Multivariate Statistical Analysis Approach Research Articles

Trials and tribulations of ‘omics data analysis: assessing quality of SIMCA-based multivariate models using examples from pulmonary medicine

Respiratory diseases are multifactorial heterogeneous diseases that have proved recalcitrant to understanding using focused molecular techniques. This trend has led to the rise of 'omics approaches (e.g., transcriptomics, proteomics) and subsequent acquisition of large-scale datasets consisting of multiple variables. In 'omics technology-based investigations, discrepancies between the number of variables analyzed (e.g., mRNA, proteins, metabolites) and the number of study subjects constitutes a major statistical challenge. The application of traditional univariate statistical methods (e.g., t-test) to these "short-and-wide" datasets may result in high numbers of false positives, while the predominant approach of p-value correction to account for these high false positive rates (e.g., FDR, Bonferroni) are associated with significant losses in statistical power. In other words, the benefit in decreased false positives must be counterbalanced with a concomitant loss in true positives. As an alternative, multivariate statistical analysis (MVA) is increasingly being employed to cope with 'omics-based data structures. When properly applied, MVA approaches can be powerful tools for integration and interpretation of complex 'omics-based datasets towards the goal of identifying biomarkers and/or subphenotypes. However, MVA methods are also prone to over-interpretation and misuse. A common software used in biomedical research to perform MVA-based analyses is the SIMCA package, which includes multiple MVA methods. In this opinion piece, we propose guidelines for minimum reporting standards for a SIMCA-based workflow, in terms of data preprocessing (e.g., normalization, scaling) and model statistics (number of components, R2, Q2, and CV-ANOVA p-value). Examples of these applications in recent COPD and asthma studies are provided. It is expected that readers will gain an increased understanding of the power and utility of MVA methods for applications in biomedical research.

A multivariate statistical analysis approach to highlight molecular processes in plant cell walls through ATR FT-IR microspectroscopy: The role of the α-expansin PhEXPA1 in Petunia hybrida

Mid-infrared ATR FT-IR microspectroscopy is applied in conjunction with multivariate statistical analysis on petal samples of Petunia hybrida from wild-type and from two transgenic lines in which the PhEXPA1 expansin gene expression was down-regulated and up-regulated, respectively. New insights are given on the role of expansin in the rearrangement of the cell wall polymer network. Measurements are done without any previous sample treatment to preserve the native cell wall structure and natural biological variability. An original combination of data analysis techniques is proposed to highlight molecular processes in plant cells, based on an automated spectra selection procedure, Principal Component Analysis, Wilcoxon rank sum test and heat map data representation.

Multivariate statistical analysis and 3D-coupled Markov chain modeling approach for the prediction of subsurface heterogeneity of contaminated soil management in abandoned Guryong Mine Tailings, Korea

Various geological materials on the ground surface can be natural or artificial sources of pollutions. The spatial distribution of tailings is required to investigate the geological material pollutions. The objectives of this study were to determine the main factors influencing tailing zonations using a factor analysis, to determine the zonation of tailings with a cluster analysis, and to simulate zonations with three-dimensional coupled Markov chain (3D-CMC) modeling. The database was composed of 12 excavated exploratory holes in the Guryong mine tailings, for which there were analytical data covering the physical, chemical, and mineralogical aspects. The principal component analysis indicated that the tailing composition was mainly affected by three factors out of 21 variables: pH, cation exchange capacity, and mineral composition. Based on these main factors, the tailings were classified into five groups using a cluster analysis. Group I was approximately 50 cm deep from surface and had secondary gypsum (CaSO4·2H2O) and jarosite (KFe3(SO4)2(OH)6). Group II had low pH values caused by strong pyrite oxidation and the greatest amounts of the secondary minerals. In group III and IV, the quantity of the secondary minerals decreased. Group V was characterized by primary calcite (CaCO3) composition. These results were applied to the CMC modeling, and the quantitative 3D distribution of tailing was verified. For the cost-saving prediction of subsurface heterogeneity, 3D-CMC modeling was executed using the selected eight holes data among twelve holes. The unknown four holes, GS3, GS6, GS8 and GS11, are identified as 89.7, 88.6, 80.7 and 81.1 %, respectively. They are recognized as 85.0 % of the total zonation. The zonation method of tailings executed in this study can be utilized in predicting the 3D distribution of the pollution factor. This may be a useful and economical method to identify the environmentally hazardous materials in underground systems.

Multivariate statistical analysis strategy for multiple misfire detection in internal combustion engines

This paper proposes a multivariate statistical analysis approach to processing the instantaneous engine speed signal for the purpose of locating multiple misfire events in internal combustion engines. The state of each cylinder is described with a characteristic vector extracted from the instantaneous engine speed signal following a three-step procedure. These characteristic vectors are considered as the values of various procedure parameters of an engine cycle. Therefore, determination of occurrence of misfire events and identification of misfiring cylinders can be accomplished by a principal component analysis (PCA) based pattern recognition methodology. The proposed algorithm can be implemented easily in practice because the threshold can be defined adaptively without the information of operating conditions. Besides, the effect of torsional vibration on the engine speed waveform is interpreted as the presence of super powerful cylinder, which is also isolated by the algorithm. The misfiring cylinder and the super powerful cylinder are often adjacent in the firing sequence, thus missing detections and false alarms can be avoided effectively by checking the relationship between the cylinders.

Characterization of Composition C4 Explosives using Time-of-Flight Secondary Ion Mass Spectrometry and X-ray Photoelectron Spectroscopy

The application of surface analytical techniques such as time-of-flight secondary ion mass spectrometry (ToF-SIMS) and X-ray photoelectron spectroscopy (XPS) is explored as a means of differentiating between composition C4 plastic explosives (C-4). Three different C-4 samples including U.S. military grade C-4, commercial C-4 (also from the United States), and C-4 from England (PE-4) were obtained and analyzed using both ToF-SIMS and XPS. ToF-SIMS was able to successfully discriminate between different C-4 samples with the aid of principal component analysis, a multivariate statistical analysis approach often used to reduce the dimensionality of complex data. ToF-SIMS imaging was also used to obtain information about the spatial distribution of the various additives contained within the samples. The results indicated that the samples could potentially be characterized by their 2-D chemical and morphological structure, which varied from sample to sample. XPS analysis also showed significant variation between samples, with changes in the atomic concentrations, as well as changes in the shapes of the high-resolution C 1s and O 1s spectra. These results clearly demonstrate the feasibility of utilizing both ToF-SIMS and XPS as tools for the direct characterization and differentiation of C-4 samples for forensic applications.

Finding diabetic nephropathy biomarkers in the plasma peptidome by high‐throughput magnetic bead processing and MALDI‐TOF‐MS analysis

Diabetic nephropathy (DN) is the most common cause of end-stage renal disease and improved biomarkers would help identify high-risk individuals. The aim of this study was to discover candidate biomarkers for DN in the plasma peptidome in an in-house cross-sectional cohort (n=122) of type 1 diabetic patients diagnosed with normo-, micro-, and macroalbuminuria. Automated, high-throughput, and reproducible (interassay median CV: 13-14%) plasma peptide profiling protocols involving RPC18 and weak cation exchange magnetic beads on a liquid handling workstation with a MALDI-TOF-MS readout were successfully established. Using these protocols and a combined univariate (Kruskal-Wallis) and multivariate (independent component analysis) statistical analysis approach, ten single peptides and three multi-peptide candidate biomarkers were found. Employment of RPC18 and weak cation exchange magnetic beads proved to be complementary. The proteins found in this study, including C3f and apolipoprotein C-I, represent new candidate biomarkers for DN from the plasma peptidome. The automated procedures and implementation of independent components analysis provide a fast and informative system for analyzing individual patient samples in protein biomarker discovery.

Combining multivariate analysis and geochemical approaches for assessing heavy metal level in sediments from Sudanese harbors along the Red Sea coast

Multivariate statistical analysis and geochemical approaches were exploited for the assessment of the level of some heavy metals (Mn, Fe, Ni, Cu, Zn and Pb) in sediments from Sudanese harbors along the Red Sea coast. Principal component analysis, as a multivariate statistical analysis approach, was applied to identify contribution sources by heavy metals in sediments. While a single source (crustal) was recorded in the bulk sediments and coarse sediment grains (grain-size 1000–500 µm), two sources (crustal and anthropogenic) were recorded in fine sediment grains (grain-size < 500 µm). Furthermore, enrichment factor (EF), as a geochemical approach, appointed polluted sites by heavy metals in the study area. Based upon a previous study addressed the interpretation of EF values, minor to moderate anthropogenic enrichment were recorded in sediments from some sites in the study area. The main anthropogenic activities that believed to be the major sources of pollution by heavy metals in the study area are discharges from oil refinery, industry, shipping activity and domestic waste. Hierarchical cluster analysis (HCA), as another multivariate statistical analysis approach, was applied for the concentrations of heavy metals in bulk sediments to group sediments according to their mineralogical composition. The output of HCA is that sediments from the Port-Sudan harbor can be divided mainly into three areas — east, west and south. For the Sawakin harbor, no apparent trend for the spatial distribution of heavy metals in sediments was recorded.

Multivariate statistical approach to electron backscattered diffraction

This paper assesses the potential of multivariate statistical analysis (MSA) applied to electron backscattered diffraction (EBSD) data. Instead of directly indexing EBSD patterns on an individual basis, this multivariate approach reduces a large (thousands) set of individual EBSD patterns into a core set of statistically derived component EBSD patterns which can be subsequently indexed. The following hypotheses are considered in this paper: (1) experimental EBSD patterns from a microstructure can be analytically treated as linear combinations of spatially simple components, (2) MSA has an angular resolution on par with standard EBSD, (3) MSA can discriminate between similar and dissimilar phases, and (4) the MSA approach can improve the effective spatial resolution of automated EBSD.

An integrated approach for the consideration of uncertainty in decision making supported by Life Cycle Assessment

This paper presents an approach for the integrated consideration of both technical and valuation uncertainties during decision making supported by environmental performance information based on Life Cycle Assessment (LCA). Key elements of this approach include “distinguishability analysis” to determine whether the uncertainty in the performance information is likely to make it impossible to distinguish between the activities under consideration, and the use of a multivariate statistical analysis approach, called principal components analysis (PCA), which facilitates the rapid analysis of large numbers of parallel sets of results, and enables the identification of choices that lead to similar and/or opposite evaluations of activities. The integrated approach for the management of uncertainty is demonstrated for a technology selection decision for the recommissioning of a coal-based power station. The results of the case study decision suggest that stakeholder involvement in preference modelling is important, and that the “encoding” of value judgements and preferences into LCA environmental performance information is to be avoided. The approach presented in this paper provides a foundation for the consideration of the implications of diversity in values and preferences as part of an overall approach to promote effective decision making based on LCA environmental performance information. However, the approach is more universally applicable – it can be used wherever multiple criteria decision analysis is used to assist in the resolution of complex decision situations.

Characterization of gunpowder samples using time-of-flight secondary ion mass spectrometry (TOF-SIMS)

Time-of-flight secondary ion mass spectrometry (TOF-SIMS) was utilized to obtain characteristic mass spectra from three different smokeless powders and six different black powder samples. In these mass spectra, peaks indicative of both the organic and inorganic additive constituents in the gunpowders were observed. TOF-SIMS was able to successfully differentiate between the different black and smokeless gunpowder samples analyzed with the aid of principal components analysis (PCA), a multivariate statistical analysis approach often used to reduce the dimensionality of complex data. TOF-SIMS was also used to obtain information about the spatial distribution of the various additives contained within the gunpowder samples. SIMS imaging demonstrated that that the samples could potentially be characterized by their 2-D structure, which varied from sample to sample. These results clearly demonstrate the feasibility of utilizing TOF-SIMS as a tool for the characterization and differentiation of gunpowder samples for general forensic applications.

Application of data mining and process knowledge discovery in sheet metal assembly dimensional variation diagnosis

In the assembly of sheet metal products such as body-in-white, dimensional control is a challenging task work for quality improvement due to the complexity of both the structure and the process. This paper has developed a dimensional variation diagnostic reasoning and decision approach through the combination of data mining (DM) and knowledge discovery techniques. Correlation analysis (CA) and maximal tree (MT) methods were applied to extract the large variation group from massive multi-dimensional measured data, while the multi-variate statistical analysis (MSA) approach was used to discover the principle variation pattern. A decision tree (DT) approach based on knowledge of product and assembly process was developed to fulfill the “hypothesis and validation” characterized variation causes reasoning procedure. The established decision support analysis (DSA) approach for sheet metal assembly variation diagnosis has been proven to be effective and efficient through practical implementation.

Performance analysis of maximal ratio combining and comparison with optimum combining for mobile radio communications with cochannel interference

The performance of maximal ratio combining for space diversity reception in digital cellular mobile radio systems is studied for communications in the presence of multiple cochannel interference (CCI) sources and is compared to optimum combining. The main contribution of the paper is that the analysis accounts for fading of the signal of interest (SOI) as well as the cochannel interference (CCI). The paper considers BPSK signalling in flat, quasi-static channels. Rayleigh or Rice fading is assumed for the SOI, while CCI is assumed subject to Rayleigh fading. Channels associated with interference sources are assumed independent and identically distributed. Using a multivariate statistical analysis approach and assuming equal-power interference sources, analytical expressions are derived for the density function of the array output signal-to-interference ratio (SIR), the outage probability, and the average probability of bit error with maximal ratio combining. Earlier results obtained for optimum combining and Rayleigh fading are extended to the case when the SOI is subject to Rice fading. A limited analysis of the equal gain combiner is also presented.

Multivariate analysis of single unit cells in electron crystallography

High-resolution electron cryomicroscopy of two-dimensional protein crystals is associated with extremely noisy raw data in which even the crystal lattice often cannot be discerned. Correlation averaging procedures, aimed at calculating the total average of all unit cells of crystals in order to reduce noise, are now used routinely in electron crystallography. Multivariate statistical analysis (MSA) may be used for finding not only the average structure but also for quantifying the systematic departures from that average within the population of individual unit cells. We show that the MSA approach is applicable to single unit-cell images in the low-dose (<10 electrons/Å 2), high-resolution (<5 Å) realm using 400 keV electron spot-scan images of ice-embedded gp32∗I protein crystals. Our feasibility study opens a pathway toward exploiting these naturally occurring variations on the unit-cell theme in order to achieve higher-resolution three-dimensional reconstruction results, or to better understand the dynamic behaviour of molecules within two-dimensional crystals. We explain how single unit-cell images can be processed and classified into homogeneous groups, and we review how the results of such discriminate averaging may subsequently be exploited within the context of conventional “ h , k ”-space electron crystallographic approaches. Variations among the individual unit cells may thus be one of the most significant resolution-limiting factors currently experienced in electron crystallography. The quantitative assessment and exploitation of such variations may lead to an increased performance of electron crystallographic procedures.

Multivariate statistical analysis of water sorption data of Argentine sorghum

Instead of using a factorial design for studying water sorption characteristics and its assumption of homogeneity of variances among cells, a multivariate statistical analysis approach is presented. This considers interactions and heterogeneous variances and leads to simultaneous comparisons of all a w levels. By applying this approach to a study of the water sorption characteristics of Argentine sorghum, significant differences were obtained between hybrids with the conclusion that they should not be mixed in storage. Confidence intervals were presented which will be of use both in predicting storage behavior and in comparing results from different researchers.

Analysis of permeability controls: a new approach

AbstractBy modelling a range of rock-forming processes such as compaction and various styles of cementation, a new understanding of how they affect pore-system geometry, and hence permeability, has been gained. For example, almost identical permeability-porosity trends result from progressive compaction or grain overgrowth cementation in a clean sandstone, and these trends are curvilinear on the traditional log-linear plot. The steepening which defines the curve marks the onset of pore-throat blocking. Other cement styles, such as pore-filling carbonates or grain-rimming clays, show different porosity-permeability trends. This new understanding can be used predictively (predicting permeability from predictions of grain size and diagenetic style), or as a tool for identifying the important permeability controls in a set of field data. This latter application is presented and illustrated using data from a variety of sandstone types. This approach has important advantages over commonly used multivariate statistical analysis approaches. It can quickly provide a good understanding of what are (and are not) the important controls on permeability. It also provides a basis for more focused and meaningful statistical analysis to quantify these controls.

Geochemical characteristics of some rare element-bearing granites in southeast China and physico-chemical conditions of their formation

The formation of ore-bearing granites in the Yenshanian movement in southeast China and the geochemical characteristics of some RE-bearing granites have been studied through multivariate statistical analysis and physicochemical approach. The main conclusions have Been drawn as follows: (1) The granites are believed to be products of anatexis of the crustal materials. The formation temperature of granitic magma is estimated at about 600°C and the crystallization temperatures range from 600° to 500°C. The temperature of Li-, Fand H2O-rich residual magma in the latest stage of magmatism is probably below 500°C. (2) A rock series from early lepidomelane-granite through protolithionite-and zinnwalditegranite to lithioniteor lepidolite-granite is considered as a result of actual crystallization. (3) The mineral paragenesis and fades zonation of granite plutons are mainly controlled by Ph2o, μNa2O and μK2O in the magma. (4) During the magmatic evolution the ore-forming elements (REE, Nb, Ta, etc.) are variable in geochemistry. REEs, similar to mafic components, were highly concentrated at the early stage of the magmatic evolution and deposited under favourable conditions in the zinnwaldite-and protolithionite-granites; Nb and Ta have a preference for felsic and volatile components, thus are mainly concentrated at later stages of the magmatic evolution. Nb ore deposits are formed in the lithionite and lepidolite granites, for Ta is intimately associated with Na2O, Li2O, F and H2O.