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.

Early and late skin reactions to radiotherapy for breast cancer and their correlation with radiation-induced DNA damage in lymphocytes

INTRODUCTION Radiotherapy outcomes might be further improved by a greater understanding of the individual variations in normal tissue reactions that determine tolerance. Most published studies on radiation toxicity have been performed retrospectively. Our prospective study was launched in 1996 to measure the in vitro radiosensitivity of peripheral blood lymphocytes before treatment with radical radiotherapy in patients with breast cancer, and to assess the early and the late radiation skin side effects in the same group of patients. We prospectively recruited consecutive breast cancer patients receiving radiation therapy after breast surgery. To evaluate whether early and late side effects of radiotherapy can be predicted by the assay, a study was conducted of the association between the results of in vitro radiosensitivity tests and acute and late adverse radiation effects. METHODS Intrinsic molecular radiosensitivity was measured by using an initial radiation-induced DNA damage assay on lymphocytes obtained from breast cancer patients before radiotherapy. Acute reactions were assessed in 108 of these patients on the last treatment day. Late morbidity was assessed after 7 years of follow-up in some of these patients. The Radiation Therapy Oncology Group (RTOG) morbidity score system was used for both assessments. RESULTS Radiosensitivity values obtained using the in vitro test showed no relation with the acute or late adverse skin reactions observed. There was no evidence of a relation between acute and late normal tissue reactions assessed in the same patients. A positive relation was found between the treatment volume and both early and late side effects. CONCLUSION After radiation treatment, a number of cells containing major changes can have a long survival and disappear very slowly, becoming a chronic focus of immunological system stimulation. This stimulation can produce, in a stochastic manner, late radiation-related adverse effects of varying severity. Further research is warranted to identify the major determinants of normal tissue radiation response to make it possible to individualize treatments and improve the outcome of radiotherapy in cancer patients.

Differential cognitive impairment for diverse forms of multiple sclerosis.

BACKGROUND Cognitive impairment is a common feature in multiple sclerosis (MS) patients and occurs in 60% of all cases. Unfortunately, neurological examination does not always agree with the neuropsychological evaluation in determining the cognitive profile of the patient. On the other hand, psychophysiological techniques such as event-related potentials (ERPs) can help in evaluating cognitive impairment in different pathologies. Behavioural responses and EEG signals were recorded during the experiment in three experimental groups: 1) a relapsing-remitting group (RRMS), 2) a benign multiple sclerosis group (BMS) and 3) a Control group. The paradigm employed was a spatial attention task with central cues (Posner experiment). The main aim was to observe the differences in the performance (behavioural variables) and in the latency and amplitude of the ERP components among these groups. RESULTS Our data indicate that both MS groups showed poorer task performance (longer reaction times and lower percentage of correct responses), a latency delay for the N1 and P300 component, and a different amplitude for the frontal N1. Moreover, the deficit in the BMS group, indexed by behavioural and pyschophysiological variables, was more pronounced compared to the RRMS group. CONCLUSION The present results suggest a cognitive impairment in the information processing in all of these patients. Comparing both pathological groups, cognitive impairment was more accentuated in the BMS group compared to the RMSS group. This suggests a silent deterioration of cognitive skills for the BMS that is not usually treated with pharmacological or neuropsychological therapy.

Combined low initial DNA damage and high radiation-induced apoptosis confers clinical resistance to long-term toxicity in breast cancer patients treated with high-dose radiotherapy

BACKGROUND. Either higher levels of initial DNA damage or lower levels of radiation-induced apoptosis in peripheral blood lymphocytes have been associated to increased risk for develop late radiation-induced toxicity. It has been recently published that these two predictive tests are inversely related. The aim of the present study was to investigate the combined role of both tests in relation to clinical radiation-induced toxicity in a set of breast cancer patients treated with high dose hyperfractionated radical radiotherapy. METHODS. Peripheral blood lymphocytes were taken from 26 consecutive patients with locally advanced breast carcinoma treated with high-dose hyperfractioned radical radiotherapy. Acute and late cutaneous and subcutaneous toxicity was evaluated using the Radiation Therapy Oncology Group morbidity scoring schema. The mean follow-up of survivors (n = 13) was 197.23 months. Radiosensitivity of lymphocytes was quantified as the initial number of DNA double-strand breaks induced per Gy and per DNA unit (200 Mbp). Radiation-induced apoptosis (RIA) at 1, 2 and 8 Gy was measured by flow cytometry using annexin V/propidium iodide. RESULTS. Mean DSB/Gy/DNA unit obtained was 1.70 ± 0.83 (range 0.63-4.08; median, 1.46). Radiation-induced apoptosis increased with radiation dose (median 12.36, 17.79 and 24.83 for 1, 2, and 8 Gy respectively). We observed that those "expected resistant patients" (DSB values lower than 1.78 DSB/Gy per 200 Mbp and RIA values over 9.58, 14.40 or 24.83 for 1, 2 and 8 Gy respectively) were at low risk of suffer severe subcutaneous late toxicity (HR 0.223, 95%CI 0.073-0.678, P = 0.008; HR 0.206, 95%CI 0.063-0.677, P = 0.009; HR 0.239, 95%CI 0.062-0.929, P = 0.039, for RIA at 1, 2 and 8 Gy respectively) in multivariate analysis. CONCLUSIONS. A radiation-resistant profile is proposed, where those patients who presented lower levels of initial DNA damage and higher levels of radiation induced apoptosis were at low risk of suffer severe subcutaneous late toxicity after clinical treatment at high radiation doses in our series. However, due to the small sample size, other prospective studies with higher number of patients are needed to validate these results.

Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation

Discrete and continuous compositions

This paper examines a dataset which is modeled well by thePoisson-Log Normal process and by this process mixed with LogNormal data, which are both turned into compositions. Thisgenerates compositional data that has zeros without any need forconditional models or assuming that there is missing or censoreddata that needs adjustment. It also enables us to model dependenceon covariates and within the composition

CODAPACK3D. A new version of Compositional Data Package

The statistical analysis of compositional data should be treated using logratios of parts,which are difficult to use correctly in standard statistical packages. For this reason afreeware package, named CoDaPack was created. This software implements most of thebasic statistical methods suitable for compositional data.In this paper we describe the new version of the package that now is calledCoDaPack3D. It is developed in Visual Basic for applications (associated with Excel©),Visual Basic and Open GL, and it is oriented towards users with a minimum knowledgeof computers with the aim at being simple and easy to use.This new version includes new graphical output in 2D and 3D. These outputs could bezoomed and, in 3D, rotated. Also a customization menu is included and outputs couldbe saved in jpeg format. Also this new version includes an interactive help and alldialog windows have been improved in order to facilitate its use.To use CoDaPack one has to access Excel© and introduce the data in a standardspreadsheet. These should be organized as a matrix where Excel© rows correspond tothe observations and columns to the parts. The user executes macros that returnnumerical or graphical results. There are two kinds of numerical results: new variablesand descriptive statistics, and both appear on the same sheet. Graphical output appearsin independent windows. In the present version there are 8 menus, with a total of 38submenus which, after some dialogue, directly call the corresponding macro. Thedialogues ask the user to input variables and further parameters needed, as well aswhere to put these results. The web site http://ima.udg.es/CoDaPack contains thisfreeware package and only Microsoft Excel© under Microsoft Windows© is required torun the software.Kew words: Compositional data Analysis, Software

News from compositions, the R package

The R-package “compositions”is a tool for advanced compositional analysis. Its basicfunctionality has seen some conceptual improvement, containing now some facilitiesto work with and represent ilr bases built from balances, and an elaborated subsys-tem for dealing with several kinds of irregular data: (rounded or structural) zeroes,incomplete observations and outliers. The general approach to these irregularities isbased on subcompositions: for an irregular datum, one can distinguish a “regular” sub-composition (where all parts are actually observed and the datum behaves typically)and a “problematic” subcomposition (with those unobserved, zero or rounded parts, orelse where the datum shows an erratic or atypical behaviour). Systematic classificationschemes are proposed for both outliers and missing values (including zeros) focusing onthe nature of irregularities in the datum subcomposition(s).To compute statistics with values missing at random and structural zeros, a projectionapproach is implemented: a given datum contributes to the estimation of the desiredparameters only on the subcompositon where it was observed. For data sets withvalues below the detection limit, two different approaches are provided: the well-knownimputation technique, and also the projection approach.To compute statistics in the presence of outliers, robust statistics are adapted to thecharacteristics of compositional data, based on the minimum covariance determinantapproach. The outlier classification is based on four different models of outlier occur-rence and Monte-Carlo-based tests for their characterization. Furthermore the packageprovides special plots helping to understand the nature of outliers in the dataset.Keywords: coda-dendrogram, lost values, MAR, missing data, MCD estimator,robustness, rounded zeros

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed atdifferent points in time. Inherently, then, a compositional time series is a multivariatetime series with important constraints on the variables observed at any instance in time.Although this type of data frequently occurs in situations of real practical interest, atrawl through the statistical literature reveals that research in the field is very much in itsinfancy and that many theoretical and empirical issues still remain to be addressed. Anyappropriate statistical methodology for the analysis of compositional time series musttake into account the constraints which are not allowed for by the usual statisticaltechniques available for analysing multivariate time series. One general approach toanalyzing compositional time series consists in the application of an initial transform tobreak the positive and unit sum constraints, followed by the analysis of the transformedtime series using multivariate ARIMA models. In this paper we discuss the use of theadditive log-ratio, centred log-ratio and isometric log-ratio transforms. We also presentresults from an empirical study designed to explore how the selection of the initialtransform affects subsequent multivariate ARIMA modelling as well as the quality ofthe forecasts

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

A unified approach for representing rows and columns in contingency tables

By using suitable parameters, we present a uni¯ed aproach for describing four methods for representing categorical data in a contingency table. These methods include:correspondence analysis (CA), the alternative approach using Hellinger distance (HD),the log-ratio (LR) alternative, which is appropriate for compositional data, and theso-called non-symmetrical correspondence analysis (NSCA). We then make an appropriate comparison among these four methods and some illustrative examples are given.Some approaches based on cumulative frequencies are also linked and studied usingmatrices.Key words: Correspondence analysis, Hellinger distance, Non-symmetrical correspondence analysis, log-ratio analysis, Taguchi inertia

Methylation alterations are not a major cause of PTTG1 misregulation.

BACKGROUND On its physiological cellular context, PTTG1 controls sister chromatid segregation during mitosis. Within its crosstalk to the cellular arrest machinery, relies a checkpoint of integrity for which gained the over name of securin. PTTG1 was found to promote malignant transformation in 3T3 fibroblasts, and further found to be overexpressed in different tumor types. More recently, PTTG1 has been also related to different processes such as DNA repair and found to trans-activate different cellular pathways involving c-myc, bax or p53, among others. PTTG1 over-expression has been correlated to a worse prognosis in thyroid, lung, colorectal cancer patients, and it can not be excluded that this effect may also occur in other tumor types. Despite the clinical relevance and the increasing molecular characterization of PTTG1, the reason for its up-regulation remains unclear. METHOD We analysed PTTG1 differential expression in PC-3, DU-145 and LNCaP tumor cell lines, cultured in the presence of the methyl-transferase inhibitor 5-Aza-2'-deoxycytidine. We also tested whether the CpG island mapping PTTG1 proximal promoter evidenced a differential methylation pattern in differentiated thyroid cancer biopsies concordant to their PTTG1 immunohistochemistry status. Finally, we performed whole-genome LOH studies using Affymetix 50 K microarray technology and FRET analysis to search for allelic imbalances comprising the PTTG1 locus. CONCLUSION Our data suggest that neither methylation alterations nor LOH are involved in PTTG1 over-expression. These data, together with those previously reported, point towards a post-transcriptional level of misregulation associated to PTTG1 over-expression.

Intrinsic test of independence in contingency tables

A condition needed for testing nested hypotheses from a Bayesianviewpoint is that the prior for the alternative model concentratesmass around the small, or null, model. For testing independencein contingency tables, the intrinsic priors satisfy this requirement.Further, the degree of concentration of the priors is controlled bya discrete parameter m, the training sample size, which plays animportant role in the resulting answer regardless of the samplesize.In this paper we study robustness of the tests of independencein contingency tables with respect to the intrinsic priors withdifferent degree of concentration around the null, and comparewith other “robust” results by Good and Crook. Consistency ofthe intrinsic Bayesian tests is established.We also discuss conditioning issues and sampling schemes,and argue that conditioning should be on either one margin orthe table total, but not on both margins.Examples using real are simulated data are given