Compositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trials

Compositional random vectors are fundamental tools in the Bayesian analysis of categorical data.Many of the issues that are discussed with reference to the statistical analysis of compositionaldata have a natural counterpart in the construction of a Bayesian statistical model for categoricaldata.This note builds on the idea of cross-fertilization of the two areas recommended by Aitchison (1986)in his seminal book on compositional data. Particular emphasis is put on the problem of whatparameterization to use

Correspondence analysis of raw data

Correspondence analysis has found extensive use in ecology, archeology, linguisticsand the social sciences as a method for visualizing the patterns of association in a table offrequencies or nonnegative ratio-scale data. Inherent to the method is the expression of the datain each row or each column relative to their respective totals, and it is these sets of relativevalues (called profiles) that are visualized. This relativization of the data makes perfect sensewhen the margins of the table represent samples from sub-populations of inherently differentsizes. But in some ecological applications sampling is performed on equal areas or equalvolumes so that the absolute levels of the observed occurrences may be of relevance, in whichcase relativization may not be required. In this paper we define the correspondence analysis ofthe raw unrelativized data and discuss its properties, comparing this new method to regularcorrespondence analysis and to a related variant of non-symmetric correspondence analysis.

What trees tell us: dendrochronological and statistical analysis of the data

Trees are a great bank of data, named sometimes for this reason as the "silentwitnesses" of the past. Due to annual formation of rings, which is normally influenced directly by of climate parameters (generally changes in temperature and moisture or precipitation) and other environmental factors; these changes, occurred in the past, are"written" in the tree "archives" and can be "decoded" in order to interpret what hadhappened before, mainly applied for the past climate reconstruction.Using dendrochronological methods for obtaining samples of Pinus nigra fromthe Catalonian PrePirineous region, the cores of 15 trees with total time spine of about 100 - 250 years were analyzed for the tree ring width (TRW) patterns and had quite high correlation between them (0.71 ¿ 0.84), corresponding to a common behaviour for the environmental changes in their annual growth.After different trials with raw TRW data for standardization in order to take outthe negative exponential growth curve dependency, the best method of doubledetrending (power transformation and smoothing line of 32 years) were selected for obtaining the indexes for further analysis.Analyzing the cross-correlations between obtained tree ring width indexes andclimate data, significant correlations (p<0.05) were observed in some lags, as forexample, annual precipitation in lag -1 (previous year) had negative correlation with TRW growth in the Pallars region. Significant correlation coefficients are between 0.27- 0.51 (with positive or negative signs) for many cases; as for recent (but very short period) climate data of Seu d¿Urgell meteorological station, some significant correlation coefficients were observed, of the order of 0.9.These results confirm the hypothesis of using dendrochronological data as aclimate signal for further analysis, such as reconstruction of climate in the past orprediction in the future for the same locality.

Dual activation of pathways regulated by steroid receptors and peptide growth factors in primary prostate cancer revealed by Factor Analysis of microarray data

Background: We use an approach based on Factor Analysis to analyze datasets generated for transcriptional profiling. The method groups samples into biologically relevant categories, and enables the identification of genes and pathways most significantly associated to each phenotypic group, while allowing for the participation of a given gene in more than one cluster. Genes assigned to each cluster are used for the detection of pathways predominantly activated in that cluster by finding statistically significant associated GO terms. We tested the approach with a published dataset of microarray experiments in yeast. Upon validation with the yeast dataset, we applied the technique to a prostate cancer dataset. Results: Two major pathways are shown to be activated in organ-confined, non-metastatic prostate cancer: those regulated by the androgen receptor and by receptor tyrosine kinases. A number of gene markers (HER3, IQGAP2 and POR1) highlighted by the software and related to the later pathway have been validated experimentally a posteriori on independent samples. Conclusion: Using a new microarray analysis tool followed by a posteriori experimental validation of the results, we have confirmed several putative markers of malignancy associated with peptide growth factor signalling in prostate cancer and revealed others, most notably ERRB3 (HER3). Our study suggest that, in primary prostate cancer, HER3, together or not with HER4, rather than in receptor complexes involving HER2, could play an important role in the biology of these tumors. These results provide new evidence for the role of receptor tyrosine kinases in the establishment and progression of prostate cancer.

Study of tergal glands morphogenesis through an integrative analysis of genomic data

About 50% of living species are holometabolan insects. Therefore, unraveling the ori- gin of insect metamorphosis from the hemimetabolan (gradual metamorphosis) to the holometabolan (sudden metamorphosis at the end of the life cycle) mode is equivalent to explaining how all this biodiversity originated. One of the problems with studying the evolution from hemimetaboly to holometaboly is that most information is available only in holometabolan species. Within the hemimetabolan group, our model, the cock- roach Blattella germanica, is the most studied species. However, given that the study of adult morphogenesis at organismic level is still complex, we focused on the study of the tergal gland (TG) as a minimal model of metamorphosis. The TG is formed in tergites 7 and 8 (T7-8) in the last days of the last nymphal instar (nymph 6). The comparative study of four T7-T8 transcriptomes provided us with crucial keys of TG formation, but also essential information about the mechanisms and circuitry that allows the shift from nymphal to adult morphogenesis.

Regression analysis of compositional data when both the dependent variable and independent variable are components

It is well known that regression analyses involving compositional data need special attention because the data are not of full rank. For a regression analysis where both the dependent and independent variable are components we propose a transformation of the components emphasizing their role as dependent and independent variables. A simple linear regression can be performed on the transformed components. The regression line can be depicted in a ternary diagram facilitating the interpretation of the analysis in terms of components. An exemple with time-budgets illustrates the method and the graphical features

Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last twodecades have made possible a much deeper exploration of the nature of variability,and the possible processes associated with compositional data sets from manydisciplines. In this paper we concentrate on geochemical data sets. First we explainhow hypotheses of compositional variability may be formulated within the naturalsample space, the unit simplex, including useful hypotheses of subcompositionaldiscrimination and specific perturbational change. Then we develop through standardmethodology, such as generalised likelihood ratio tests, statistical tools to allow thesystematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require specialconstruction. We comment on the use of graphical methods in compositional dataanalysis and on the ordination of specimens. The recent development of the conceptof compositional processes is then explained together with the necessary tools for astaying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland.Finally we point out a number of unresolved problems in the statistical analysis ofcompositional processes

CoDaPack. An Excel and Visual Basic based software of compositional data analysis. Current version and discussion form upcoming versions

In the eighties, John Aitchison (1986) developed a new methodological approach for the statistical analysis of compositional data. This new methodology was implemented in Basic routines grouped under the name CODA and later NEWCODA inMatlab (Aitchison, 1997). After that, several other authors have published extensions to this methodology: Marín-Fernández and others (2000), Barceló-Vidal and others (2001), Pawlowsky-Glahn and Egozcue (2001, 2002) and Egozcue and others (2003). (...)

The Spanish cadet in the European military context a comparative analysis of the professional socialisation

Research on the attitudes, motivations and social and political behavior of European cadets have been made throughout the last decade. Nowadays Spain also joins those surveys. Thru the analysis of polling data, we can consider the different attitudes of Spanish cadets in relation with the other European ones. The conclusion is that although the Spanish political transition to democracy has not ended already in the military teaching system, there are a lot of similarities among Spanish and European cadets.

Assessing the Precision of Compositional Data in a Stratified Double Stage Cluster Sample: Application to the Swiss Earnings Structure Survey

Precision of released figures is not only an important quality feature of official statistics,it is also essential for a good understanding of the data. In this paper we show a casestudy of how precision could be conveyed if the multivariate nature of data has to betaken into account. In the official release of the Swiss earnings structure survey, the totalsalary is broken down into several wage components. We follow Aitchison's approachfor the analysis of compositional data, which is based on logratios of components. Wefirst present diferent multivariate analyses of the compositional data whereby the wagecomponents are broken down by economic activity classes. Then we propose a numberof ways to assess precision

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

Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.

Univariate versus multivariate modeling of panel data

Panel data can be arranged into a matrix in two ways, called 'long' and 'wide' formats (LFand WF). The two formats suggest two alternative model approaches for analyzing paneldata: (i) univariate regression with varying intercept; and (ii) multivariate regression withlatent variables (a particular case of structural equation model, SEM). The present papercompares the two approaches showing in which circumstances they yield equivalent?insome cases, even numerically equal?results. We show that the univariate approach givesresults equivalent to the multivariate approach when restrictions of time invariance (inthe paper, the TI assumption) are imposed on the parameters of the multivariate model.It is shown that the restrictions implicit in the univariate approach can be assessed bychi-square difference testing of two nested multivariate models. In addition, commontests encountered in the econometric analysis of panel data, such as the Hausman test, areshown to have an equivalent representation as chi-square difference tests. Commonalitiesand differences between the univariate and multivariate approaches are illustrated usingan empirical panel data set of firms' profitability as well as a simulated panel data.

Analysis of the mitochondrial DNA of Schizophrenia patients by next generation sequencing

Mitochondrial DNA (mtDNA), a maternally inherited 16.6-Kb molecule crucial for energy production, is implicated in numerous human traits and disorders. It has been hypothesized that the presence of mutations in the mtDNA may contribute to the complex genetic basis of schizophreniadisease, due to the evidence of maternal inheritance and the presence of schizophrenia symptoms in patients affected of a mitochondrial disorder related to a mtDNA mutation. The present project aims to study the association of variants of mitochondrial DNA (mtDNA), and an increased risk of schizophrenia in a cohort of patients and controls from the same population. The entire mtDNA of 55 schizophrenia patients with an apparent maternal transmission of the disease and 38 controls was sequenced by Next Generation Sequencing (Ion Torrent PGM, Life Technologies) and compared to the reference sequence. The current method for establishing mtDNA haplotypes is Sanger sequencing, which is laborious, timeconsuming, and expensive. With the emergence of Next Generation Sequencing technologies, this sequencing process can be much more quickly and cost-efficiently. We have identified 14 variants that have not been previously reported. Two of them were missense variants: MTATP6 p.V113M and MTND5 p.F334L ,and also three variants encoding rRNA and one variant encoding tRNA. Not significant differences have been found in the number of variants between the two groups. We found that the sequence alignment algorithm employed to align NGS reads played a significant role in the analysis of the data and the resulting mtDNA haplotypes. Further development of the bioinformatics analysis and annotation step would be desirable to facilitate the application of NGS in mtDNA analysis.