The statistical analysis of multivariate serological frequency data

Data occurring in the form of frequencies are common in genetics—for example, in serology. Examples are provided by the AB0 group, the Rhesus group, and also DNA data. The statistical analysis of tables of frequencies is carried out using the available methods of multivariate analysis with usually three principal aims. One of these is to seek meaningful relationships between the components of a data set, the second is to examine relationships between populations from which the data have been obtained, the third is to bring about a reduction in dimensionality. This latter aim is usually realized by means of bivariate scatter diagrams using scores computed from a multivariate analysis. The multivariate statistical analysis of tables of frequencies cannot safely be carried out by standard multivariate procedures because they represent compositions and are therefore embedded in simplex space, a subspace of full space. Appropriate procedures for simplex space are compared and contrasted with simple standard methods of multivariate analysis (“raw” principal component analysis). The study shows that the differences between a log-ratio model and a simple logarithmic transformation of proportions may not be very great, particularly as regards graphical ordinations, but important discrepancies do occur. The divergencies between logarithmically based analyses and raw data are, however, great. Published data on Rhesus alleles observed for Italian populations are used to exemplify the subject.     

Comparison of fatty acids of marine fungi using multivariate statistical analysis

Summary Ten obligate marine fungi have as their principal fatty acids 160, 180, 181n9 and 182n6. The fatty acids ranged from 14 to 22 carbons, completely dominated by those with even numbers of carbons. The amount of unsaturated fatty acids varied between 35% and 80%. Each isolate contained small amounts of the acids 183n3 and 204n6. Branched, hydroxy- or cyclic fatty acids were not detected. Multivariate statistical, i.e. principal component analysis, showed that all ten strains could be distinguished on the basis of their fatty acid composition. These results indicate that the marine fungi do not have an unusual fatty acid composition and suggest that chemometric, multivariate analysis might be employed to confirm taxonomic relationships among these organisms.     

Impact of meteorological factors on ozone concentrations modelled by time series analysis and multivariate statistical methods

The ozone concentrations in Slavonia (eastern part of Croatia) were measured for the first time in spring–summer season 2002. Fourier analysis, principal components analysis (PCA) and multiple linear regression analysis (MLR) were applied to these time series. Weekday effect in spring and weekend effect in summer period were observed. Correlation with meteorological parameters is strongly emphasized from 10 a.m.–3 p.m. MLR models showed that variations in ozone concentrations are attributed to variation of few meteorological parameters with R² ≈ 0.7 and 0.8 in the spring and summer, respectively.     

Metabolomic analysis using optimized NMR and statistical methods

NMR-based metabolomics requires robust automated methodologies, and the accuracy of NMR-based metabolomics data is greatly influenced by the reproducibility of data acquisition and processing methods. Effective water resonance signal suppression and reproducible spectral phasing and baseline traces across series of related samples are crucial for statistical analysis. We assess robustness, repeatability, sensitivity, selectivity, and practicality of commonly used solvent peak suppression methods in the NMR analysis of biofluids with respect to the automated processing of the NMR spectra and the impact of pulse sequence and data processing methods on the sensitivity of pattern recognition and statistical analysis of the metabolite profiles. We introduce two modifications to the excitation sculpting pulse sequence whereby the excitation solvent suppression pulse cascade is preceded by low-power water resonance presaturation pulses during the relaxation delay. Our analysis indicates that combining water presaturation with excitation sculpting water suppression delivers the most reproducible and information-rich NMR spectra of biofluids.     

Structural components of the arch of the foot analyzed by radiogrammetric and multivariate statistical methods

The structural component of the arches of the human foot were analyzed by a radiogrammetric method and multivariate statistical procedures. The right feet of 101 male university students were radiographed in the standing position from a lateromedial direction. 6 joint heights were measured directly on the radiographs. Factor analysis with varimax rotation showed 3 basic underlying factors for arch heights: (1) calcaneonavicular joint, cuneonavicular joint and first tarsometatarsal joint; (2) calcaneocuboidal joint and 5th tarsometatarsal joint and (3) subtalar joint. The first factor represented the medial longitudinal arch height, the second was associated with the lateral longitudinal arch height. No transverse factor indicating tarsometatarsal or transverse tarsal joints was found. Cluster analysis showed a similar configuration to that in factor analysis. Analysis suggested a key role of the subtalar joint which integrated both the medial and lateral longitudinal arch heights.     

The use of different statistical methods in epidemiological analysis to assess the seasonality and territorial spread of infectious diseases

To solve the problems connected with the evaluation of the seasonal and territorial distribution of infectious diseases, indications and limitations for the use of the following statistical methods have been worked out: the calculation of the monthly morbidity level, the proportion of cases of infectious diseases falling on the months of seasonal morbidity rises, the proportion of such cases appearing due to the influence of seasonal factors, the total and partial indices, the average monthly rate of increase in seasonal morbidity, the complex evaluation of seasonal morbidity, the evaluation of the nonparallelism of two curves, the determination of the mean quadratic deviations and Shannon's entropy. The algorithms based on these methods lie in the foundation of 11 computer programs, forming the software complex "Epidanalysis" and provided with the service menu permitting an epidemiologist to proceed from the task via indications and limitations to the corresponding program. The programs are intended for different types of computers (IBM PC XT, EC-1640, Robotron 1715).     

Evaluation of the long term monitoring of phytoplankton assemblages in a canyon-shape reservoir using multivariate statistical methods

Hydrobiologia - Long term monitoring of the Římov Reservoir provided a data set for the analysis of phytoplankton composition and biomass in coincidence with physical, chemical,...     

Enhanced process monitoring of fed-batch penicillin cultivation using time-varying and multivariate statistical analysis

On-line monitoring of penicillin cultivation processes is crucial to the safe production of high-quality products. In the past, multiway principal component analysis (MPCA), a multivariate projection method, has been widely used to monitor batch and fed-batch processes. However, when MPCA is used for on-line batch monitoring, the future behavior of each new batch must be inferred up to the end of the batch operation at each time and the batch lengths must be equalized. This represents a major shortcoming because predicting the future observations without considering the dynamic relationships may distort the data information, leading to false alarms. In this paper, a new statistical batch monitoring approach based on variable-wise unfolding and time-varying score covariance structures is proposed in order to overcome the drawbacks of conventional MPCA and obtain better monitoring performance. The proposed method does not require prediction of the future values while the dynamic relations of data are preserved by using time-varying score covariance structures, and can be used to monitor batch processes in which the batch length varies. The proposed method was used to detect and identify faults in the fed-batch penicillin cultivation process, for four different fault scenarios. The simulation results clearly demonstrate the power and advantages of the proposed method in comparison to MPCA.     

Selection of biomarkers by a multivariate statistical processing of composite metabonomic data sets using multiple factor analysis

We introduce a statistical approach for integrating data from several analytical platforms. We illustrate this approach using (1)H-(13)C Heteronuclear Multiple Bond Connectivity nuclear magnetic resonance spectroscopy ((1)H-(13)C HMBC NMR) and Pyrolysis Metastable Atom Bombardment Time-of-Flight mass spectrometry (Py-MAB-TOF-MS) to perform metabolic fingerprinting on cattle treated with anabolic steroids. Multiple factor analysis (MFA) integrates complementary aspects from NMR and MS data into a unique metabolic signature describing the biomarkers related to the dose-response. This work also indicates that, from a practical point of view, metabonomics and other "-omics" biotechnologies can benefit significantly from a generalized multi-platform integrative approach using multiple factor analysis.     

Taxonomic discrimination of cyanobacteria by metabolic fingerprinting using proton nuclear magnetic resonance spectra and multivariate statistical analysis

When whole-cell extracts are analyzed, proton nuclear magnetic resonance (¹H NMR) spectroscopy provides biochemical profiles that contain overlapping signals of the majority of the compounds. To determine whether cyanobacteria could be taxonomically discriminated on the basis of metabolic fingerprinting, we subjected whole-cell extracts of the cyanobacteria to¹H NMR. The¹H NMR spectra revealed a predominance of signals in the aliphatic region. Principal component analysis (PCA) of the data then enabled discrimination of the cyanobacteria. The hierarchical dendrogram, based on PCA of the aliphatic region data, showed that six cyanobacterial taxa were discriminated from two eukaryotic microalgal species, and that the six taxa could be subsequently divided into three groups. This agrees with the current taxonomy of cyanobacteria. Therefore, our overall results indicate that metabolic fingerprinting using¹H NMR spectra and multivariate statistical analysis provide a simple, rapid method for the taxonomical discrimination of cyanobacteria.     

The indications for the use of different statistical methods of epidemiological analysis and delimitation in the assessment of a dynamic epidemic process

To solve various problems connected with epidemiological analysis concerning evaluation of the level, direction and intensity of the time course of the epidemic process and character of the cyclic component, the indications and limitations to the use of the following statistical methods have been worked out: equalizing by the method of the least squares on a straight line, a parabola, an exponential or power curve; calculation of the average annual rate of increase; leveling of dynamic series by the methods of internal prolongation, sliding and suspended sliding mean values; calculation of deviations from the theoretical tendency line; autocorrection. 11 computer programs have been compiled on the basis of the algorithms of the above methods, complete with the service menu, for the program complex "Epidanalysis" which permits an epidemiologist to proceed from the problem via indications and limitations to the adequate statistical method and the corresponding software. The programs are intended for different types of computers (EC-1840, Robotron 1715, IBM PC XT).     

Quality evaluation of Astragali Radix using a multivariate statistical approach

The quality of 43 Astragali Radix samples collected in China and Mongolia was evaluated using multivariate statistical analysis of data obtained from liquid chromatography-ion trap-time of flight (LC-IT-TOF) mass spectrometry. The samples were classified into four characteristic groups and most of the marker compounds were identified by elemental composition data and the results of MS/MS analysis. The approach provides useful information and gives an overview of the difference between crude drugs originating from different production environments and the genetic nature of the medicinal plants. In addition, the ease with which particular marker compounds could be identified and the effectiveness of the comparison by means of multivariate statistics, such as principal component analysis (PCA), indicates that this method could be utilized for the establishment of standardization and quality control procedures for crude drugs.     

Problems with the statistical testing of panbiogeographic hypotheses

Abstract

Croizat regarded generalised tracks as having a statistical basis, their degree of justification being directly related to the number of individual tracks consistent with them. In order to be logically valid, however, such an approach needs to have an explicit statistical basis. Page (1987) attempts to provide this, proposing the following protocol. Tracks are treated as geographic minimum-spanning trees which in turn are represented numerically as binary connectivity matrices. The statistical significance of similarities between two connectivity matrices is assessed using a permutation-test of association, a test that was developed for comparing distancematrices. The null hypothesis for this test is defined by the set of alternative connectivity matrices corresponding to all possible permutations of the track-vertices. There are however, a number of problems with this statistical test when applied to connectivity matrices derived from panbiogeographic tracks, and these render invalid the procedure advocated by Page.     

Therapeutic prognosis of prostate cancer using surface-enhanced Raman scattering of patient urine and multivariate statistical analysis

Surface-enhanced Raman scattering (SERS) is highly sensitive and label-free analytical technique based on Raman spectroscopy aided by field-multiplying plasmonic nanostructures. We report the use of SERS measurements of patient urine in conjunction with biostatistical algorithms to assess the treatment response of prostate cancer (PCa) in 12 recurrent (Re) and 63 nonrecurrent (NRe) patient cohorts. Multiple Raman spectra are collected from each urine sample using monodisperse silver nanoparticles (AgNPs) for Raman signal enhancement. Genetic algorithms-partial least squares-linear discriminant analysis (GA-PLS-LDA) was employed to analyze the Raman spectra. Comprehensive GA-PLS-LDA analyses of these Raman spectral features (p = 3.50 × 10⁻¹⁶ ) yield an accuracy of 86.6%, sensitivity of 86.0%, and specificity 87.1% in differentiating the Re and NRe cohorts. Our study suggests that SERS combined with multivariate GA-PLS-LDA algorithm can potentially be used to detect and monitor the risk of PCa relapse and to aid with decision-making for optimal intermediate secondary therapy to recurred patients.