A novel definition of the multivariate coefficient of variation

The coefficient of variation CV (%) is widely used to measure the relative variation of a random variable to its mean or to assess and compare the performance of analytical techniques/equipments. A review is made of the existing multivariate extensions of the univariate CV where, instead of a random variable, a random vector is considered, and a novel definition is proposed. The multivariate CV obtained only requires the calculation of the mean vector, the covariance matrix and simple quadratic forms. No matrix inversion is needed which makes the new approach equally attractive in high dimensional as in very small sample size problems. As an illustration, the method is applied to electrophoresis data from external quality assessment in laboratory medicine, to phenotypic characteristics of pocket gophers and to a microarray data set.     

Biallelic and triallelic approaches of 5-HTTLPR polymorphism are associated with food intake and nutritional status in childhood

BackgroundThe 5-HTT gene contains polymorphisms in its promoter region, the insertion/deletion (5-HTTLPR) that creates long (L) or short (S) alleles (biallelic approach) and SNP (rs25531) in L allele (triallelic approach).ObjectivesThe aim of this study is to investigate the association of the 5-HTTLPR and rs25531 polymorphisms, using bi- and triallelic approach, with dietary intake and anthropometric parameters in children followed until 8 years old.MethodsThe sample were 303 children who were recruited at birth and examined at 1, 3 to 4 and 7 to 8 years old. The polymorphisms were analyzed by polymerase-chain-reaction-based methods.ResultsIn the biallelic approach, children with the S/S genotype presented a higher body mass index Z-score in the three developmental stages and higher sum of skinfolds at 3 to 4 and 7 to 8 years old than carriers of the L allele. In the triallelic approach, S/S, Lg/S plus Lg/Lg genotypes were associated with higher energy intake daily at 1 year old and with waist circumference at 3 to 4 years old.ConclusionsIn the biallelic approach, the 5-HTTLPR polymorphism is associated with food intake, body mass index Z-score and sum of skinfolds in children, reinforcing the role of the serotonin transporter in childhood obesity. Our data indicate that the biallelic approach is more sensible than the triallelic approach for detected associations with food intake and nutritional status in childhood. Identifying susceptibility genes in early life could provide the foundations for interventions in lifestyle to prevent children to become obese adults.     

Rectangular tolerance regions and multivariate normal reference regions in laboratory medicine

Reference intervals are widely used in the interpretation of results of biochemical and physiological tests of patients. When there are multiple biochemical analytes measured from each subject, a multivariate reference region is needed. Because of their greater specificity against false positives, such reference regions are more desirable than separate univariate reference intervals that disregard the cross-correlations between variables. Traditionally, under multivariate normality, reference regions have been constructed as ellipsoidal regions. This approach suffers from a major drawback: it cannot detect component-wise extreme observations. In the present work, procedures are developed to construct rectangular reference regions in the multivariate normal setup. The construction is based on the criteria for tolerance intervals. The problems addressed include the computation of a rectangular tolerance region and simultaneous tolerance intervals. Also addressed is the computation of mixed reference intervals that include both two-sided and one-sided limits, simultaneously. A parametric bootstrap approach is used in the computations, and the accuracy of the proposed methodology is assessed using estimated coverage probabilities. The problem of sample size determination is also addressed, and the results are illustrated using examples that call for the computation of reference regions.     

An empirical approach for reliable microsatellite genotyping of wolf DNA from multiple noninvasive sources

Wildlife management and conservation take advantage of the possibility to study free-living populations by collecting and analysing noninvasive samples. Nevertheless, the commonly adopted approaches, aimed at preventing results being affected by genotyping errors, considerably limit the applicability of noninvasive genotyping. An empirical approach is presented for achieving a reliable data set of wolf (Canis lupus) genotypes from multiple sources of DNA collected in a monitored population. This method relies on the relationship between sample quality and amplification outcome, which is ultimately related to the occurrence of typing errors (allelic dropout, false alleles). After DNA extraction, templates are amplified once at each locus and a conservative rating system (Q-score) is adopted to define the quality of single-locus amplifications. A significant relationship was found between quality scores and error rate (ER) (r ²=0.982). Thus it was possible to predict the chance a genotype has of being affected by errors on the basis of its Q-score. Genotypes not reaching a satisfactory confidence level can either be replicated to become reliable or excluded from the data set. Accordingly, in the present case study, 48–73% of all single-locus and 51–53% of all multilocus (ML) genotypes reached a sufficient (99 and 95%, respectively) reliability level after a single amplification per locus. Despite the possible decrease in overall yield, this method could provide a good compromise between accuracy in genotyping and effectiveness in screening large data sets for long-term or large-scale population surveys. However, to achieve complete and reliable data sets, replicated amplifications are necessary for those samples and loci providing poor results.An erratum to this article can be found at     

Critical points of DNA quantification by real-time PCR – effects of DNA extraction method and sample matrix on quantification of genetically modified organisms

Background  

Real-time PCR is the technique of choice for nucleic acid quantification. In the field of detection of genetically modified organisms (GMOs) quantification of biotech products may be required to fulfil legislative requirements. However, successful quantification depends crucially on the quality of the sample DNA analyzed. Methods for GMO detection are generally validated on certified reference materials that are in the form of powdered grain material, while detection in routine laboratories must be performed on a wide variety of sample matrixes. Due to food processing, the DNA in sample matrixes can be present in low amounts and also degraded. In addition, molecules of plant origin or from other sources that affect PCR amplification of samples will influence the reliability of the quantification. Further, the wide variety of sample matrixes presents a challenge for detection laboratories. The extraction method must ensure high yield and quality of the DNA obtained and must be carefully selected, since even components of DNA extraction solutions can influence PCR reactions. GMO quantification is based on a standard curve, therefore similarity of PCR efficiency for the sample and standard reference material is a prerequisite for exact quantification. Little information on the performance of real-time PCR on samples of different matrixes is available.     

Gene selection for sample classifications in microarray experiments

DNA microarray technology provides useful tools for profiling global gene expression patterns in different cell/tissue samples. One major challenge is the large number of genes relative to the number of samples. The use of all genes can suppress or reduce the performance of a classification rule due to the noise of nondiscriminatory genes. Selection of an optimal subset from the original gene set becomes an important prestep in sample classification. In this study, we propose a family-wise error (FWE) rate approach to selection of discriminatory genes for two-sample or multiple-sample classification. The FWE approach controls the probability of the number of one or more false positives at a prespecified level. A public colon cancer data set is used to evaluate the performance of the proposed approach for the two classification methods: k nearest neighbors (k-NN) and support vector machine (SVM). The selected gene sets from the proposed procedure appears to perform better than or comparable to several results reported in the literature using the univariate analysis without performing multivariate search. In addition, we apply the FWE approach to a toxicogenomic data set with nine treatments (a control and eight metals, As, Cd, Ni, Cr, Sb, Pb, Cu, and AsV) for a total of 55 samples for a multisample classification. Two gene sets are considered: the gene set omegaF formed by the ANOVA F-test, and a gene set omegaT formed by the union of one-versus-all t-tests. The predicted accuracies are evaluated using the internal and external crossvalidation. Using the SVM classification, the overall accuracies to predict 55 samples into one of the nine treatments are above 80% for internal crossvalidation. OmegaF has slightly higher accuracy rates than omegaT. The overall predicted accuracies are above 70% for the external crossvalidation; the two gene sets omegaT and omegaF performed equally well.     

A Universal Approach to Prepare Reagents for DNA-Assisted Protein Analysis

The quality of DNA-labeled affinity probes is critical in DNA-assisted protein analyses, such as proximity ligation and extension assays, immuno-PCR, and immuno-rolling circle amplification reactions. Efficient, high-performance methods are therefore required for isolation of pure conjugates from reactions where DNA strands have been coupled to antibodies or recombinant affinity reagents. Here we describe a universal, scalable approach for preparing high-quality oligonucleotide-protein conjugates by sequentially removing any unconjugated affinity reagents and remaining free oligonucleotides from conjugation reactions. We applied the approach to generate high-quality probes using either antibodies or recombinant affinity reagents. The purified high-grade probes were used in proximity ligation assays in solution and in situ, demonstrating both augmented assay sensitivity and improved signal-to-noise ratios.     

Reference Valence Effects of Affective S–R Compatibility: Are Visual and Auditory Results Consistent?

Humans may be faster to avoid negative words than to approach negative words, and faster to approach positive words than to avoid positive words. That is an example of affective stimulus–response (S–R) compatibility. The present study identified the reference valence effects of affective stimulus–response (S–R) compatibility when auditory stimulus materials are used. The researchers explored the reference valence effects of affective S–R compatibility using a mixed-design experiment based on visual words, visual pictures and audition. The study computed the average compatibility effect size. A t-test based on visual pictures showed that the compatibility effect size was significantly different from zero, t (22) = 2.43, p<.05 (M = 485 ms). Smaller compatibility effects existed when switching the presentation mode from visual stimuli to auditory stimuli. This study serves as an important reference for the auditory reference valence effects of affective S–R compatibility.     

Probability binning comparison: a metric for quantitating multivariate distribution differences

BACKGROUND: While several algorithms for the comparison of univariate distributions arising from flow cytometric analyses have been developed and studied for many years, algorithms for comparing multivariate distributions remain elusive. Such algorithms could be useful for comparing differences between samples based on several independent measurements, rather than differences based on any single measurement. It is conceivable that distributions could be completely distinct in multivariate space, but unresolvable in any combination of univariate histograms. Multivariate comparisons could also be useful for providing feedback about instrument stability, when only subtle changes in measurements are occurring. METHODS: We apply a variant of Probability Binning, described in the accompanying article, to multidimensional data. In this approach, hyper-rectangles of n dimensions (where n is the number of measurements being compared) comprise the bins used for the chi-squared statistic. These hyper-dimensional bins are constructed such that the control sample has the same number of events in each bin; the bins are then applied to the test samples for chi-squared calculations. RESULTS: Using a Monte-Carlo simulation, we determined the distribution of chi-squared values obtained by comparing sets of events from the same distribution; this distribution of chi-squared values was identical as for the univariate algorithm. Hence, the same formulae can be used to construct a metric, analogous to a t-score, that estimates the probability with which distributions are distinct. As for univariate comparisons, this metric scales with the difference between two distributions, and can be used to rank samples according to similarity to a control. We apply the algorithm to multivariate immunophenotyping data, and demonstrate that it can be used to discriminate distinct samples and to rank samples according to a biologically-meaningful difference. CONCLUSION: Probability binning, as shown here, provides a useful metric for determining the probability with which two or more multivariate distributions represent distinct sets of data. The metric can be used to identify the similarity or dissimilarity of samples. Finally, as demonstrated in the accompanying paper, the algorithm can be used to gate on events in one sample that are different from a control sample, even if those events cannot be distinguished on the basis of any combination of univariate or bivariate displays. Published 2001 Wiley-Liss, Inc.     

Application of partial least squares discriminant analysis to two-dimensional difference gel studies in expression proteomics

Two-dimensional difference gel electrophoresis (DIGE) is a tool for measuring changes in protein expression between samples involving pre-electrophoretic labeling ith cyanine dyes. In multi-gel experiments, univariate statistical tests have been used to identify differential expression between sample types by looking for significant changes in spot volume. Multivariate statistical tests, which look for correlated changes between sample types, provide an alternate approach for identifying spots with differential expression. Partial least squares-discriminant analysis (PLS-DA), a multivariate statistical approach, was combined with an iterative threshold process to identify which protein spots had the greatest contribution to the model, and compared to univariate test for three datasets. This included one dataset where no biological difference was expected. The novel multivariate approach, detailed here, represents a method to complement the univariate approach in identification of differentially expressed protein spots. This new approach has the advantages of reduced risk of false-positives and the identification of spots that are significantly altered in terms of correlated expression rather than absolute expression values.     

A kinetic-based sigmoidal model for the polymerase chain reaction and its application to high-capacity absolute quantitative real-time PCR

Background

Based upon defining a common reference point, current real-time quantitative PCR technologies compare relative differences in amplification profile position. As such, absolute quantification requires construction of target-specific standard curves that are highly resource intensive and prone to introducing quantitative errors. Sigmoidal modeling using nonlinear regression has previously demonstrated that absolute quantification can be accomplished without standard curves; however, quantitative errors caused by distortions within the plateau phase have impeded effective implementation of this alternative approach.

Results

Recognition that amplification rate is linearly correlated to amplicon quantity led to the derivation of two sigmoid functions that allow target quantification via linear regression analysis. In addition to circumventing quantitative errors produced by plateau distortions, this approach allows the amplification efficiency within individual amplification reactions to be determined. Absolute quantification is accomplished by first converting individual fluorescence readings into target quantity expressed in fluorescence units, followed by conversion into the number of target molecules via optical calibration. Founded upon expressing reaction fluorescence in relation to amplicon DNA mass, a seminal element of this study was to implement optical calibration using lambda gDNA as a universal quantitative standard. Not only does this eliminate the need to prepare target-specific quantitative standards, it relegates establishment of quantitative scale to a single, highly defined entity. The quantitative competency of this approach was assessed by exploiting "limiting dilution assay" for absolute quantification, which provided an independent gold standard from which to verify quantitative accuracy. This yielded substantive corroborating evidence that absolute accuracies of ± 25% can be routinely achieved. Comparison with the LinReg and Miner automated qPCR data processing packages further demonstrated the superior performance of this kinetic-based methodology.

Conclusion

Called "linear regression of efficiency" or LRE, this novel kinetic approach confers the ability to conduct high-capacity absolute quantification with unprecedented quality control capabilities. The computational simplicity and recursive nature of LRE quantification also makes it amenable to software implementation, as demonstrated by a prototypic Java program that automates data analysis. This in turn introduces the prospect of conducting absolute quantification with little additional effort beyond that required for the preparation of the amplification reactions.     

A fixed-point algorithm for estimating amplification efficiency from a polymerase chain reaction dilution series

Background

The polymerase chain reaction amplifies and quantifies small amounts of DNA. It is a cyclic process, during each cycle of which each strand of template DNA is copied with probability approaching one: the amount of DNA approximately doubles and this amount can be estimated fluorimetrically each cycle, producing a set of fluorescence values hereafter referred to as the amplification curve. Commonly the biological question of relevance is one of the ratio of DNA concentrations in two samples: a ratio that is deduced by comparing the two amplification curves, usually by way of a plot of fluorescence against cycle number. Central to this analysis is measuring the extent to which one amplification curve is shifted relative to the other, a measurement often accomplished by defining a threshold or quantification cycle, C_q, for each curve: the fractional cycle number at which fluorescence reaches some threshold or at which some other criterion (maximum slope, maximum rate of change of slope) is satisfied.We propose an alternative where position is measured relative to a reference curve; position equates to the cycle shift which maximizes the correlation between the reference and the observed fluorescence sequence. A key parameter of the reference curve is obtained by fixed-point convergence.

Results

We consider the analysis of dilution series constructed for the estimation of qPCR amplification efficiency. The estimate of amplification efficiency is based on the slope of the regression line when the C_q is plotted against the logarithm of dilution. We compare the approach to three commonly used methods for determining C_q; each is applied to publicly accessible calibration data sets, and to ten from our own laboratory. As in the established literature we judge their relative merits both from the standard deviation of the slope of the calibration curve, and from the variance in C_q for replicate fluorescence curves.

Conclusions

The approach does not require modification of experimental protocols, and can be applied retrospectively to existing data. We recommend that it be added to the methodological toolkit with which laboratories interpret their real-time PCR data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0372-4) contains supplementary material, which is available to authorized users.     

A Multivariate Analysis of Genetic Constraints to Life History Evolution in a Wild Population of Red Deer

Evolutionary theory predicts that genetic constraints should be widespread, but empirical support for their existence is surprisingly rare. Commonly applied univariate and bivariate approaches to detecting genetic constraints can underestimate their prevalence, with important aspects potentially tractable only within a multivariate framework. However, multivariate genetic analyses of data from natural populations are challenging because of modest sample sizes, incomplete pedigrees, and missing data. Here we present results from a study of a comprehensive set of life history traits (juvenile survival, age at first breeding, annual fecundity, and longevity) for both males and females in a wild, pedigreed, population of red deer (Cervus elaphus). We use factor analytic modeling of the genetic variance–covariance matrix (G) to reduce the dimensionality of the problem and take a multivariate approach to estimating genetic constraints. We consider a range of metrics designed to assess the effect of G on the deflection of a predicted response to selection away from the direction of fastest adaptation and on the evolvability of the traits. We found limited support for genetic constraint through genetic covariances between traits, both within sex and between sexes. We discuss these results with respect to other recent findings and to the problems of estimating these parameters for natural populations.     

Near-Complete Genome Sequencing of Swine Vesicular Disease Virus Using the Roche GS FLX Sequencing Platform

Swine vesicular disease virus (SVDV) is an enterovirus that is both genetically and antigenically closely related to human coxsackievirus B5 within the Picornaviridae family. SVDV is the causative agent of a highly contagious (though rarely fatal) vesicular disease in pigs. We report a rapid method that is suitable for sequencing the complete protein-encoding sequences of SVDV isolates in which the RNA is relatively intact. The approach couples a single PCR amplification reaction, using only a single PCR primer set to amplify the near-complete SVDV genome, with deep-sequencing using a small fraction of the capacity of a Roche GS FLX sequencing platform. Sequences were initially verified through one of two criteria; either a match between a de novo assembly and a reference mapping, or a match between all of five different reference mappings performed against a fixed set of starting reference genomes with significant genetic distances within the same species of viruses. All reference mappings used an iterative method to avoid bias. Further verification was achieved through phylogenetic analysis against published SVDV genomes and additional Enterovirus B sequences. This approach allows high confidence in the obtained consensus sequences, as well as provides sufficiently high and evenly dispersed sequence coverage to allow future studies of intra-host variation.     

Comparison of Univariate and Multivariate Models of 13C SSNMR and XRPD Techniques for Quantification of Nimodipine Polymorphs

The focus of the present investigation was to explore the use of solid-state nuclear magnetic resonance (¹³C ssNMR) and X-ray powder diffraction (XRPD) for quantification of nimodipine polymorphs (form I and form II) crystallized in a cosolvent formulation. The cosolvent formulation composed of polyethylene glycol 400, glycerin, water, and 2.5% drug, and was stored at 5°C for the drug crystallization. The ¹³C ssNMR and XRPD data of the sample matrices containing varying percentages of nimodipine form I and form II were collected. Univariate and multivariate models were developed using the data. Least square method was used for the univariate model generation. Partial least square and principle component regressions were used for the multivariate models development. The univariate models of the ¹³C ssNMR were better than the XRPD as indicated by statistical parameters such as correlation coefficient, R², root mean square error, and standard error. On the other hand, the XRPD multivariate models were better than the ¹³C ssNMR as indicated by precision and accuracy parameters. Similar values were predicted by the univariate and multivariate models for independent samples. In conclusion, the univariate and multivariate models of ¹³C ssNMR and XRPD can be used to quantitate nimodipine polymorphs.KEY WORDS: nimodipine polymorphs, X-ray powder diffraction, solid-state nuclear magnetic resonance, univariate, multivariate     

Bivariate Genome-Wide Association Analysis of the Growth and Intake Components of Feed Efficiency

Single nucleotide polymorphisms (SNPs) associated with average daily gain (ADG) and dry matter intake (DMI), two major components of feed efficiency in cattle, were identified in a genome-wide association study (GWAS). Uni- and multi-SNP models were used to describe feed efficiency in a training data set and the results were confirmed in a validation data set. Results from the univariate and bivariate analyses of ADG and DMI, adjusted by the feedlot beef steer maintenance requirements, were compared. The bivariate uni-SNP analysis identified (P-value <0.0001) 11 SNPs, meanwhile the univariate analyses of ADG and DMI identified 8 and 9 SNPs, respectively. Among the six SNPs confirmed in the validation data set, five SNPs were mapped to KDELC2, PHOX2A, and TMEM40. Findings from the uni-SNP models were used to develop highly accurate predictive multi-SNP models in the training data set. Despite the substantially smaller size of the validation data set, the training multi-SNP models had slightly lower predictive ability when applied to the validation data set. Six Gene Ontology molecular functions related to ion transport activity were enriched (P-value <0.001) among the genes associated with the detected SNPs. The findings from this study demonstrate the complementary value of the uni- and multi-SNP models, and univariate and bivariate GWAS analyses. The identified SNPs can be used for genome-enabled improvement of feed efficiency in feedlot beef cattle, and can aid in the design of empirical studies to further confirm the associations.     

Association of birth weight and length with air temperature, sunlight, humidity and rainfall in the city of Warsaw, Poland

Several studies have shown the month of birth effect on birth weight and height of children. The mechanism of this phenomenon is not fully explained. Using data from Warsaw hospitals, the influence of four climatic factors (temperature, sunlight, humidity and rainfall) on birth outcomes was studied. The sample consisted of 10,631 neonates (5450 boys and 5181 girls) born between May 2004 and April 2005. Individual values for birth weight and length were standardised on the overall mean and standard deviation for all subjects, separately for each sex. Differences in means of Z-score birth outcomes between months, seasons and semi-annual periods of birth were assessed by one-way analysis of variance, separately for each sex. The relation between average values of four atmospheric factors and average neonatal outcomes for each month of birth was assessed by a weighted Spearman rank correlation. The results revealed significant differences in average Z-scores of neonate weight and length between months of birth for boys and girls. Significant seasonal variation in Z-scores means was only found for birth length in boys. The correlation between four atmospheric factors during pregnancy and birth length was the highest for boys and occurred in the second trimester. Second trimester of fetal growth is the period most sensitive to influences of climatic factors.