Statistical hypothesis testing of factor loading in principal component analysis and its application to metabolite set enrichment analysis
 Hiroyuki Yamamoto^{1}Email author,
 Tamaki Fujimori^{1},
 Hajime Sato^{1},
 Gen Ishikawa^{1},
 Kenjiro Kami^{1} and
 Yoshiaki Ohashi^{1}
DOI: 10.1186/147121051551
© Yamamoto et al.; licensee BioMed Central Ltd. 2014
Received: 25 August 2013
Accepted: 13 February 2014
Published: 21 February 2014
Abstract
Background
Principal component analysis (PCA) has been widely used to visualize highdimensional metabolomic data in a two or threedimensional subspace. In metabolomics, some metabolites (e.g., the top 10 metabolites) have been subjectively selected when using factor loading in PCA, and biological inferences are made for these metabolites. However, this approach may lead to biased biological inferences because these metabolites are not objectively selected with statistical criteria.
Results
We propose a statistical procedure that selects metabolites with statistical hypothesis testing of the factor loading in PCA and makes biological inferences about these significant metabolites with a metabolite set enrichment analysis (MSEA). This procedure depends on the fact that the eigenvector in PCA for autoscaled data is proportional to the correlation coefficient between the PC score and each metabolite level. We applied this approach to two sets of metabolomic data from mouse liver samples: 136 of 282 metabolites in the first case study and 66 of 275 metabolites in the second case study were statistically significant. This result suggests that to set the number of metabolites before the analysis is inappropriate because the number of significant metabolites differs in each study when factor loading is used in PCA. Moreover, when an MSEA of these significant metabolites was performed, significant metabolic pathways were detected, which were acceptable in terms of previous biological knowledge.
Conclusions
It is essential to select metabolites statistically to make unbiased biological inferences from metabolomic data when using factor loading in PCA. We propose a statistical procedure to select metabolites with statistical hypothesis testing of the factor loading in PCA, and to draw biological inferences about these significant metabolites with MSEA. We have developed an R package “mseapca” to facilitate this approach. The “mseapca” package is publicly available at the CRAN website.
Keywords
Principal component analysis Statistical hypothesis testing of factor loading Metabolite set enrichment analysisBackground
Metabolomics is a science based on the exhaustive profiling of metabolites. Various analytical technologies are used in metabolomic research, including capillary electrophoresis–mass spectrometry (CE–MS), liquid chromatography–MS, gas chromatography–MS, and nuclear magnetic resonance. The statistical analysis of the analytical data obtained has been studied in chemometrics research [1]. Chemometric approaches that commence with a multivariate analysis, such as principal component analysis (PCA) [2], partial least squares [3], canonical correlation analysis [4], and so on, have been predominantly applied in metabolomics.
PCA [2] is routinely used to visualize highdimensional metabolomic data in a two or threedimensional subspace. A scatter plot of PC score vectors (a “scores plot”) can be used to detect outliers or to identify biologically interpretable patterns. Typically, when a specific PC score is found to be related to a phenotype of interest [5, 6], such as a time course or group information, the corresponding factor loading is evaluated to discern meaningful metabolites from which to draw biological inferences.
In many metabolomic research articles [7–9], an eigenvector in PCA (Eq. 1–1) has been used as the factor loading. To draw biological inferences, some metabolites (e.g., the top 10 metabolites) are subjectively selected using the eigenvector. However, this approach has several problems. For example, many metabolites may vary with phenotype in one study, whereas only a few metabolites vary with phenotype in another study. With the existing approach, which uses the eigenvector, this is equivalent to using the same number of metabolites to draw biological inferences from these different studies. Consequently, biological interpretations might be made using an insignificant metabolite that varies irrelevantly with phenotype.
The eigenvectors for autoscaled data in PCA [10] are proportional to the correlation coefficients between the PC scores and the variables. This fact is well established in the multivariate analysis literature [11], but does not appear to be appreciated in metabolomic analyses. In the present study, “factor loading” is defined as the correlation coefficients between the PC scores and the variables. This definition can be used to perform statistical hypothesis testing and to select significant metabolites objectively using statistical criteria. The significance of factor loading in PCA can also be computed with a resampling approach, such as bootstrapping, although this is not exact [12].
Significant metabolites are selected according to the significance of factor loading or other methods of variable selection in supervised learning approaches, such as support vector machine, random forest, and so on, and then biological inferences are drawn for these metabolites by biologists. Biologists often draw these inferences with respect to a biological functional unit, such as a metabolic pathway (e.g., “glycolysis is notably activated” or “amino acid metabolism is significantly suppressed”). In gene expression analyses, gene set enrichment analysis (GSEA) has been used to identify significant gene sets using gene ontology (GO) terms. In metabolomics, metabolite set enrichment analysis (MSEA) [13, 14] can be used to identify significant metabolic pathways. MSEA has been computed with several approaches, including overrepresentation analysis (ORA) [15], Subramanian’s GSEA [16], and the global test [17]. MSEA is a convenient method for drawing biological inferences from metabolomic data, but this approach has not been applied to metabolites selected by factor loading in PCA. Recently, web tools for MSEA have been developed [13, 14]. However, no tools that can perform our workflow, including the statistical hypothesis testing of factor loading in PCA, have existed in a single platform. In the present study, we performed statistical hypothesis testing of the factor loading in PCA for two metabolomic datasets from mouse liver samples as case studies. This approach can be used to select significant metabolites when using factor loading in PCA, and MSEA with an ORA approach can be applied to these significant metabolites. We developed the R package “mseapca” to compute the sequence from the statistical hypothesis testing of factor loading in PCA to MSEA.
Methods
Statistical hypothesis testing of factor loading in PCA
The eigenvector w and eigenvalue λ of eq. (1–2) can be computed using numerical computation libraries for singular value decomposition. The eigenvalue λ corresponds to the variance of the PC score vector formed using the associated eigenvector as the weight vector.
has a tdistribution with (n – 2) degrees of freedom. We can then select variables that have a statistically significant correlation to the PC score and draw biological inferences using these variables.
Sample preparation, metabolomic analysis, and data processing
BKS.Cgm+/m+/Jcl (normal) mice, 12 hfasted normal mice, BKS.C  +Lepr^{db}/+Lepr^{db}/Jcl (db/db) mice, and db/db mice orally administered pioglitazone for 10 days were used. The mice were 7weekold males, and were given unlimited access to food and water, except those on the 12 h fast. The concentration of pioglitazone administered was 100 mg/10 mL per kg. The pioglitazone was purchased from Takeda Pharmaceutical Co. Ltd (Doshomachi, Osaka, Japan), and was purified by the NARD Institute Ltd (Amagasaki, Hyogo, Japan). After sampling, the livers were excised and stored at 80°C. All experiments, from the purchase and breeding of the mice to the collection of their liver samples, were performed at Kitayama Labes Co. Ltd (Ina, Nagano, Japan). The sample preparation procedure used to extract the metabolites has been described by Ooga et al. [18].
The metabolite extracts were measured with CE–timeofflight MS (CE–TOFMS) using the Agilent Capillary Electrophoresis System equipped with an Agilent 6210 timeofflight mass spectrometer, an Agilent 1100 isocratic highperformance liquid chromatography pump, an Agilent G1603A CE–MS adapter kit, and an Agilent G1607A CE–ESI–MS Sprayer Kit (Agilent Technologies, Waldbronn, Germany). The system was controlled with the G2201AA ChemStation Software version B.03.01 for CE (Agilent Technologies). Modified analytical methods for the measurement of cationic [19] and anionic metabolites [20] were used. The measurement data were processed with peak processing software [21]. The signal peaks corresponding to isotopomers, adduct ions, and other product ions of known metabolites were excluded. All signal peaks potentially corresponding to authentic compounds were then extracted, and their migration times (MTs) were normalized using those of the internal standards (methionine sulfone and dcamphor10sulfonic acid for cations and anions, respectively). The peaks were then aligned according to their m/z values and normalized MT values. Finally, the peak areas were normalized against those of the internal standards. The resultant relative area values were further normalized by the sample weight. Annotation tables were produced from the CE–TOFMS measurements of standard compounds, and were aligned with the datasets according to their similar m/z values and normalized MT values.
Statistical analysis
In this study, all computations were performed with R [22] and the “mseapca” [23] package. A value of 0 was imputed to missing values for the computation of PCA. A metabolite set list was created with reference to the Kyoto Encyclopedia of Genes and Genomes (KEGG) [24], which was partly modified by manual curation. The xml file of the metabolite set list used in this study is included in the “mseapca” package.
Software
The second feature is the “pca_scaled” function, with which to perform PCA. A data frame constructed from metabolite IDs and a metabolome data matrix is input for the “pca_scaled” function. Metabolite IDs should be matched with those in the metabolite set list. With this function, the data matrix is automatically scaled to a zero mean and unit variance (autoscaling) for each metabolite. This function can output the PC scores, factor loadings, and pvalues and qvalues of Benjamini and Hochberg [25], which are the results of the statistical hypothesis testing of factor loading. In this function, “factor loading” is defined as the correlation coefficient between the PC score and each metabolite level.
The third feature is the performance of MSEA. The “msea_ora” function can perform MSEA with ORA [15]. With this function, statistical hypothesis testing of the crosstabulation is performed with the onesided Fisher’s exact test. The “msea_sub” function performs MSEA in the same way as GSEA is implemented by Subramanian et al. [16]. Subramanian’s GSEA has two types of random permutation. In one, the class label is randomly permuted and in the other, the metabolites in the metabolite set list are randomly selected to generate the null distribution of the enrichment score. The pvalue for the enrichment score can then be computed with both approaches. In the “msea_sub” function, the latter approach is implemented. This procedure corresponds to the “gene set” of the permutation type in the GSEAP software [26]. A leadingedge subset analysis is also undertaken following the GSEA procedure [25].
The R package “mseapca” is freely available from the CRAN website [23]. See the reference manual for “mseapca” at the CRAN website [23] for more information.
Results
Case study 1: a comparative study of control and 12 hfasted mice
We describe the use of the statistical hypothesis testing of factor loading in PCA using metabolome data from two studies. The first case study is a comparative analysis of normal and 12 hfasted mice. Five liver samples each from the control and 12 hfasted mice were used for the metabolomic analysis and 282 metabolites were identified.
Results of MSEA in a comparative study of normal and 12 hfasted mice
ORA  Subramanian's approach  

Positive correlation with PC1  Negative correlation with PC1  Positive correlation with PC1  
pvalue  qvalue  pvalue  qvalue  NES  pvalue  qvalue  
Glycolysis  1.0000  1.0000  0.0001*  0.0036**  2.0048  0.0000*  0.0074** 
Pentose phosphate pathway  1.0000  1.0000  0.0308*  0.2000  1.6040  0.0283*  0.1781 
TCA cycle  1.0000  1.0000  0.0040*  0.0519  1.6208  0.0165*  0.2433 
Glutamic acid and glutamine metabolism  1.0000  1.0000  0.4901  0.9801  1.0936  0.3497  0.5193 
Alanine, aspartic acid and asparagine metabolism  0.8254  1.0000  0.2878  0.8313  1.1897  0.2625  0.4379 
Lysine metabolism  0.8567  1.0000  0.8681  1.0000  0.8172  0.7078  0.8274 
Valine, leucine and isoleucine metabolism  1.0000  1.0000  0.7735  1.0000  0.9392  0.5636  0.7311 
Glycine, serine and threonine metabolism  0.7434  1.0000  0.0720  0.2445  1.2557  0.1803  0.3704 
Cysteine metabolism  0.6489  1.0000  0.0412*  0.2142  1.3259  0.1611  0.3371 
Methionine metabolism  0.6178  1.0000  0.8444  1.0000  0.8697  0.6147  0.7197 
Shikimic acid metabolism  1.0000  1.0000  0.4901  0.9801  1.2676  0.1745  0.3901 
Histidine metabolism  0.5434  1.0000  1.0000  1.0000  1.8978  0.0080*  0.0520 
Urea cycle  0.8567  1.0000  0.0507  0.2197  1.3352  0.1524  0.3705 
Proline metabolism  1.0000  1.0000  0.6001  1.0000  1.1524  0.3041  0.4619 
Polyamine metabolism  1.0000  1.0000  0.0308*  0.2000  1.5785  0.0309*  0.1581 
Tryptophan metabolism  0.7413  1.0000  0.9269  1.0000  0.7141  0.8260  0.8764 
Tyrosine metabolism  1.0000  1.0000  0.0752  0.2445  1.3601  0.1176  0.3820 
betaalanine metabolism  0.2111  1.0000  0.8616  1.0000  0.9218  0.5531  0.7578 
Taurine metabolism  1.0000  1.0000  0.3721  0.9675  1.4114  0.1010  0.3535 
Creatine metabolism  0.7874  1.0000  0.4705  0.9801  0.8041  0.7093  0.7984 
Purine metabolism  0.0285*  0.7411  0.9983  1.0000  1.6391  0.0220*  0.1290 
Pyrimidine metabolism  0.9649  1.0000  0.9860  1.0000  0.7965  0.7355  0.7258 
Ribonucleotide metabolism  0.3473  1.0000  1.0000  1.0000  1.1184  0.2800  0.6998 
Deoxyribonucleotide  1.0000  1.0000  1.0000  1.0000  0.6743  0.9776  0.8725 
Conjugated bile acid  0.5361  1.0000  1.0000  1.0000  1.0384  0.3671  0.6834 
Nicotinic acid metaboilsm  0.3473  1.0000  0.5357  0.9949  0.8360  0.6536  0.8510 
The results of the MSEA of factor loading in PC1 suggested that the processes of energy metabolism, including glycolysis and the TCA cycle, decreased during the 12 h fast. The suppression of these metabolic pathways suggests that glycogen is drained and glucose supplementation is restricted in the mouse liver during a 12 h fast. The mean bodyweight of the normal mice was 22.20 ± 0.84 g (mean ± SD) and that of the 12 hfasted mice was 20.0 ± 0.71 g, indicating a statistically significant reduction (p = 0.0021) during the 12 h fast, according to Welch’s t test. This result suggests that the suppression of energy metabolism results in a reduction in bodyweight.
Case study 2: a comparative study of diabetic model mice with and without pioglitazone treatment
The db/db mouse is a model of obesity, diabetes, and dyslipidemia, in which leptin receptor activity is deficient because the mice are homozygous for a point mutation in the leptin receptor gene [27]. Pioglitazone reduces insulin resistance in the liver and reduces glucose levels in the blood [28, 29]. Therefore, it is used for the treatment of diabetes.
We compared the metabolomic data for mouse liver samples from db/db mice treated with or without pioglitazone to examine the effects of administering pioglitazone to diabetic mice. Five liver samples from the untreated db/db mice and five from db/db mice administered pioglitazone were used for the metabolomic analysis and 275 metabolites were identified.
Results of MSEA in a comparative study of db / db mice treated with and without pioglitazone
ORA  Subramanian’s approach  

Positive correlation with PC1  Negative correlation with PC1  Positive correlation with PC1  
pvalue  qvalue  pvalue  qvalue  NES  pvalue  qvalue  
Glycolysis  0.0090*  0.2250  0.7982  1.0000  1.6888  0.0198*  0.3485 
Pentose phosphate pathway  1.0000  1.0000  1.0000  1.0000  1.3813  0.1378  0.9520 
TCA cycle  1.0000  1.0000  1.0000  1.0000  1.4237  0.0916  0.8261 
Glutamic acid and glutamine metabolism  1.0000  1.0000  0.5471  1.0000  1.2740  0.2062  0.4203 
Alanine, aspartic acid and asparagine metabolism  0.5531  1.0000  1.0000  1.0000  0.7161  0.8049  1.0000 
Lysine metabolism  1.0000  1.0000  1.0000  1.0000  0.6892  0.8152  0.9603 
Valine, leucine and isoleucine metabolism  0.3294  1.0000  1.0000  1.0000  0.8275  0.6150  0.9834 
Glycine, serine and threonine metabolism  0.1405  0.7024  0.8617  1.0000  1.1241  0.2699  0.9823 
Cysteine metabolism  0.7041  1.0000  0.2461  1.0000  0.9727  0.4840  0.8845 
Methionine metabolism  1.0000  1.0000  1.0000  1.0000  1.0388  0.4167  0.9189 
Shikimic acid metabolism  0.3294  1.0000  1.0000  1.0000  1.1493  0.3098  1.0000 
Histidine metabolism  1.0000  1.0000  1.0000  1.0000  0.7463  0.7770  1.0000 
Urea cycle  1.0000  1.0000  1.0000  1.0000  0.6208  0.9293  0.9238 
Proline metabolism  0.5051  1.0000  1.0000  1.0000  0.6493  0.8869  1.0000 
Polyamine metabolism  0.1344  0.7024  0.2701  1.0000  1.0695  0.3818  0.9813 
Tryptophan metabolism  0.1018  0.7024  1.0000  1.0000  1.2380  0.2247  1.0000 
Tyrosine metabolism  0.4521  1.0000  1.0000  1.0000  0.9319  0.5367  0.8548 
betaalanine metabolism  0.3893  1.0000  0.6321  1.0000  0.6450  0.8899  0.9596 
Taurine metabolism  0.0577  0.7024  0.4410  1.0000  0.9952  0.4654  0.8048 
Creatine metabolism  1.0000  1.0000  0.7206  1.0000  0.7887  0.7230  0.9414 
Purine metabolism  1.0000  1.0000  0.2583  1.0000  1.3788  0.0947  0.5203 
Pyrimidine metabolism  1.0000  1.0000  0.9252  1.0000  0.7940  0.7196  1.0000 
Ribonucleotide metabolism  1.0000  1.0000  0.2461  1.0000  1.3605  0.1215  0.3792 
Conjugated bile acid  1.0000  1.0000  0.4687  1.0000  0.5472  0.9689  0.9709 
Nicotinic acid metaboilsm  0.3161  1.0000  0.5431  1.0000  0.9991  0.4427  0.8973 
In the present study, the glucose blood level was 369.6 ± 64.8 mg/dL (mean ± SD) in the db/db mice and 332.8 ± 131.9 mg/dL in the db/db mice administered pioglitazone. The reduction in blood glucose was not significant (p = 0.596) after the administration of pioglitazone, according to Welch’s t test. This result suggests that a metabolomic analysis can detect subtle changes in the glycolysis pathway caused by the administration of pioglitazone, although confirmatory experiments (e.g., evaluating the expression levels of PPARα) might be required to confirm our biological inferences.
Discussion
Metabolite selection by statistical hypothesis testing of the factor loading in PCA has several advantages. This approach was applied to metabolomic data in two case studies of mouse liver samples. In the first case study, 136 of 282 metabolites correlated significantly with the PC1 score associated with the groups, and in the second study, 66 of 275 metabolites showed such a correlation. Thus, the number of significant metabolites was twofold higher in the first case study than in the second case study. This suggests that to set a previously determined number of metabolites (e.g., the top 10 metabolites) is inappropriate because the number of significant metabolites differs in each study. We also note the relationship between the contribution ratio and the number of significant metabolites for factor loading in PCA. The ratio of the number of significant metabolites to all the detected metabolites was 0.482 (= 136/282) in the first case study and 0.24 (= 66/275) in the second case study. The contribution ratio in PC1 was 40.5% in the first case study and 24.2% in the second case study. This result suggests that an implicit relationship exists between the contribution ratio and the number of significant metabolites in samples of the same size.
In both case studies, we focused on PC1 (Figure 2 and Figure 3), which differed between the groups. We then compared this approach with ordinary statistical hypothesis testing, such as with a t test. According to Welch’s t test, 122 metabolites were significant in the first case study and 56 metabolites were significant in the second case study. When we compared the metabolites selected with Welch’s t test and those selected with the statistical test of factor loading, 112 metabolites and 47 metabolites in case studies 1 and 2, respectively, were common to both studies. Most significant metabolites were selected with both approaches. This fact suggests that the statistical testing of factor loading in PCA can be readily used to select metabolites as a special case of the twosample test when the difference between the groups appears in the PC score. The result of MSEA for statistically significant metabolites with positive t statistics on Welch’s t test showed that purine metabolism was statistically significant at p < 0.05, and the negative t statistics showed that glycolysis and the pentose phosphate pathway were statistically significant at p < 0.05 (Additional file 1: Table S3). In a positive case, the statistically significant metabolic pathway identified by MSEA was consistent with both approaches. In a negative case, the statistically significant metabolic pathway was partly consistent, but the number of statistically significant metabolic pathways was fewer with Welch’s t test than with the statistical hypothesis testing of factor loading in PCA. These results depend on the result that the number of significant metabolites was almost same with Welch’s t test (51 metabolites) and with statistical hypothesis testing of factor loading in PCA (49 metabolites) in positive cases, but was fewer with Welch’s t test (71 metabolites) than with the statistical hypothesis testing of factor loading in PCA (87 metabolites) in negative cases.
In metabolomics, complex studies (e.g., the fermentation process by a microorganism [31]) can involve various time points or groups, or the administration of drugs at various concentrations under various conditions [32]. In these complex studies, a statistical method for testing should be selected from various methods, such as analysis of variance and multiple comparison procedures, depending on the situation. In our analytical workflow of PCA, a specific PC score was selected and we simply performed the statistical hypothesis testing for factor loading corresponding to this selected PC under any circumstances. The statistical testing of factor loading in PCA can be widely used, not only in twosample studies but also in various studies when an association between the PC score and the phenotype can be found.
MSEA was performed for significant metabolites and acceptable biological inferences were drawn in the two case studies. With the conventional approach, a previously determined number of metabolites (e.g., 10 metabolites) from which to draw biological inferences is subjectively selected. Using this approach, MSEA was performed for the top 10 metabolites with large negative factor loadings in the first case study. No significant metabolic pathway was detected at p < 0.05 (data not shown). In this case, 10 metabolites was too small a sample from which to draw acceptable biological inferences. Even if significant metabolic pathways are detected when MSEA is applied to insignificant metabolites, it is doubtful whether these metabolic pathways are statistically or biologically meaningful. To draw unbiased biological inferences using a statistical analysis, significant metabolites must be selected with statistical tests of factor loading when using PCA.
In this study, two MSEA methods were used, with either ORA or Subramanian’s approach. As a way of using factor loading for GSEA, Fehrmann et al. [33] designated the PC score associated with phenotype as the “transcriptional system regulator” (TSR) score, and factor loading corresponding to the TSR score is used for GSEA with Subramanian’s approach. This method directly uses factor loading, but does not use the results of statistical hypothesis testing of factor loading. As far as we know, an approach combining GSEA or MSEA with the results of statistical hypothesis testing of factor loading in PCA has not been reported until now.
The results of both MSEA with ORA or Subramanian’s approach produced almost the same results in our two case studies. In a comparison of the computational time required by the two MSEA approaches, the first case study required 441.43 seconds using Subramanian’s approach and 0.83 seconds with ORA. This result shows that MSEA with ORA has the advantage of lower computational cost. Conventionally, PCA and MSEA can be computed independently in different steps or with different software. There has been no software that can compute the sequence from PCA and statistical hypothesis testing of factor loading to MSEA. Therefore, we developed the R package “mseapca” to compute the whole sequence from the statistical hypothesis testing of factor loading in PCA to MSEA.
Conclusions
In metabolomics, the targeted metabolites from which biological inferences are drawn are selected subjectively when factor loading is used in PCA. We have proposed a statistical procedure to select metabolites using the statistical hypothesis testing of factor loading in PCA. These significant metabolites are then used to identify significant metabolic pathways with MSEA. We applied this approach to two metabolomic datasets from mouse liver samples, with acceptable results in terms of previous biological knowledge. We developed an R package “mseapca” to allow the ready use of our approach. Many researchers use PCA in metabolomics. Our approach can improve the existing use of PCA in this field and is expected to be widely applicable to other omics data, including gene expression and proteomic data.
Abbreviations
 CE–MS:

Capillary electrophoresis–mass spectrometry
 PCA:

Principal component analysis
 MSEA:

Metabolite set enrichment analysis
 GSEA:

Gene set enrichment analysis
 GO:

Gene ontology
 ORA:

Overrepresentation analysis
 KEGG:

Kyoto Encyclopedia of Genes and Genomes
 TCA:

Tricarboxylic acid
 NESs:

Normalized enrichment scores
 TSR:

Transcriptional system regulator.
Declarations
Acknowledgments
We thank Ms Mutsuko Sato and Ms Kaori Honda for sample preparation and Ms Yumiko Ikarashi and Ms Sumiko Kumaki for their assistance with the metabolomic analysis. We also thank Mr Seira Nakamura and Dr Makoto Suzuki for their valuable discussions about statistical analysis in metabolomics.
Authors’ Affiliations
References
 Lavine B, Workman J: Chemometrics. Anal Chem. 2010, 82 (12): 46994711. 10.1021/ac101202z.View ArticlePubMedGoogle Scholar
 Jolliffe IT: Principal component analysis. 2002, New York: SpringerVerlag, 2Google Scholar
 Barker M, Rayens W: Partial least squares for discrimination. J Chemometr. 2003, 17 (3): 166173. 10.1002/cem.785.View ArticleGoogle Scholar
 Yamamoto H, Yamaji H, Fukusaki E, Ohno H, Fukuda H: Canonical correlation analysis for multivariate regression and its application to metabolic fingerprinting. Biochem Eng J. 2007, 40: 199204.View ArticleGoogle Scholar
 Ringnér M: What is principal component analysis?. Nat Biotechnol. 2008, 26: 303304. 10.1038/nbt0308303.View ArticlePubMedGoogle Scholar
 Landgrebe J, Wurst W, Welzl G: Permutationvalidated principal components analysis of microarray data. Genome Biol. 2002, 3 (4): 111.View ArticleGoogle Scholar
 Dileo MV, Strahan GD, den Bakker M, Hoekenga OA: Weighted correlation network analysis (WGCNA) applied to the tomato fruit metabolome. PLoS One. 2011, 6 (10): e2668310.1371/journal.pone.0026683.View ArticlePubMed CentralPubMedGoogle Scholar
 Dewar BJ, Keshari K, Jeffries R, Dzeja P, Graves LM, Macdonald JM: Metabolic assessment of a novel chronic myelogenous leukemic cell line and an imatinib resistant subline by H NMR spectroscopy. Metabolomics. 2010, 6 (3): 439450. 10.1007/s1130601002040.View ArticlePubMed CentralPubMedGoogle Scholar
 Maruyama K, Takeda M, Kidokoro S, Yamada K, Sakuma Y, Urano K, Fujita M, Yoshiwara K, Matsukura S, Morishita Y, Sasaki R, Suzuki H, Saito K, Shibata D, Shinozaki K, YamaguchiShinozaki K: Metabolic pathways involved in cold acclimation identified by integrated analysis of metabolites and transcripts regulated by DREB1A and DREB2A. Plant Physiol. 2009, 150 (4): 19721980. 10.1104/pp.109.135327.View ArticlePubMed CentralPubMedGoogle Scholar
 Van den Berg RA, Hoefsloot HC, Westerhuis JA, Smilde AK, van der Werf MJ: Centering, scaling, and transformations: improving the biological information content of metabolomics data. BMC Genomics. 2006, 7: 14210.1186/147121647142.View ArticlePubMed CentralPubMedGoogle Scholar
 Afifi A, May S, Clark VA, Practical Multivariate Analysis: 2011, London: Chapman and Hall/CRC, 364366. 5
 Pedro RP, Donald AJ, Keith MS: Giving meaningful interpretation to ordination axes: assessing loading significance in principal component analysis. Ecology. 2003, 84: 23472363. 10.1890/000634.View ArticleGoogle Scholar
 Xia J, Wishart DS: MSEA: a webbased tool to identify biologically meaningful patterns in quantitative metabolomic data. Nucleic Acids Res. 2010, 38 (Web Server issue): W71W77.View ArticlePubMed CentralPubMedGoogle Scholar
 Xia J, Wishart DS: Webbased inference of biological patterns, functions and pathways from metabolomic data using MetaboAnalyst. Nat Protoc. 2011, 6: 743760.15. 10.1038/nprot.2011.319.View ArticlePubMedGoogle Scholar
 Draghici S, Khatri P, Martins RP, Ostermeier GC, Krawetz SA: Global function profiling of gene expression. Genomics. 2003, 81: 98104. 10.1016/S08887543(02)000216.View ArticlePubMedGoogle Scholar
 Subramanian A, Tamayo P, Mootha VK, Mukherjee S, Ebert BL, Gillette MA, Paulovich A, Pomeroy SL, Golub TR, Lander ES, Mesirov JP: Gene set enrichment analysis: a knowledgebased approach for interpreting genomewide expression profiles. Proc Natl Acad Sci U S A. 2005, 102 (43): 1554515550. 10.1073/pnas.0506580102.View ArticlePubMed CentralPubMedGoogle Scholar
 Goeman JJ, van de Geer SA, de Kort F, van Houwelingen HC: A global test for groups of genes: testing association with a clinical outcome. Bioinformatics. 2004, 20 (1): 9399. 10.1093/bioinformatics/btg382.View ArticlePubMedGoogle Scholar
 Ooga T, Sato H, Nagashima A, Sasaki K, Tomita M, Soga T, Ohashi Y: Metabolomic anatomy of an animal model revealing homeostatic imbalances in dyslipidaemia. Mol Biosyst. 2011, 7 (4): 12171223. 10.1039/c0mb00141d.View ArticlePubMedGoogle Scholar
 Soga T, Heiger DN: Amino acid analysis by capillary electrophoresis electrospray ionization mass spectrometry. Anal Chem. 2000, 72: 12361241. 10.1021/ac990976y.View ArticlePubMedGoogle Scholar
 Soga T, Ueno Y, Naraoka H, Ohashi Y, Tomita M, Nishioka T: Analysis of nucleotides by pressureassisted capillary electrophoresis mass spectrometry using silanol mask technique. J Chromatogr A. 2007, 1159: 125133. 10.1016/j.chroma.2007.05.054.View ArticlePubMedGoogle Scholar
 Sugimoto M, Wong D, Hirayama A, Soga T, Tomita M: Capillary electrophoresis mass spectrometrybased saliva metabolomics identifies oral, breast and pancreatic cancerspecific profiles. Metabolomics. 2010, 6: 7895. 10.1007/s113060090178y.View ArticlePubMed CentralPubMedGoogle Scholar
 R Development Core Team: R: A language and environment for statistical computing. 2005, Vienna, Austria: R Foundation for Statistical ComputingGoogle Scholar
 mseapca: Metabolite set enrichment analysis for factor loading in principal component analysis: http://cran.rproject.org/web/packages/mseapca/,
 Kanehisa M, Goto S: KEGG: Kyoto encyclopedia of genes and genomes. Nucleic Acids Res. 2000, 28: 2730. 10.1093/nar/28.1.27.View ArticlePubMed CentralPubMedGoogle Scholar
 Benjamini Y, Hochberg Y: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B. 1995, 57 (1): 289300.Google Scholar
 Subramanian A, Kuehn H, Gould J, Tamayo P, Mesirov JP: GSEAP: a desktop application for gene Set enrichment analysis. Bioinformatics. 2007, 23 (23): 32513253. 10.1093/bioinformatics/btm369.View ArticlePubMedGoogle Scholar
 Sharma K, McCue P, Dunn SR: Diabetic kidney disease in the db/db mouse. Am J Physiol Renal Physiol. 2003, 284: F1138F1144.View ArticlePubMedGoogle Scholar
 Kemnitz JW, Elson DF, Roecker EB, Baum ST, Bergman RN, Maglasson MD: Pioglitazone increases insulin sensitivity, reduces blood glucose, insulin, and lipid levels, and lowers blood pressure, in obese, insulinresistant rhesus monkeys. Diabetes. 1994, 43: 204211. 10.2337/diab.43.2.204.View ArticlePubMedGoogle Scholar
 Smith U: Pioglitazone: mechanism of action. Int J Clin Pract. 2001, 121: 1318.Google Scholar
 Lee CH, Olson P, Hevener A, Mehl I, Chong LW, Olefsky JM, Gonzalez FJ, Ham J, Kang H, Peters JM, Evans RM: PPARδ regulates glucose metabolism and insulin sensitivity. Proc Natl Acad Sci U S A. 2006, 103 (9): 34443449. 10.1073/pnas.0511253103.View ArticlePubMed CentralPubMedGoogle Scholar
 Yamamoto H, Yamaji H, Abe Y, Harada K, Waluyo D, Fukusaki E, Kondo A, Ohno H, Fukuda H: Dimensionality reduction for metabolome data using PCA, PLS, OPLS, and RFDA with differential penalties to latent variables. Chemom Intell Lab Syst. 2009, 98 (2): 136142. 10.1016/j.chemolab.2009.05.006.View ArticleGoogle Scholar
 Timmerman ME, van der Greef J, Lamers RAN, Huub C, Hoefsloot J, Smilde AK, Jansen JJ: ANOVAsimultaneous component analysis (ASCA): a new tool for analyzing designed metabolomics data. Bioinformatics. 2005, 21 (13): 30433048. 10.1093/bioinformatics/bti476.View ArticlePubMedGoogle Scholar
 Fehrmann RSN, de Jonge HJM, ter Elst A, de Vries A, Crijns AGP, Weidenaar AC, Gerbens F, de Jong S, van der Zee AGJ, de Vries EGE, Kamps WA, Hofstra RMW, te Meerman GJ, de Bont ESJM: A New perspective on transcriptional system regulation (TSR): towards TSR profiling. PLoS One. 2008, 3 (2): e165610.1371/journal.pone.0001656.View ArticlePubMed CentralPubMedGoogle Scholar
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