Interpretation of ANOVA models for microarray data using PCA.

MOTIVATION: ANOVA is a technique, which is frequently used in the analysis of microarray data, e.g. to assess the significance of treatment effects, and to select interesting genes based on P-values. However, it does not give information about what exactly is causing the effect. Our purpose is to improve the interpretation of the results from ANOVA on large microarray datasets, by applying PCA on the individual variance components. Interaction effects can be visualized by biplots, showing genes and variables in one plot, providing insight in the effect of e.g. treatment or time on gene expression. Because ANOVA has removed uninteresting sources of variance, the results are much more interpretable than without ANOVA. Moreover, the combination of ANOVA and PCA provides a simple way to select genes, based on the interactions of interest. RESULTS: It is shown that the components from an ANOVA model can be summarized and visualized with PCA, which improves the interpretability of the models. The method is applied to a real time-course gene expression dataset of mesenchymal stem cells. The dataset was designed to investigate the effect of different treatments on osteogenesis. The biplots generated with the algorithm give specific information about the effects of specific treatments on genes over time. These results are in agreement with the literature. The biological validation with GO annotation from the genes present in the selections shows that biologically relevant groups of genes are selected. AVAILABILITY: R code with the implementation of the method for this dataset is available from http://www.cac.science.ru.nl under the heading "Software".

Estimating the number of components and detecting outliers using Angle Distribution of Loading Subspaces (ADLS) in PCA analysis.

Principal Component Analysis (PCA) is widely used in analytical chemistry, to reduce the dimensionality of a multivariate data set in a few Principal Components (PCs) that summarize the predominant patterns in the data. An accurate estimate of the number of PCs is indispensable to provide meaningful interpretations and extract useful information. We show how existing estimates for the number of PCs may fall short for datasets with considerable coherence, noise or outlier presence. We present here how Angle Distribution of the Loading Subspaces (ADLS) can be used to estimate the number of PCs based on the variability of loading subspace across bootstrap resamples. Based on comprehensive comparisons with other well-known methods applied on simulated dataset, we show that ADLS (1) may quantify the stability of a PCA model with several numbers of PCs simultaneously; (2) better estimate the appropriate number of PCs when compared with the cross-validation and scree plot methods, specifically for coherent data, and (3) facilitate integrated outlier detection, which we introduce in this manuscript. We, in addition, demonstrate how the analysis of different types of real-life spectroscopic datasets may benefit from these advantages of ADLS.

Plasma biomarker discovery for early chronic kidney disease diagnosis based on chemometric approaches using LC-QTOF targeted metabolomics data.

Chronic kidney disease (CKD) is a progressive pathological condition in which renal function deteriorates in time. The first diagnosis of CKD is often carried out in general care attention by general practitioners by means of serum creatinine (CNN) levels. However, it lacks sensitivity and thus, there is a need for new robust biomarkers to allow the detection of kidney damage particularly in early stages. Multivariate data analysis of plasma concentrations obtained from LC-QTOF targeted metabolomics method may reveal metabolites suspicious of being either up-regulated or down-regulated from urea cycle, arginine methylation and arginine-creatine metabolic pathways in CKD pediatrics and controls. The results show that citrulline (CIT), symmetric dimethylarginine (SDMA) and S-adenosylmethionine (SAM) are interesting biomarkers to support diagnosis by CNN: early CKD samples and controls were classified with an increase in classification accuracy of 18% when using these 4 metabolites compared to CNN alone. These metabolites together allow classification of the samples into a definite stage of the disease with an accuracy of 74%, being the 90% of the misclassifications one level above or below the CKD stage set by the nephrologists. Finally, sex-related, age-related and treatment-related effects were studied, to evaluate whether changes in metabolite concentration could be attributable to these factors, and to correct them in case a new equation is developed with these potential biomarkers for the diagnosis and monitoring of pediatric CKD.

Identification of Pseudomonas aeruginosa and Aspergillus fumigatus mono- and co-cultures based on volatile biomarker combinations.

Volatile organic compound (VOC) analysis in exhaled breath is proposed as a non-invasive method to detect respiratory infections in cystic fibrosis patients. Since polymicrobial infections are common, we assessed whether we could distinguish Pseudomonas aeruginosa and Aspergillus fumigatus mono- and co-cultures using the VOC emissions. We took headspace samples of P. aeruginosa, A. fumigatus and co-cultures at 16, 24 and 48 h after inoculation, in which VOCs were identified by thermal desorption combined with gas chromatography - mass spectrometry. Using multivariate analysis by Partial Least Squares Discriminant Analysis we found distinct VOC biomarker combinations for mono- and co-cultures at each sampling time point, showing that there is an interaction between the two pathogens, with P. aeruginosa dominating the co-culture at 48 h. Furthermore, time-independent VOC biomarker combinations were also obtained to predict correct identification of P. aeruginosa and A. fumigatus in mono-culture and in co-culture. This study shows that the VOC combinations in P. aeruginosa and A. fumigatus co-microbial environment are different from those released by these pathogens in mono-culture. Using advanced data analysis techniques such as PLS-DA, time-independent pathogen specific biomarker combinations can be generated that may help to detect mixed respiratory infections in exhaled breath of cystic fibrosis patients.

Detection of Staphylococcus aureus in cystic fibrosis patients using breath VOC profiles.

Staphylococcus aureus (S. aureus) is a common bacterium infecting children with cystic fibrosis (CF). Since current detection methods are difficult to perform in children, there is need for an alternative. This proof of concept study investigates whether breath profiles can discriminate between S. aureus infected and non-infected CF patients based on volatile organic compounds (VOCs). We collected exhaled breath of CF patients with and without S. aureus airways infections in which VOCs were identified using gas chromatography-mass spectrometry. We classified these VOC profiles with sparse partial least squares discriminant analysis. Multivariate breath VOC profiles discriminated infected from non-infected CF patients with high sensitivity (100%) and specificity (80%). We identified the nine compounds most important for this discrimination. We successfully detected S. aureus infection in CF patients, using breath VOC profiles. Nine highlighted compounds can be used as a focus point in further biomarker identification research. The results show considerable potential for non-invasive diagnosis of airway infections.

Diagnostic analysis of experimental artefacts in DOSY NMR data by covariance matrix of the residuals.

Multivariate curve resolution (MCR) has been applied to separate pure spectra and pure decay profiles of DOSY NMR data. Given good initial guesses of the pure decay profiles, and combined with the nonlinear least square regression (NLR), MCR can result in good separation of the pure components. Nevertheless, due to the presence of artefacts in experimental data, validation of a MCR model is still necessary. In this paper, the covariance matrix of the residuals (CMR), obtained by postmultiplying the residual matrix with its transpose, is proposed to evaluate the quality of the results of an experimental data set. Plots of the rows of this matrix give a general impression of the covariance in the frequency domain of the residual matrix. Different patterns in the plot indicate possible causes of experimental imperfections. This new criterion can be used as diagnosis in order to improve experimental settings as well as suggest appropriate preprocessing of DOSY NMR data.

The use of multivariate MR imaging intensities versus metabolic data from MR spectroscopic imaging for brain tumour classification.

This study investigated the value of information from both magnetic resonance imaging and magnetic resonance spectroscopic imaging (MRSI) to automated discrimination of brain tumours. The influence of imaging intensities and metabolic data was tested by comparing the use of MR spectra from MRSI, MR imaging intensities, peak integration values obtained from the MR spectra and a combination of the latter two. Three classification techniques were objectively compared: linear discriminant analysis, least squares support vector machines (LS-SVM) with a linear kernel as linear techniques and LS-SVM with radial basis function kernel as a nonlinear technique. Classifiers were evaluated over 100 stratified random splittings of the dataset into training and test sets. The area under the receiver operating characteristic (ROC) curve (AUC) was used as a global performance measure on test data. In general, all techniques obtained a high performance when using peak integration values with or without MR imaging intensities. For example for low- versus high-grade tumours, low- versus high-grade gliomas and gliomas versus meningiomas, the mean test AUC was higher than 0.91, 0.94, and 0.99, respectively, when both MR imaging intensities and peak integration values were used. The use of metabolic data from MRSI significantly improved automated classification of brain tumour types compared to the use of MR imaging intensities solely.

Regularized MANOVA (rMANOVA) in untargeted metabolomics.

Many advanced metabolomics experiments currently lead to data where a large number of response variables were measured while one or several factors were changed. Often the number of response variables vastly exceeds the sample size and well-established techniques such as multivariate analysis of variance (MANOVA) cannot be used to analyze the data. ANOVA simultaneous component analysis (ASCA) is an alternative to MANOVA for analysis of metabolomics data from an experimental design. In this paper, we show that ASCA assumes that none of the metabolites are correlated and that they all have the same variance. Because of these assumptions, ASCA may relate the wrong variables to a factor. This reduces the power of the method and hampers interpretation. We propose an improved model that is essentially a weighted average of the ASCA and MANOVA models. The optimal weight is determined in a data-driven fashion. Compared to ASCA, this method assumes that variables can correlate, leading to a more realistic view of the data. Compared to MANOVA, the model is also applicable when the number of samples is (much) smaller than the number of variables. These advantages are demonstrated by means of simulated and real data examples. The source code of the method is available from the first author upon request, and at the following github repository: https://github.com/JasperE/regularized-MANOVA.

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting.

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.

Automated correction of unwanted phase jumps in reference signals which corrupt MRSI spectra after eddy current correction.

A commonly applied step in the postprocessing of gradient localized proton MR spectroscopy, is correction for eddy current effects using the water signal as a reference. However, this method can degrade some of the metabolite signals, in particular if applied on proton MR spectroscopic imaging data. This artifact arises from the water reference signal in the presence of a second signal which resonates close to the main water resonance. The interference of both resonances will introduce jumps in the phase of the reference time domain signal. Using this phase for eddy current correction will result in a ringing artifact in the frequency domain of the metabolite signal over the whole frequency range. We propose a moving window correction algorithm, which screens the phase of reference signals and removes phase jumps in time domain caused by interference of signals from multiple spin systems. The phase jumps may be abrupt or gradually distributed over several time data points. Because the correction algorithm only corrects time data points which contain phase jumps, the phase is minimally disrupted. Furthermore, the algorithm is automated for large datasets, correcting only those water reference signals which are corrupted. After correction of the corrupted reference signals, normal eddy current correction may be performed. The algorithm is compared with a method which uses a low-pass filter and tested on simulated data as well as on in vivo proton spectroscopic imaging data from a healthy volunteer and from patients with a brain tumor.

Effect on the partial least-squares prediction of yarn properties combining raman and infrared measurements and applying wavelength selection.

The combination of Raman and infrared spectroscopy on the one hand and wavelength selection on the other hand is used to improve the partial least-squares (PLS) prediction of seven selected yarn properties. These properties are important for on-line quality control during production. From 71 yarn samples, the Raman and infrared spectra are measured and reference methods are used to determine the selected properties. Making separate PLS models for all yarn properties using the Raman and infrared spectra, prior to wavelength selection, reveals that Raman spectroscopy outperforms infrared spectroscopy. If wavelength selection is applied, the PLS prediction error decreases and the correlation coefficient increases for all properties. However, a substantial wavelength selection effect is present for the infrared spectra compared to the Raman spectra. For the infrared spectra, wavelength selection results in PLS prediction errors comparable with the prediction performance of the Raman spectra prior to wavelength selection. Concatenating the Raman and infrared spectra does not enhance the PLS prediction performance, not even after wavelength selection. It is concluded that an infrared spectrometer, combined with a wavelength selection procedure, can be used if no (suitable) Raman instrument is available.

Exploring field vegetation reflectance as an indicator of soil contamination in river floodplains.

This study investigated the relation between vegetation reflectance and elevated concentrations of the metals Ni, Cd, Cu, Zn and Pb in river floodplain soils. High-resolution vegetation reflectance spectra in the visible to near-infrared (400-1350 nm) were obtained using a field radiometer. The relations were evaluated using simple linear regression in combination with two spectral vegetation indices: the Difference Vegetation Index (DVI) and the Red-Edge Position (REP). In addition, a multivariate regression approach using partial least squares (PLS) regression was adopted. The three methods achieved comparable results. The best R(2) values for the relation between metals concentrations and vegetation reflectance were obtained for grass vegetation and ranged from 0.50 to 0.73. Herbaceous species displayed a larger deviation from the established relationships, resulting in lower R(2) values and larger cross-validation errors. The results corroborate the potential of hyperspectral remote sensing to contribute to the survey of elevated metal concentrations in floodplain soils under grassland using the spectral response of the vegetation as an indicator. Additional constraints will, however, have to be taken into account, as results are resolution- and location-dependent.

Use of the bootstrap and permutation methods for a more robust variable importance in the projection metric for partial least squares regression.

Bio-pharmaceutical manufacturing is a multifaceted and complex process wherein the manufacture of a single batch hundreds of processing variables and raw materials are monitored. In these processes, identifying the candidate variables responsible for any changes in process performance can prove to be extremely challenging. Within this context, partial least squares (PLS) has proven to be an important tool in helping determine the root cause for changes in biological performance, such as cellular growth or viral propagation. In spite of the positive impact PLS has had in helping understand bio-pharmaceutical process data, the high variability in measured response (Y) and predictor variables (X), and weak relationship between X and Y, has at times made root cause determination for process changes difficult. Our goal is to demonstrate how the use of bootstrapping, in conjunction with permutation tests, can provide avenues for improving the selection of variables responsible for manufacturing process changes via the variable importance in the projection (PLS-VIP) statistic. Although applied uniquely to the PLS-VIP in this article, the generality of the aforementioned methods can be used to improve other variable selection methods, in addition to increasing confidence around other estimates obtained from a PLS model.

On the relevance of glycolysis process on brain gliomas.

The proposed analysis considers aspects of both statistical and biological validation of the glycolysis effect on brain gliomas, at both genomic and metabolic level. In particular, two independent datasets are analyzed in parallel, one engaging genomic (Microarray Expression) data and the other metabolomic (Magnetic Resonance Spectroscopy Imaging) data. The aim of this study is twofold. First to show that, apart from the already studied genes (markers), other genes such as those involved in the human cell glycolysis significantly contribute in gliomas discrimination. Second, to demonstrate how the glycolysis process can open new ways towards the design of patient-specific therapeutic protocols. The results of our analysis demonstrate that the combination of genes participating in the glycolytic process (ALDOA, ALDOC, ENO2, GAPDH, HK2, LDHA, LDHB, MDH1, PDHB, PFKM, PGI, PGK1, PGM1 and PKLR) with the already known tumor suppressors (PTEN, Rb, TP53), oncogenes (CDK4, EGFR, PDGF) and HIF-1, enhance the discrimination of low versus high-grade gliomas providing high prediction ability in a cross-validated framework. Following these results and supported by the biological effect of glycolytic genes on cancer cells, we address the study of glycolysis for the development of new treatment protocols.

Statistical methods for improving verification of claims of origin for Italian wines based on stable isotope ratios.

Wine derives its economic value to a large extent from geographical origin, which has a significant impact on the quality of the wine. According to the food legislation, wines can be without geographical origin (table wine) and wines with origin. Wines with origin must have characteristics which are essential due to its region of production and must be produced, processed and prepared, exclusively within that region. The development of fast and reliable analytical methods for the assessment of claims of origin is very important. The current official method is based on the measurement of stable isotope ratios of water and alcohol in wine, which are influenced by climatic factors. The results in this paper are based on 5220 Italian wine samples collected in the period 2000-2010. We evaluate the univariate approach underlying the official method to assess claims of origin and propose several new methods to get better geographical discrimination between samples. It is shown that multivariate methods are superior to univariate approaches in that they show increased sensitivity and specificity. In cases where data are non-normally distributed, an approach based on mixture modelling provides additional improvements.

Opening the kernel of kernel partial least squares and support vector machines.

Kernel partial least squares (KPLS) and support vector regression (SVR) have become popular techniques for regression of complex non-linear data sets. The modeling is performed by mapping the data in a higher dimensional feature space through the kernel transformation. The disadvantage of such a transformation is, however, that information about the contribution of the original variables in the regression is lost. In this paper we introduce a method which can retrieve and visualize the contribution of the variables to the regression model and the way the variables contribute to the regression of complex data sets. The method is based on the visualization of trajectories using so-called pseudo samples representing the original variables in the data. We test and illustrate the proposed method to several synthetic and real benchmark data sets. The results show that for linear and non-linear regression models the important variables were identified with corresponding linear or non-linear trajectories. The results were verified by comparing with ordinary PLS regression and by selecting those variables which were indicated as important and rebuilding a model with only those variables.

Discrimination between metastasis and glioblastoma multiforme based on morphometric analysis of MR images.

BACKGROUND AND PURPOSE: Solitary MET and GBM are difficult to distinguish by using MR imaging. Differentiation is useful before any metastatic work-up or biopsy. Our hypothesis was that MET and GBM tumors differ in morphology. Shape analysis was proposed as an indicator for discriminating these 2 types of brain pathologies. The purpose of this study was to evaluate the accuracy of this approach in the discrimination of GBMs and brain METs. MATERIALS AND METHODS: The dataset consisted of 33 brain MR imaging sets of untreated patients, of which 18 patients were diagnosed as having a GBM and 15 patients, as having solitary metastatic brain tumor. The MR imaging was segmented by using the K-means algorithm. The resulting set of classes (also called "clusters") represented the variety of tissues observed. A morphology-based approach allowed discrimination of the 2 types of tumors. This approach was validated by a leave-1-patient-out procedure. RESULTS: A method was developed for the discrimination of GBMs and solitary METs. Two masses out of 33 were wrongly classified; the overall results were accurate in 93.9% of the observed cases. CONCLUSIONS: A semiautomated method based on a morphologic analysis was developed. Its application was found to be useful in the discrimination of GBM from solitary MET.

Revealing the metabolic profile of brain tumors for diagnosis purposes.

The metabolic behavior of complex brain tumors, like Gliomas and Meningiomas, with respect to their type and grade was investigated in this paper. Towards this direction the smallest set of the most representative metabolic markers for each brain tumor type was identified, using ratios of peak areas of well established metabolites, from (1)H-MRSI (Proton Magnetic Resonance Spectroscopy Imaging) data of 24 patients and 4 healthy volunteers. A feature selection method that embeds Fisher's filter criterion into a wrapper selection scheme was applied; Support Vector Machine (SVM) and Least Squares-SVM (LS-SVM) classifiers were used to evaluate the ratio markers classification significance. The area under the Receiver Operating Characteristic curve (AUROC) was adopted to evaluate the classification significance. It is found that the NAA/CHO, CHO/S, MI/S ratios can be used to discriminate Gliomas and Meningiomas from Healthy tissue with AUROC greater than 0.98. Ratios CHO/S, CRE/S, MI/S, LAC/CRE, ALA/CRE, ALA/S and LIPS/CRE can identify type and grade differences in Gliomas giving AUROC greater than 0.98 apart from the scheme of Gliomas grade II vs grade III where 0.84 was recorded due to high heterogeneity. Finally NAA/CRE, NAA/S, CHO/S, MI/S and ALA/S manage to discriminate Gliomas from Meningiomas providing AUROC exceeding 0.90.

Visualisation and interpretation of Support Vector Regression models.

This paper introduces a technique to visualise the information content of the kernel matrix and a way to interpret the ingredients of the Support Vector Regression (SVR) model. Recently, the use of Support Vector Machines (SVM) for solving classification (SVC) and regression (SVR) problems has increased substantially in the field of chemistry and chemometrics. This is mainly due to its high generalisation performance and its ability to model non-linear relationships in a unique and global manner. Modeling of non-linear relationships will be enabled by applying a kernel function. The kernel function transforms the input data, usually non-linearly related to the associated output property, into a high dimensional feature space where the non-linear relationship can be represented in a linear form. Usually, SVMs are applied as a black box technique. Hence, the model cannot be interpreted like, e.g., Partial Least Squares (PLS). For example, the PLS scores and loadings make it possible to visualise and understand the driving force behind the optimal PLS machinery. In this study, we have investigated the possibilities to visualise and interpret the SVM model. Here, we exclusively have focused on Support Vector Regression to demonstrate these visualisation and interpretation techniques. Our observations show that we are now able to turn a SVR black box model into a transparent and interpretable regression modeling technique.