Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developedto explore patterns in high-dimensional multivariate data. The conventional versionof the algorithm involves the use of Euclidean metric in the process of adaptation ofthe model vectors, thus rendering in theory a whole methodology incompatible withnon-Euclidean geometries.In this contribution we explore the two main aspects of the problem:1. Whether the conventional approach using Euclidean metric can shed valid resultswith compositional data.2. If a modification of the conventional approach replacing vectorial sum and scalarmultiplication by the canonical operators in the simplex (i.e. perturbation andpowering) can converge to an adequate solution.Preliminary tests showed that both methodologies can be used on compositional data.However, the modified version of the algorithm performs poorer than the conventionalversion, in particular, when the data is pathological. Moreover, the conventional ap-proach converges faster to a solution, when data is \well-behaved".Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Scoring Methods for Ordinal Multidimensional Forced-Choice Items

In most psychological tests and questionnaires, a test score is obtained bytaking the sum of the item scores. In virtually all cases where the test orquestionnaire contains multidimensional forced-choice items, this traditionalscoring method is also applied. We argue that the summation of scores obtained with multidimensional forced-choice items produces uninterpretabletest scores. Therefore, we propose three alternative scoring methods: a weakand a strict rank preserving scoring method, which both allow an ordinalinterpretation of test scores; and a ratio preserving scoring method, whichallows a proportional interpretation of test scores. Each proposed scoringmethod yields an index for each respondent indicating the degree to whichthe response pattern is inconsistent. Analysis of real data showed that withrespect to rank preservation, the weak and strict rank preserving methodresulted in lower inconsistency indices than the traditional scoring method;with respect to ratio preservation, the ratio preserving scoring method resulted in lower inconsistency indices than the traditional scoring method

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observedfor each individual. A particular case of FDA is when the observed functions are densityfunctions, that are also an example of infinite dimensional compositional data. In thiswork we compare several methods for dimensionality reduction for this particular typeof data: functional principal components analysis (PCA) with or without a previousdata transformation and multidimensional scaling (MDS) for diferent inter-densitiesdistances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (householdsincome distributions)

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different startingpoint. Chemical compositional data, as used in provenance studies on archaeologicalmaterials, will be approached from the measurement theory. The results will show, in avery intuitive way that chemical data can only be treated by using the approachdeveloped for compositional data. It will be shown that compositional data analysis is aparticular case in projective geometry, when the projective coordinates are in thepositive orthant, and they have the properties of logarithmic interval metrics. Moreover,it will be shown that this approach can be extended to a very large number ofapplications, including shape analysis. This will be exemplified with a case study inarchitecture of Early Christian churches dated back to the 5th-7th centuries AD

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) ofdifferent vertebrates using the Compositional Data Analysis (CDA) methodologicalapproach it’s presented.355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda,Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) wereanalyzed with CDA.A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinsondistance has been used as a measure of disparity in limb elements proportions to infersome aspects of functional morphology

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr)transformation to obtain the random vector y of dimension D. The factor model istheny = Λf + e (1)with the factors f of dimension k & D, the error term e, and the loadings matrix Λ.Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon a full-rank data matrix Y which is not the case for clr transformed data (see,e.g., Aitchison, 1986).The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Rac2 GTPase activation by angiotensin II is modulated by Ca2C/calcineurin and mitogen-activated protein kinases in human neutrophils

Angiotensin II (Ang II) highly stimulates superoxide anion production by neutrophils. The G-protein Rac2 modulates the activity of NADPH oxidase in response to various stimuli. Here, we describe that Ang II induced both Rac2 translocation from the cytosol to the plasma membrane and Rac2 GTP-binding activity. Furthermore, Clostridium difficile toxin A, an inhibitor of the Rho-GTPases family Rho, Rac and Cdc42, prevented Ang II-elicited O2-/ROS production, phosphorylation of the mitogen-activated protein kinases (MAPKs) p38, extracellular signal-regulated kinase 1/2 (ERK1/2) and c-Jun N-terminal kinase 1/2, and Rac2 activation. Rac2 GTPase inhibition by C. difficile toxin A was accompanied by a robust reduction of the cytosolic Ca(2)(+) elevation induced by Ang II in human neutrophils. Furthermore, SB203580 and PD098059 act as inhibitors of p38MAPK and ERK1/2 respectively, wortmannin, an inhibitor of phosphatidylinositol-3-kinase, and cyclosporin A, a calcineurin inhibitor, hindered both translocation of Rac2 from the cytosol to the plasma membrane and enhancement of Rac2 GTP-binding elicited by Ang II. These results provide evidence that the activation of Rac2 by Ang II is exerted through multiple signalling pathways, involving Ca(2)(+)/calcineurin and protein kinases, the elucidation of which should be insightful in the design of new therapies aimed at reversing the inflammation of vessel walls found in a number of cardiovascular diseases.

Comportamiento del orificio de implantación del catéter en pacientes en diálisis peritoneal en relación a los cuidados

Infections of the catheter wound in peritoneal dialysis are the most frequent cause of morbility in patients who undergo this technique. There are a number of procedures for the care of the wound and it is not easy to define a single method that will guarantee good condition of the wound. In order to evaluate the behaviour of the wound related to the procedure used in their care, we studied 306 patients over 24 months, compiling socio-demographic and clinical variables. We found a high incidence of infections caused by gram-positive skin and mucous germs, with a strong correlation with the fact that the patient/family carer is a nasal carrier of staphylococcus aureus and that they appear more frequently in patients who do not remove the wound dressing in the shower. We also detected an increase in pseudomonas infections when the patient does not dry the wound with a hair-dryer

Giant proliferating trichilemmal malignant tumor

Proliferating trichilemmal cyst is a benign tumor that originates in the outer root sheath of hair follicle. Usually, it is located on the scalp in older women, but also have been reported in other sites such as back, chest, axilla, groin, gluteal region, thigh, vulva, and face. Malignant transformation of proliferating trichilemmal cyst is confirmed only on histological findings. This tumor has a variable biologic behavior with local recurrence and lymph node metastasis.

Influence of HLA DRB1 alleles in the susceptibility of rheumatoid arthritis and the regulation of antibodies against citrullinated proteins and rheumatoid factor.

INTRODUCTION The purpose of this study was to investigate the association between HLA-DRB1 alleles with susceptibility to rheumatoid arthritis (RA) and production of antibodies against citrullinated proteins (ACPA) and rheumatoid factor (RF). METHODS We studied 408 patients (235 with RA, 173 non-RA) and 269 controls. ACPA, RF and HLA-DR typing were determined. RESULTS We found an increased frequency of HLA DRB1 alleles with the shared epitope (SE) in ACPA-positive RA. Inversely, HLA DRB1 alleles encoding DERAA sequences were more frequent in controls than in ACPA-positive RA, and a similar trend was found for HLA DR3. However, these results could not be confirmed after stratification for the presence of the SE, probably due to the relatively low number of patients. These data may suggest that the presence of these alleles may confer a protective role for ACPA-positive RA. In RA patients we observed association between SE alleles and ACPA titers in a dose-dependent effect. The presence of HLA DR3 or DERAA-encoding alleles was associated with markedly reduced ACPA levels. No association between RF titers and HLA DR3 or DERAA-encoding alleles was found. CONCLUSIONS HLA DRB1 alleles with the SE are associated with production of ACPA. DERAA-encoding HLA-DR alleles and HLA DR3 may be protective for ACPA-positive RA.

CD40: Novel Association with Crohn's Disease and Replication in Multiple Sclerosis Susceptibility

Background: A functional polymorphism located at 21 from the start codon of the CD40 gene, rs1883832, was previously reported to disrupt a Kozak sequence essential for translation. It has been consistently associated with Graves’ disease risk in populations of different ethnicity and genetic proxies of this variant evaluated in genome-wide association studies have shown evidence of an effect in rheumatoid arthritis and multiple sclerosis (MS) susceptibility. However, the protective allele associated with Graves’ disease or rheumatoid arthritis has shown a risk role in MS, an effect that we aimed to replicate in the present work. We hypothesized that this functional polymorphism might also show an association with other complex autoimmune condition such as inflammatory bowel disease, given the CD40 overexpression previously observed in Crohn’s disease (CD) lesions. Methodology: Genotyping of rs1883832C.T was performed in 1564 MS, 1102 CD and 969 ulcerative colitis (UC) Spanish patients and in 2948 ethnically matched controls by TaqMan chemistry. Principal Findings: The observed effect of the minor allele rs1883832T was replicated in our independent Spanish MS cohort [p= 0.025; OR (95% CI)= 1.12 (1.01–1.23)]. The frequency of the minor allele was also significantly higher in CD patients than in controls [p= 0.002; OR (95% CI)= 1.19 (1.06–1.33)]. This increased predisposition was not detected in UC patients [p= 0.5; OR (95% CI)= 1.04 (0.93–1.17)]. Conclusion: The impact of CD40 rs1883832 on MS and CD risk points to a common signaling shared by these autoimmune conditions

The value of metabolic imaging to predict tumour response after chemoradiation in locally advanced rectal cancer

Background: We aim to investigate the possibility of using 18F-positron emission tomography/computer tomography (PET-CT) to predict the histopathologic response in locally advanced rectal cancer (LARC) treated with preoperative chemoradiation (CRT). Methods: The study included 50 patients with LARC treated with preoperative CRT. All patients were evaluated by PET-CT before and after CRT, and results were compared to histopathologic response quantified by tumour regression grade (patients with TRG 1-2 being defined as responders and patients with grade 3-5 as non-responders). Furthermore, the predictive value of metabolic imaging for pathologic complete response (ypCR) was investigated. Results: Responders and non-responders showed statistically significant differences according to Mandard's criteria for maximum standardized uptake value (SUVmax) before and after CRT with a specificity of 76,6% and a positive predictive value of 66,7%. Furthermore, SUVmax values after CRT were able to differentiate patients with ypCR with a sensitivity of 63% and a specificity of 74,4% (positive predictive value 41,2% and negative predictive value 87,9%); This rather low sensitivity and specificity determined that PET-CT was only able to distinguish 7 cases of ypCR from a total of 11 patients. Conclusions: We conclude that 18-F PET-CT performed five to seven weeks after the end of CRT can visualise functional tumour response in LARC. In contrast, metabolic imaging with 18-F PET-CT is not able to predict patients with ypCR accurately

Psychometric characteristics of the Spanish version of instruments to measure neck pain disability

BACKGROUND. The NDI, COM and NPQ are evaluation instruments for disability due to NP. There was no Spanish version of NDI or COM for which psychometric characteristics were known. The objectives of this study were to translate and culturally adapt the Spanish version of the Neck Disability Index Questionnaire (NDI), and the Core Outcome Measure (COM), to validate its use in Spanish speaking patients with non-specific neck pain (NP), and to compare their psychometric characteristics with those of the Spanish version of the Northwick Pain Questionnaire (NPQ). METHODS. Translation/re-translation of the English versions of the NDI and the COM was done blindly and independently by a multidisciplinary team. The study was done in 9 primary care Centers and 12 specialty services from 9 regions in Spain, with 221 acute, subacute and chronic patients who visited their physician for NP: 54 in the pilot phase and 167 in the validation phase. Neck pain (VAS), referred pain (VAS), disability (NDI, COM and NPQ), catastrophizing (CSQ) and quality of life (SF-12) were measured on their first visit and 14 days later. Patients' self-assessment was used as the external criterion for pain and disability. In the pilot phase, patients' understanding of each item in the NDI and COM was assessed, and on day 1 test-retest reliability was estimated by giving a second NDI and COM in which the name of the questionnaires and the order of the items had been changed. RESULTS. Comprehensibility of NDI and COM were good. Minutes needed to fill out the questionnaires [median, (P25, P75)]: NDI. 4 (2.2, 10.0), COM: 2.1 (1.0, 4.9). Reliability: [ICC, (95%CI)]: NDI: 0.88 (0.80, 0.93). COM: 0.85 (0.75,0.91). Sensitivity to change: Effect size for patients having worsened, not changed and improved between days 1 and 15, according to the external criterion for disability: NDI: -0.24, 0.15, 0.66; NPQ: -0.14, 0.06, 0.67; COM: 0.05, 0.19, 0.92. Validity: Results of NDI, NPQ and COM were consistent with the external criterion for disability, whereas only those from NDI were consistent with the one for pain. Correlations with VAS, CSQ and SF-12 were similar for NDI and NPQ (absolute values between 0.36 and 0.50 on day 1, between 0.38 and 0.70 on day 15), and slightly lower for COM (between 0.36 and 0.48 on day 1, and between 0.33 and 0.61 on day 15). Correlation between NDI and NPQ: r = 0.84 on day 1, r = 0.91 on day 15. Correlation between COM and NPQ: r = 0.63 on day 1, r = 0.71 on day 15. CONCLUSION. Although most psychometric characteristics of NDI, NPQ and COM are similar, those from the latter one are worse and its use may lead to patients' evolution seeming more positive than it actually is. NDI seems to be the best instrument for measuring NP-related disability, since its results are the most consistent with patient's assessment of their own clinical status and evolution. It takes two more minutes to answer the NDI than to answer the COM, but it can be reliably filled out by the patient without assistance. TRIAL REGISTRATION Clinical Trials Register NCT00349544.