrantly low withingroup variability and (iii) Automated test optimization linked to permutationbased FDR analysis allows sensitivity to be maximised without compromising specificity. Indeed, such an approach could be prone to overfitting i.e. identification of apparently optimal settings, which are highly dependent on the dataset. Of particular relevance to this issue is the fact that in the abovedescribed dual platformdataset the Mulcom test, albeit having been separately optimized on each of the two microarray platforms, yielded the most concordant lists of significant genes. Mulcom can also easily be applied to other omics studies, like miRNomics, proteomics and metabolomics, where multiple experimental points are compared against the same reference.
Preprocessing
Microarray Data generation and preliminary treatment
Gene expression profiling was performed on the same set of RNAs independently on Affymetrix hgu133a and Illumina Human 8V1 arrays, according to the manufacturer's protocols. Affymetrix raw data were processed with the RBioconductor suite http://www.bioconductor.org. Technical quality analysis was performed with the "Affy" package [13]. Probe data was summarized and normalized with RMA [14] Probe sets without a positive presence call in at least two samples were excluded from further analyses. Illumina data were processed with the BeadStudio software 1.5.13 (Illumina) with Rank Invariant Normalization. Probes for which all samples showed a Detection Score lower than 0.99 were excluded from further analyses. Raw and normalized microarray data from both platforms are deposited in NCBI's Gene Expression Omnibus repository (accession ID: GSE26736).
Ingenuity Pathway Analysis
All lists of gene symbols generated by the various tests were uploaded on IPA http://www.ingenuity.com and tested for enrichment in molecular and cellular functions. Enrichment (chisquare pvalue) was estimated against the MDAMB435 background provided by the IPA software.
Availability and requirements
Project name: Mulcom
Project home page: Operating system(s): Platform independent
Programming language: R
License: GNU GPL
Any restrictions to use by nonacademics: none
Availability: http://bioconductor.org/help/biocviews/2.8/bioc/html/Mulcom.html
Abbreviations
 EP:

Experimental Positives
 FC:

Fold Change
 FDR:

False Discovery Rate
 GPSC:

germ line cellderived pluripotent stem cells
 HGF:

Hepatocyte Growth Factor
 IPA:

Ingenuity Pathway Analysis
 ITGB4:

IntegrinBeta4
 MRP:

Median Random Positives
 MSE:

Mean Square Error
 SAM:

Significance Analysis of Microarray
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Acknowledgements
We thank Daniela Cantarella for technical support, Simona Destefanis for secretarial support and Riccardo Roasio, George Church and Eva Maria Pinatel for early discussions and helpful suggestions. We warmly thank Emily Hannah Crowley for careful language revision. This work was supported by Fondazione Piemontese per la Ricerca sul CancroONLUS, Associazione Italiana per la Ricerca sul Cancro (IG 9127 and "5xMille Project" n. 9970), Regione Piemonte (PRESTO and ELAB) and Ministero della Salute.
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Authors' contributions
EM and CI conceived the Mulcom Test, CI conceived the package and performed all the analyses. DC and TR developed part of the code. CI, TR, DC and EM wrote the manuscript. All authors read and approved the final manuscript.
Electronic supplementary material
Figure S1: Comparison between Mulcom, Limma and SAM on a timecourse stem cell differentiation dataset
Additional file 1:. Two timecourse series conducted in parallel have been analyzed, A and B. Blue, red and green columns indicate the number of significant genes at each time point detected by, respectively, Mulcom, Limma and Sam. Internal columns in light blue, orange and light green indicate the number of genes significant in series A that were also significant in series B as identified by, respectively, Mulcom, Limma and SAM. (PNG 52 KB)
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Isella, C., Renzulli, T., Corà, D. et al. Mulcom: a multiple comparison statistical test for microarray data in Bioconductor. BMC Bioinformatics 12, 382 (2011). https://doi.org/10.1186/1471210512382
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Keywords
 False Discovery Rate
 Hepatocyte Growth Factor
 Illumina Dataset
 False Discovery Rate Analysis
 Null Hypothesis Rejection