Amplification efficiency: linking baseline and bias in the analysis of quantitative PCR data.

Despite the central role of quantitative PCR (qPCR) in the quantification of mRNA transcripts, most analyses of qPCR data are still delegated to the software that comes with the qPCR apparatus. This is especially true for the handling of the fluorescence baseline. This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as 'fold-difference' results. Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value. An algorithm that estimates the baseline by reconstructing the log-linear phase downward from the early plateau phase of the PCR reaction was developed and shown to lead to very reproducible PCR efficiency values. PCR efficiency values were determined per sample by fitting a regression line to a subset of data points in the log-linear phase. The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample.

Obesity markers and blood pressure in a sample of Portuguese children and adolescents.

Little information exists regarding the effect of several obesity markers on blood pressure (BP) levels in youth. Transverse study including 2494 boys and 2589 girls. Height, weight and waist were measured according to the international criteria and body fat (BF) by bioimpedance. BP was measured by an automated device. Hypertension was defined using sex-specific, age-specific and height-specific observation-points. Body mass index (BMI) and waist were positively related with systolic blood pressure (SBP) and diastolic blood pressure (DBP) and heart rate in both sexes, whereas the relationships with BF were less consistent. Stepwise linear regression analysis showed that BMI was positively related with SBP and DBP in both sexes, whereas BF was negatively related with SBP in both sexes and with heart rate in boys only; finally, waist was positively related with SBP in boys and heart rate in girls. Age and heart rate-adjusted values of SBP and DBP increased with BMI: for SBP, 117+/-1, 123+/-1 and 124+/-1 mmHg in normal, overweight and obese boys, respectively; corresponding values for girls were 111+/-1, 114+/-1 and 116+/-2 mmHg (mean+/-SE, P<0.001). Overweight and obese boys had an odds ratio for being hypertensive of 2.26 (95% confidence interval: 1.79-2.86) and 3.36 (2.32-4.87), respectively; corresponding values for girls were 1.58 (confidence interval 1.25-1.99) and 2.31 (1.53-3.50). BMI, not BF or waist, is consistently and independently related to BP levels in children; overweight and obesity considerably increase the risk of hypertension.

Attachment among Adoptive Families: Two Emipirical Studies in an International Context

The present dissertation analyzed the construct of attachment at different time points, specifically focusing on two phases of adoptive family life that have so far received little attention from investigators. Study 1 focused on the first months of adoption, and analyzed the development of the attachment relationship to new caregivers. The sample was composed of a small but homogeneous group (n=6) of Korean-born children, adopted by Italian parents. The Parent Attachment Diary (Dozier & Stovall, 1997) was utilized to assess the child's attachment behavior. We assessed these behavior for the first 3 months after placement into adoption. Results showed a double variability of attachment behavior: within subjects during the 3-months, and between subjects, with just half of the children developing a stable pattern of attachment. In order to test the growth trajectories of attachment behavior, Hierarchical Linear Models (Bryk & Raudenbush, 1992) were also applied, but no significant population trend was identified. Study 2 analyzed attachment among adoptees during the sensitive period of adolescence. Data was derived from an international collection (n= 104, from Belgium Italy, and Romania) of semi-structured clinical interviews (with adolescents and with their adoptive parents), as well as from questionnaires. The purpose of this study was to detect the role played by risk and protective factors on the adoptee's behavioral and socio-emotional outcomes. In addition, we tested the possible interactions between the different attachment representations within the adoptive family. Results showed that pre-adoptive risk predicted the adolescent's adjustment; however, parental representations constituted an important moderator of this relationship. Moreover, the adolescent's security of attachment partially mediated the relationship between age at placement and later behavioral problems. In conclusion, the two present attachment studies highlighted the notable rate of change of attachment behavior over time, which showed its underlying plasticity, and thus the possible reparatory value of the adoption practice. Since parents have been proven to play an important role, especially in adolescence, the post-adoption support acquires even more importance in order to help parents promoting a positive and stable relational environment over time. - L'objectif de cette thèse est de décrire la formation des relations d'attachement chez les enfants et les adolescents adoptés, lors de deux phases particulières de la vie de la famille adoptive, qui ont été relativement peu étudiées. L'Étude 1 analyse les premiers mois après l'adoption, avec le but de comprendre si, et comment, une relation d'attachement aux nouveaux parents se développe. L'échantillon est composé d'un petit groupe (n = 6) d'enfants provenant de Corée du Sud, adoptés par des parents Italiens. A l'aide du Parent Attachment Diary (Dozier & Stovall, 1997), des observations des comportements d'attachement de l'enfant ont été recueillies chaque jour au cours des 3 premiers mois après l'arrivée. Les résultats montrent une double variabilité des comportements d'attachement: au niveau inter- et intra-individuel ; au premier de ces niveaux, seuleme la moitié des enfants parvient à développer un pattern stable d'attachement ; au niveau intra-individuel, les trajectoires de développement des comportements d'attachement ont été testées à l'aide de Modèles Linéaires Hiérarchiques (Bryk et Raudenbush, 1992), mais aucune tendance significative n'a pu être révélée. L'Étude 2 vise à analyser l'attachement chez des enfants adoptés dans l'enfance, lors de la période particulièrement sensible de l'adolescence. Les données sont issues d'un base de données internationale (n = 104, Belgique, Italie et Roumanie), composée d' entretiens cliniques semi-structurées (auprès de l'adolescents et des ses parents adoptifs), ainsi que de questionnaires. Les analyses statistiques visent à détecter la présence de facteurs de risque et de protection relativement à l'attachement et aux problèmes de comportement de l'enfant adopté. En outre, la présence d'interactions entre les représentations d'attachement des membres de la famille adoptive est évaluée. Les résultats montrent que les risques associés à la période pré-adoptive prédisent la qualité du bien-être de l'adolescent, mais les représentations parentales constituent un modérateur important de cette relation. En outre, la sécurité de l'attachement du jeune adopté médiatise partiellement la relation entre l'âge au moment du placement et les problèmes de comportement lors de l'adolescence. En conclusion, à l'aide de multiples données relatives à l'attachement, ces deux études soulignent son évolution notable au fil du temps, ce qui sous-tend la présence d'une certaine plasticité, et donc la possible valeur réparatrice de la pratique de l'adoption. Comme les parents semblent jouer un rôle important de ce point de vue, surtout à l'adolescence, cela renforce la notion d'un soutien post-adoption, en vue d'aider les parents à la promotion d'un environnement relationnel favorable et stable. - Il presente lavoro è volto ad analizzare l'attaccamento durante le due fasi della vita della famiglia adottiva che meno sono state indagate dalla letteratura. Lo Studio 1 aveva l'obiettivo di analizzare i primi mesi che seguono il collocamento del bambino, al fine di capire se e come una relazione di attaccamento verso i nuovi genitori si sviluppa. Il campione è composto da un piccolo gruppo (n = 6) di bambini provenienti dalla Corea del Sud e adottati da genitori italiani. Attraverso il Parent Attachment Diary (Stovall e Dozier, 1997) sono stati osservati quotidianamente, e per i primi tre mesi, i comportamenti di attaccamento del bambino. I risultati hanno mostrato una duplice variabilità: a livello intraindividuale (nell'arco dei 3 mesi), ed interindividuale, poiché solo la metà dei bambini ha sviluppato un pattern stabile di attaccamento. Per verificare le traiettorie di sviluppo di tali comportamenti, sono stati applicati i Modelli Lineari Gerarchici (Bryk & Raudenbush, 1992), che però non hanno stimato una tendenza significativa all'interno della popolazione. Obiettivo dello Studio 2 è stato quello di esaminare l'attaccamento nelle famiglie i cui figli adottivi si trovavano nella delicata fase adolescenziale. I dati, provenienti da una raccolta internazionale (n = 104, Belgio, Italia e Romania), erano costituiti da interviste cliniche semi-strutturate (con gli adolescenti e i propri genitori adottivi) e da questionari. Le analisi hanno indagato il ruolo dei fattori di rischio sullo sviluppo socio-emotivo e sugli eventuali problemi comportamentali dei ragazzi. Inoltre, sono state esaminate le possibili interazioni tra le diverse rappresentazioni di attaccamento dei membri della famiglia adottiva. I risultati hanno mostrato che il rischio pre-adottivo predice l'adattamento dell'adolescente, sebbene le rappresentazioni genitoriali costituiscano un importante moderatore di questa relazione. Inoltre, la sicurezza dell'attaccamento dell'adolescente media parzialmente la relazione tra età al momento dell'adozione e problemi comportamentali in adolescenza. In conclusione, attraverso i molteplici dati relativi all'attaccamento, i due studi ne hanno evidenziato il cambiamento nel tempo, a riprova della sua plasticità, e pertanto sottolineano il possibile valore riparativo dell'adozione. Dal momento che i genitori svolgono un ruolo importante, soprattutto in adolescenza, il supporto nel post- adozione diventa centrale per aiutarli a promuovere un ambiente relazionale favorevole e stabile nel tempo.

Reduced physical activity level and cardiorespiratory fitness in children with chronic diseases.

We aimed to compare physical activity level and cardiorespiratory fitness in children with different chronic diseases, such as type 1 diabetes mellitus (T1DM), obesity (OB) and juvenile idiopathic arthritis (JIA), with healthy controls (HC). We performed a cross-sectional study including 209 children: OB: n = 45, T1DM: n = 48, JIA: n = 31, and HC: n = 85. Physical activity level was assessed by accelerometer and cardiorespiratory fitness by a treadmill test. ANOVA, linear regressions and Pearson correlations were used. Children with chronic diseases had reduced total daily physical activity counts (T1DM 497 +/- 54 cpm, p = 0.003; JIA 518 +/- 28, p < 0.001, OB 590 +/- 25, p = 0.003) and cardiorespiratory fitness (JIA 39.3 +/- 1.7, p = 0.001, OB 41.7 +/- 1.2, p = 0.020) compared to HC (668 +/- 35 cpm; 45.3 +/- 0.9 ml kg(-1) min(-1), respectively). Only 60.4% of HC, 51.6% of OB, 38.1% of JIA and 38.5% of T1DM children met the recommended daily 60 min of moderate-to-vigorous physical activity. Low cardiorespiratory fitness was associated with female gender and low daily PA. Children with chronic diseases had reduced physical activity and cardiorespiratory fitness. As the benefits of PA on health have been well demonstrated during growth, it should be encouraged in those children to prevent a reduction of cardiorespiratory fitness and the development of comorbidities.

Not in Education, Employment, or Training status among young Swiss men. Longitudinal associations with mental health and substance use.

PURPOSE: Not in Education, Employment, or Training (NEET) youth are youth disengaged from major social institutions and constitute a worrying concern. However, little is known about this subgroup of vulnerable youth. This study aimed to examine if NEET youth differ from other contemporaries in terms of personality, mental health, and substance use and to provide longitudinal examination of NEET status, testing its stability and prospective pathways with mental health and substance use. METHODS: As part of the Cohort Study on Substance Use Risk Factors, 4,758 young Swiss men in their early 20s answered questions concerning their current professional and educational status, personality, substance use, and symptomatology related to mental health. Descriptive statistics, generalized linear models for cross-sectional comparisons, and cross-lagged panel models for longitudinal associations were computed. RESULTS: NEET youth were 6.1% at baseline and 7.4% at follow-up with 1.4% being NEET at both time points. Comparisons between NEET and non-NEET youth showed significant differences in substance use and depressive symptoms only. Longitudinal associations showed that previous mental health, cannabis use, and daily smoking increased the likelihood of being NEET. Reverse causal paths were nonsignificant. CONCLUSIONS: NEET status seemed to be unlikely and transient among young Swiss men, associated with differences in mental health and substance use but not in personality. Causal paths presented NEET status as a consequence of mental health and substance use rather than a cause. Additionally, this study confirmed that cannabis use and daily smoking are public health problems. Prevention programs need to focus on these vulnerable youth to avoid them being disengaged.

Disagreements among cohabiting and married couples in 22 European countries

Background: Cross-national research suggests that married people have higher levels of well-being than cohabiting people. However, relationship quality has both positive and negative dimensions. Researchers have paid little attention to disagreements within cohabiting and married couples. Objective: This study aims to improve our understanding of the meaning of cohabitation by examining disagreements within marital and cohabiting relationships. We examine variations in couples' disagreements about housework, paid work and money by country and gender. Methods: The data come from the 2004 European Social Survey. We selected respondents living in a heterosexual couple relationship and aged between 18 and 45. In total, the study makes use of data from 22 European countries and 9,657 people. Given that our dependent variable was dichotomous, we estimated multilevel logit models, with (1) disagree and (0) never disagree. Results: We find that cohabitors had more disagreements about housework, the same disagreements about money, but fewer disagreements about paid work than did married people. These findings could not be explained by socio-economic or demographic measures, nor did we find gender or cross-country differences in the association between union status and conflict. Conclusions: Cohabiting couples have more disagreements about housework but fewer disagreements about paid work than married people. There are no gender or cross-country differences in these associations. The results provide further evidence that the meaning of cohabitation differs from that of marriage, and that this difference remains consistent across nations.

Impact of normalization on miRNA microarray expression profiling.

Profiling miRNA levels in cells with miRNA microarrays is becoming a widely used technique. Although normalization methods for mRNA gene expression arrays are well established, miRNA array normalization has so far not been investigated in detail. In this study we investigate the impact of normalization on data generated with the Agilent miRNA array platform. We have developed a method to select nonchanging miRNAs (invariants) and use them to compute linear regression normalization coefficients or variance stabilizing normalization (VSN) parameters. We compared the invariants normalization to normalization by scaling, quantile, and VSN with default parameters as well as to no normalization using samples with strong differential expression of miRNAs (heart-brain comparison) and samples where only a few miRNAs are affected (by p53 overexpression in squamous carcinoma cells versus control). All normalization methods performed better than no normalization. Normalization procedures based on the set of invariants and quantile were the most robust over all experimental conditions tested. Our method of invariant selection and normalization is not limited to Agilent miRNA arrays and can be applied to other data sets including those from one color miRNA microarray platforms, focused gene expression arrays, and gene expression analysis using quantitative PCR.

Smoking offsets the metabolic benefits of parental longevity in women: the CoLaus study.

OBJECTIVE: We evaluated whether subjects with long-lived parents show lower levels of cardiovascular risk factors, including the metabolic syndrome. METHODS: We analyzed data from a Swiss population-based sample (1163 men and 1398 women) aged 55-75 years from Lausanne. Participants were stratified by number of parents (0, 1, 2) who survived to 85 years or more. The associations of parental longevity with cardiovascular risk factors and related metabolic variables were analyzed using multiple linear regressions. RESULTS: Age-adjusted metabolic syndrome prevalence varied from 24.8%, 20.5% to 13.8% in women (P<0.05) and from 28.8%, 32.1% to 27.6% in men (not significant) with 0, 1 and 2 long-lived parents. The association between parental longevity and metabolic syndrome prevalence was particularly strong in women who had never smoked. In this group, women with 2 long-lived parents had lower Body Mass Index and smaller waist circumference. In never-smokers of both genders, mean (95% CI) adjusted High Density Lipoprotein-cholesterol levels were 1.64(1.61-1.67), 1.67(1.65-1.70) and 1.71(1.65-1.76) mmol/L for 0, 1 and 2 long-lived parents (P<0.01), respectively. The trend was not significant in former and current smokers. CONCLUSIONS: In women, not in men, parental longevity is associated with a better metabolic profile. The metabolic benefits of having long-lived parents are offset by smoking.

Effect of antenatal corticosteroids on fetal growth and gestational age at birth.

OBJECTIVE: To estimate the effect of multiple courses of antenatal corticosteroids on neonatal size, controlling for gestational age at birth and other confounders, and to determine whether there was a dose-response relationship between number of courses of antenatal corticosteroids and neonatal size. METHODS: This is a secondary analysis of the Multiple Courses of Antenatal Corticosteroids for Preterm Birth Study, a double-blind randomized controlled trial of single compared with multiple courses of antenatal corticosteroids in women at risk for preterm birth and in which fetuses administered multiple courses of antenatal corticosteroids weighed less, were shorter, and had smaller head circumferences at birth. All women (n=1,858) and children (n=2,304) enrolled in the Multiple Courses of Antenatal Corticosteroids for Preterm Birth Study were included in the current analysis. Multiple linear regression analyses were undertaken. RESULTS: Compared with placebo, neonates in the antenatal corticosteroids group were born earlier (estimated difference and confidence interval [CI]: -0.428 weeks, CI -0.10264 to -0.75336; P=.01). Controlling for gestational age at birth and confounding factors, multiple courses of antenatal corticosteroids were associated with a decrease in birth weight (-33.50 g, CI -66.27120 to -0.72880; P=.045), length (-0.339 cm, CI -0.6212 to -0.05676]; P=.019), and head circumference (-0.296 cm, -0.45672 to -0.13528; P<.001). For each additional course of antenatal corticosteroids, there was a trend toward an incremental decrease in birth weight, length, and head circumference. CONCLUSION: Fetuses exposed to multiple courses of antenatal corticosteroids were smaller at birth. The reduction in size was partially attributed to being born at an earlier gestational age but also was attributed to decreased fetal growth. Finally, a dose-response relationship exists between the number of corticosteroid courses and a decrease in fetal growth. The long-term effect of these findings is unknown. CLINICAL TRIAL REGISTRATION: ClinicalTrials.gov, www.clinicaltrials.gov, NCT00187382. LEVEL OF EVIDENCE: II.

Accuracy profile validation of a new method for carbon monoxide measurement in the human blood using headspace-gas chromatography-mass spectrometry (HS-GC-MS).

The aim of our study was to provide an innovative headspace-gas chromatography-mass spectrometry (HS-GC-MS) method applicable for the routine determination of blood CO concentration in forensic toxicology laboratories. The main drawback of the GC/MS methods discussed in literature for CO measurement is the absence of a specific CO internal standard necessary for performing quantification. Even if stable isotope of CO is commercially available in the gaseous state, it is essential to develop a safer method to limit the manipulation of gaseous CO and to precisely control the injected amount of CO for spiking and calibration. To avoid the manipulation of a stable isotope-labeled gas, we have chosen to generate in a vial in situ, an internal labeled standard gas ((13)CO) formed by the reaction of labeled formic acid formic acid (H(13)COOH) with sulfuric acid. As sulfuric acid can also be employed to liberate the CO reagent from whole blood, the procedure allows for the liberation of CO simultaneously with the generation of (13)CO. This method allows for precise measurement of blood CO concentrations from a small amount of blood (10 μL). Finally, this method was applied to measure the CO concentration of intoxicated human blood samples from autopsies.

Assessment of coronary vasoreactivity by multidetector computed tomography: feasibility study with rubidium-82 cardiac positron emission tomography.

BACKGROUND: Positron emission tomography (PET) during the cold pressor test (CPT) has been used to assess endothelium-dependent coronary vasoreactivity, a surrogate marker of cardiovascular events. However, its use remains limited by cardiac PET availability. As multidetector computed tomography (MDCT) is more widely available, we aimed to develop a measurement of endothelium-dependent coronary vasoreactivity with MDCT and similar radiation burden as with PET. METHODS AND RESULTS: A study group of 18 participants without known cardiovascular risk factor (9F/9M; age 60±6 years) underwent cardiac PET with (82)Rb and unenhanced ECG-gated MDCT within 4h, each time at rest and during CPT. The relation between absolute myocardial blood flow (MBF) response to CPT by PET (ml·min(-1)·g(1)) and relative changes in MDCT-measured coronary artery surface were assessed using linear regression analysis and Spearman's correlation. MDCT and PET/CT were analyzed in all participants. Hemodynamic conditions during CPT at MDCT and PET were similar (P>0.3). Relative changes in coronary artery surface because of CPT (2.0-21.2%) correlated to changes in MBF (-0.10-0.52ml·min(-1)·g(1)) (ρ=0.68, P=0.02). Effective dose was 1.3±0.2mSv for MDCT and 3.1mSv for PET/CT. CONCLUSIONS: Assessment of endothelium-dependent coronary vasoreactivity using MDCT CPT appears feasible. Because of its wider availability, shorter examination time and similar radiation burden, MDCT could be attractive in clinical research for coronary status assessment.

Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristicsin a text that are rarely controlled by the author, with those in other texts. When thegoal is to settle authorship questions, these characteristics should relate to the author’s style andnot to the genre, epoch or editor, and they should be such that their variation between authors islarger than the variation within comparable texts from the same author.For an overview of the literature on stylometry and some of the techniques involved, see for exampleMosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) orLebart, Salem and Berry (1998).Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be“the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writterslike Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translatedseveral times into Spanish, Italian and French, with modern English translations by Rosenthal(1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465,but it was not printed until 1490.There is an intense and long lasting debate around its authorship sprouting from its first edition,where its introduction states that the whole book is the work of Martorell (1413?-1468), while atthe end it is stated that the last one fourth of the book is by Galba (?-1490), after the death ofMartorell. Some of the authors that support the theory of single authorship are Riquer (1990),Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer(1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990).Neither of the two candidate authors left any text comparable to the one under study, and thereforediscriminant analysis can not be used to help classify chapters by author. By using sample textsencompassing about ten percent of the book, and looking at word length and at the use of 44conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that mightindicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba andGinebra (2000) estimates that stylistic boundary to be near chapter 383.Following the lead of the extensive literature, this paper looks into word length, the use of the mostfrequent words and into the use of vowels in each chapter of the book. Given that the featuresselected are categorical, that leads to three contingency tables of ordered rows and therefore tothree sequences of multinomial observations.Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3describes the problem of the estimation of a suden change-point in those sequences, in the followingsections we propose various ways to estimate change-points in multinomial sequences; the methodin section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma modelsonto the sequence of Chi-square distances between each row profiles and the average profile, theone in Section 6 fits models onto the sequence of values taken by the first component of thecorrespondence analysis as well as onto sequences of other summary measures like the averageword length. In Section 7 we fit models onto the marginal binomial sequences to identify thefeatures that distinguish the chapters before and after that boundary. Most methods rely heavilyon the use of generalized linear models

High Prevalence of Systemic Autoimmune Diseases in Patients with Meniere's Disease

BACKGROUND. Autoimmunity appears to be associated with the pathophysiology of Meniere's disease (MD), an inner ear disorder characterized by episodes of vertigo associated with hearing loss and tinnitus. However, the prevalence of autoimmune diseases (AD) in patients with MD has not been studied in individuals with uni or bilateral sensorineural hearing loss (SNHL). METHODS AND FINDINGS. We estimated the prevalence of AD in 690 outpatients with MD with uni or bilateral SNHL from otoneurology clinics at six tertiary referral hospitals by using clinica criteria and an immune panel (lymphocyte populations, antinuclear antibodies, C3, C4 and proinflammatory cytokines TNFα, INFγ). The observed prevalence of rheumatoid arthritis (RA), systemic lupus erythematosus (SLE) and ankylosing spondylitis (AS) was higher than expected for the general population (1.39 for RA, 0.87 for SLE and 0.70 for AS, respectively). Systemic AD were more frequently observed in patients with MD and diagnostic criteria for migraine than cases with MD and tension-type headache (p = 0.007). There were clinical differences between patients with uni or bilateral SNHL, but no differences were found in the immune profile. Multiple linear regression showed that changes in lymphocytes subpopulations were associated with hearing loss and persistence of vertigo, suggesting a role for the immune response in MD. CONCLUSIONS. Despite some limitations, MD displays an elevated prevalence of systemic AD such as RA, SLE and AS. This finding, which suggests an autoimmune background in a subset of patients with MD, has important implications for the treatment of MD.

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