Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

Legal europeanization as legal transformation : some insights from Swiss 'outer Europe'

The "Europeanization" of non-EU countries' laws is predominantly seen as an "export" of the EU acquis, especially in the case of so-called "quasi-member" states such as Switzerland. Based on an examination of the Swiss experience, this paper highlights the flaws of this conceptualization: the Europeanization of Swiss Law is a highly differentiated phenomenon, encompassing several forms of approximation to EU Law. All of these forms fall short of an "export" of norms, and result in the creation of something new: a "Europeanized law" that is similar to, but qualitatively different from, EU Law. Another drawback of the "export" metaphor is the emphasis it places on the isomorphism of positive legislation. Europeanization goes deeper than that. As shown in this paper, it is a process of transformation involving not only positive law, but also legal thinking. The Swiss case demonstrates how significant such deeper transformations can be: the Europeanization of positive law has induced an alteration of the traditional canon of legal interpretation. It also demonstrates how problematic such transformations can be: the above-mentioned alteration has not given rise to a new and universally accepted canon of interpretation. This reflects the tension between the need for clear "rules of reference" for EU legal materials - which are required in order to restore coherence and predictability to an extensively Europeanized legal system - and the reluctance to give a legal value to foreign legal materials - which is rooted in a traditional understanding of the concept of "law". Such tension, in turn, shows what deep and difficult transformations are required in order to establish a viable model of legal integration outside supranational structures.

BME-based uncertainty assessment of the Chernobyl fallout

The vast territories that have been radioactively contaminated during the 1986 Chernobyl accident provide a substantial data set of radioactive monitoring data, which can be used for the verification and testing of the different spatial estimation (prediction) methods involved in risk assessment studies. Using the Chernobyl data set for such a purpose is motivated by its heterogeneous spatial structure (the data are characterized by large-scale correlations, short-scale variability, spotty features, etc.). The present work is concerned with the application of the Bayesian Maximum Entropy (BME) method to estimate the extent and the magnitude of the radioactive soil contamination by 137Cs due to the Chernobyl fallout. The powerful BME method allows rigorous incorporation of a wide variety of knowledge bases into the spatial estimation procedure leading to informative contamination maps. Exact measurements (?hard? data) are combined with secondary information on local uncertainties (treated as ?soft? data) to generate science-based uncertainty assessment of soil contamination estimates at unsampled locations. BME describes uncertainty in terms of the posterior probability distributions generated across space, whereas no assumption about the underlying distribution is made and non-linear estimators are automatically incorporated. Traditional estimation variances based on the assumption of an underlying Gaussian distribution (analogous, e.g., to the kriging variance) can be derived as a special case of the BME uncertainty analysis. The BME estimates obtained using hard and soft data are compared with the BME estimates obtained using only hard data. The comparison involves both the accuracy of the estimation maps using the exact data and the assessment of the associated uncertainty using repeated measurements. Furthermore, a comparison of the spatial estimation accuracy obtained by the two methods was carried out using a validation data set of hard data. Finally, a separate uncertainty analysis was conducted that evaluated the ability of the posterior probabilities to reproduce the distribution of the raw repeated measurements available in certain populated sites. The analysis provides an illustration of the improvement in mapping accuracy obtained by adding soft data to the existing hard data and, in general, demonstrates that the BME method performs well both in terms of estimation accuracy as well as in terms estimation error assessment, which are both useful features for the Chernobyl fallout study.

Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Obesity-related phenotypes are associated to parental longevity in a Swiss population-based study

PURPOSE. Longevity has been attributed to decreased cardiovascular mortality. Subjects with long-lived parents may represent a valuable group to study cardiovascular risk factors (CVRF) associated with longevity, possibly leading to new ways of preventing cardiovascular disease. Purpose: Longevity has been attributed to decreased cardiovascular mortality. Subjects with long-lived parents may represent a valuable group to study cardiovascular risk factors (CVRF) associated with longevity, possibly leading to new ways of preventing cardiovascular disease. Methods: We analyzed data from a population-based sample of 2561 participants (1163 men and 1398 women) aged 55--75 years from the city of Lausanne, Switzerland (CoLaus study). Participants were stratified by the number of parents (0, 1, 2) who survived to 85 years or more. Trend across these strata was assessed using a non-parametric kmean test. The associations of parental age (independent covariate used as a proxy for longevity) with fasting blood glucose, blood pressures, blood lipids, body mass index (BMI), weight, height or liver enzymes (continuous dependent variables) were analyzed using multiple linear regressions. Models were adjusted for age, sex, alcohol consumption, smoking and educational level, and BMI for liver enzymes. Results: For subjects with 0 (N=1298), 1 (N=991) and 2 (N=272) long-lived parents, median BMI (interquartile range) was 25.4 (6.5), 24.9 (6.1) and 23.7 (4.8) kg/m2 in women (P<0.001), and 27.3 (4.8), 27.0 (4.5) and 25.9 (4.9) kg/m2 in men (P=0.04), respectively; median weight was 66.5 (16.1), 65.0 (16.4) and 63.4 (13.7) kg in women (P=0.003), and 81.5 (17.0), 81.4 (16.4) and 80.3 (17.1) kg in men (P=0.36). Median height was 161 (8), 162 (9) and 163 (8) cm in women (P=0.005), and 173 (9), 174 (9) and 174 (11) cm in men (P=0.09). The corresponding medians for AST (Aspartate Aminotransferase) were 31 (13), 29 (11) and 28 (10) U/L (P=0.002), and 28 (17), 27 (14) and 26 (19) U/L for ALT (Alanin Aminotransferase, P=0.053) in men. In multivariable analyses, greater parental longevity was associated with lower BMI, lower weight and taller stature in women (P<0.01) and lower AST in men (P=0.011). No significant associations were observed for the other variables analyzed. Sensitivity analyses restricted to subjects whose parents were dead (N=1844) led to similar results, with even stronger associations of parental longevity with liver enzymes in men. Conclusion: In women, increased parental longevity was associated with smaller BMI, attributable to lower weight and taller stature. In men, the association of increased parental longevity with lower liver enzymes, independently of BMI, suggests that parental longevity may be associated with decreased nonalcoholic fatty liver disease.

Parametric imaging for characterizing focal liver lesions in contrast-enhanced ultrasound.

The differentiation between benign and malignant focal liver lesions plays an important role in diagnosis of liver disease and therapeutic planning of local or general disease. This differentiation, based on characterization, relies on the observation of the dynamic vascular patterns (DVP) of lesions with respect to adjacent parenchyma, and may be assessed during contrast-enhanced ultrasound imaging after a bolus injection. For instance, hemangiomas (i.e., benign lesions) exhibit hyper-enhanced signatures over time, whereas metastases (i.e., malignant lesions) frequently present hyperenhanced foci during the arterial phase and always become hypo-enhanced afterwards. The objective of this work was to develop a new parametric imaging technique, aimed at mapping the DVP signatures into a single image called a DVP parametric image, conceived as a diagnostic aid tool for characterizing lesion types. The methodology consisted in processing a time sequence of images (DICOM video data) using four consecutive steps: (1) pre-processing combining image motion correction and linearization to derive an echo-power signal, in each pixel, proportional to local contrast agent concentration over time; (2) signal modeling, by means of a curve-fitting optimization, to compute a difference signal in each pixel, as the subtraction of adjacent parenchyma kinetic from the echopower signal; (3) classification of difference signals; and (4) parametric image rendering to represent classified pixels as a support for diagnosis. DVP parametric imaging was the object of a clinical assessment on a total of 146 lesions, imaged using different medical ultrasound systems. The resulting sensitivity and specificity were 97% and 91%, respectively, which compare favorably with scores of 81 to 95% and 80 to 95% reported in medical literature for sensitivity and specificity, respectively.

Processus et fonctions psychiques de l'écriture : de la création littéraire au groupe à médiation

Ce travail porte sur l'étude des processus et fonctions psychiques de la création littéraire et de l'écriture dans une perspective psychanalytique, à partir d'une méthodologie de recherche qualitative exploratoire. Un premier volet de la recherche s'attache à étudier les processus et fonctions psychiques dans la création littéraire à partir de six entretiens semi-structurés avec des écrivains romands publiés. Les entretiens sont analysés en profondeur à partir de la méthodologie qualitative Interpretative Phenomenological Analysis (Smith, Flowers & Larkin, 2009). Un second volet de la recherche étudie les processus et fonctions psychiques de l'écriture dans un atelier de groupe à médiation écriture prenant place dans un Centre de Jour pour adultes, à partir de l'élaboration de deux cas. L'articulation des analyses de ces expériences d'écriture dans les deux contextes étudiés permet de mettre en évidence des enjeux de continuité/discontinuité dans le passage du premier mouvement créateur de l'écriture - le « miroir-papier » - vers le mouvement de la publication/lecture - le « miroir-lecteur ». Ces enjeux de partage invitent à penser le travail créateur de l'écriture à partir de la notion de « Moi- peau » (Anzieu, 1995) et à préciser cinq fonctions psychiques de l'écriture : transformation ; protection ; échange ; réassurance narcissique ; partage. Un accent particulier est porté sur la fonction de protection, dans la tension qu'elle entretient avec celle de transformation, au travers de la mise en évidence de six formes d'enveloppes d'écriture protectrice. Finalement, les analyses mettent en évidence la manière dont cette tension entre un investissement défensif de l'écriture et un investissement de transformation se déploie par des voies singulières en vue d'une tentative de résolution du conflit subjectif interne entre les exigences du « public intérieur » (De M'Uzan, 1964) et la rencontre avec l'objet réel. Ces pistes d'analyses permettent de préciser les modalités de contribution de l'écriture aux processus de symbolisation et d'enrichir la pratique du champ des médiations thérapeutiques de repères d'appréciation clinique. - Based on an exploratory qualitative research methodology, this work focuses on the psychical processes and functions of literary creation and writing from a psychoanalytic perspective. The first part of the research investigates psychical processes and functions in creative writing through the analysis of six semi-structured interviews with published Swiss writers. The interviews are analyzed according to the exploratory qualitative methodology Interpretative Phenomenological Analysis (Smith, Flowers & Larkin, 2009). The second area of research examines the processes of writing in the context of an art-therapy writing group that took place in an adult day center. The observations lead to the elaboration of two case studies. The joint analysis of these writing experiences highlights issues of continuity/discontinuity in passing from the first creative writing movement - the « mirror-paper » - to the final publication/reading of the work - the «mirror-reader». These issues enable us to understand the creative writing processes from the concept of the « skin-ego » (Anzieu, 1995). Five functions of writing are proposed: transformation, protection, exchange, narcissistic reassurance, and sharing. An emphasis on the tension between the protection and the transformation functions is highlighted through the identification of six forms of protective writing psychical envelopes. Finally, the analysis shows how this tension between a defensive and a transformative investment in writing takes place in an attempt to resolve the internal conflict between the « inner audience » (De M'Uzan, 1964) and the encounter with the real object. This study clarifies the way creative writing can contribute to symbolization and can enrich clinical assessment in the field of art-therapy.

Existential values transformation in all organ transplantation : a qualitative prospective study

The aim of this qualitative study was to analyze psychological concerns in wait-listed patients T1 and six months after transplantation T2. Semi-structured interviews were conducted and qualitative analysis performed. T1 Kidney patients maintained apparent normality, building emotional protection, and a fatalist attitude. Liver patients set physical limits, reevaluation of life values was reported. Lung patients developed physical and psychological self-protection. Modified life values, fatalism and spirituality were mentioned. Heart patients husbanded ressources and self-protection. Modified life values, fatalist attitude were reported. T2 Kidney patients described new life perspectives and increase of empathy. Liver patients underlined positive identity and life values modifications. Lack of respect of life values generated anger. Heart and lung patients set their existential priorities and underlined increase in spirituality, greater openness and more closeness to significant ones. Lack of respect of human values induced negative feelings. TX comes with physical benefits, but also with positive existential values transformations and a humanistic, altruistic attitude.

Discovery of the faithfulness gene: a model of transmission and transformation of scientific information.

The purpose of this paper is to study the diffusion and transformation of scientific information in everyday discussions. Based on rumour models and social representations theory, the impact of interpersonal communication and pre-existing beliefs on transmission of the content of a scientific discovery was analysed. In three experiments, a communication chain was simulated to investigate how laypeople make sense of a genetic discovery first published in a scientific outlet, then reported in a mainstream newspaper and finally discussed in groups. Study 1 (N=40) demonstrated a transformation of information when the scientific discovery moved along the communication chain. During successive narratives, scientific expert terminology disappeared while scientific information associated with lay terminology persisted. Moreover, the idea of a discovery of a faithfulness gene emerged. Study 2 (N=70) revealed that transmission of the scientific message varied as a function of attitudes towards genetic explanations of behaviour (pro-genetics vs. anti-genetics). Pro-genetics employed more scientific terminology than anti-genetics. Study 3 (N=75) showed that endorsement of genetic explanations was related to descriptive accounts of the scientific information, whereas rejection of genetic explanations was related to evaluative accounts of the information.

A protein interaction atlas for the nuclear receptors: properties and quality of a hub-based dimerisation network.

BACKGROUND: The nuclear receptors are a large family of eukaryotic transcription factors that constitute major pharmacological targets. They exert their combinatorial control through homotypic heterodimerisation. Elucidation of this dimerisation network is vital in order to understand the complex dynamics and potential cross-talk involved. RESULTS: Phylogeny, protein-protein interactions, protein-DNA interactions and gene expression data have been integrated to provide a comprehensive and up-to-date description of the topology and properties of the nuclear receptor interaction network in humans. We discriminate between DNA-binding and non-DNA-binding dimers, and provide a comprehensive interaction map, that identifies potential cross-talk between the various pathways of nuclear receptors. CONCLUSION: We infer that the topology of this network is hub-based, and much more connected than previously thought. The hub-based topology of the network and the wide tissue expression pattern of NRs create a highly competitive environment for the common heterodimerising partners. Furthermore, a significant number of negative feedback loops is present, with the hub protein SHP [NR0B2] playing a major role. We also compare the evolution, topology and properties of the nuclear receptor network with the hub-based dimerisation network of the bHLH transcription factors in order to identify both unique themes and ubiquitous properties in gene regulation. In terms of methodology, we conclude that such a comprehensive picture can only be assembled by semi-automated text-mining, manual curation and integration of data from various sources.

Associations of Serum Uric Acid and SLC2A9 Variant with Depressive and Anxiety Disorders: A Population-Based Study.

BACKGROUND: Limited information exists regarding the association between serum uric acid (SUA) and psychiatric disorders. We explored the relationship between SUA and subtypes of major depressive disorder (MDD) and specific anxiety disorders. Additionally, we examined the association of SLC2A9 rs6855911 variant with anxiety disorders. METHODS: We conducted a cross-sectional analysis on 3,716 individuals aged 35-66 years previously selected for the population-based CoLaus survey and who agreed to undergo further psychiatric evaluation. SUA was measured using uricase-PAP method. The French translation of the semi-structured Diagnostic Interview for Genetic Studies was used to establish lifetime and current diagnoses of depression and anxiety disorders according to the DSM-IV criteria. RESULTS: Men reported significantly higher levels of SUA compared to women (357±74 µmol/L vs. 263±64 µmol/L). The prevalence of lifetime and current MDD was 44% and 18% respectively while the corresponding estimates for any anxiety disorders were 18% and 10% respectively. A quadratic hockey-stick shaped curve explained the relationship between SUA and social phobia better than a linear trend. However, with regards to the other specific anxiety disorders and other subtypes of MDD, there was no consistent pattern of association. Further analyses using SLC2A9 rs6855911 variant, known to be strongly associated with SUA, supported the quadratic relationship observed between SUA phenotype and social phobia. CONCLUSIONS: A quadratic relationship between SUA and social phobia was observed consistent with a protective effect of moderately elevated SUA on social phobia, which disappears at higher concentrations. Further studies are needed to confirm our observations.

Geomodelling of a fluvial system with semi-supervised support vector regression

Fluvial deposits are a challenge for modelling flow in sub-surface reservoirs. Connectivity and continuity of permeable bodies have a major impact on fluid flow in porous media. Contemporary object-based and multipoint statistics methods face a problem of robust representation of connected structures. An alternative approach to model petrophysical properties is based on machine learning algorithm ? Support Vector Regression (SVR). Semi-supervised SVR is able to establish spatial connectivity taking into account the prior knowledge on natural similarities. SVR as a learning algorithm is robust to noise and captures dependencies from all available data. Semi-supervised SVR applied to a synthetic fluvial reservoir demonstrated robust results, which are well matched to the flow performance

Foam pore size is a critical interface parameter of suction-based wound healing devices.

BACKGROUND: Suction-based wound healing devices with open-pore foam interfaces are widely used to treat complex tissue defects. The impact of changes in physicochemical parameters of the wound interfaces has not been investigated. METHODS: Full-thickness wounds in diabetic mice were treated with occlusive dressing or a suction device with a polyurethane foam interface varying in mean pore size diameter. Wound surface deformation on day 2 was measured on fixed tissues. Histologic cross-sections were analyzed for granulation tissue thickness (hematoxylin and eosin), myofibroblast density (α-smooth muscle actin), blood vessel density (platelet endothelial cell adhesion molecule-1), and cell proliferation (Ki67) on day 7. RESULTS: Polyurethane foam-induced wound surface deformation increased with polyurethane foam pore diameter: 15 percent (small pore size), 60 percent (medium pore size), and 150 percent (large pore size). The extent of wound strain correlated with granulation tissue thickness that increased 1.7-fold in small pore size foam-treated wounds, 2.5-fold in medium pore size foam-treated wounds, and 4.9-fold in large pore size foam-treated wounds (p < 0.05) compared with wounds treated with an occlusive dressing. All polyurethane foams increased the number of myofibroblasts over occlusive dressing, with maximal presence in large pore size foam-treated wounds compared with all other groups (p < 0.05). CONCLUSIONS: The pore size of the interface material of suction devices has a significant impact on the wound healing response. Larger pores increased wound surface strain, tissue growth, and transformation of contractile cells. Modification of the pore size is a powerful approach for meeting biological needs of specific wounds.

Molecular phylogenetics of soricid shrews (Mammalia) based on mitochondrial cytochrome b gene sequences: with special reference to the Soricinae

Molecular phylogeny of soricid shrews (Soricidae, Eulipotyphla, Mammalia) based on 1140 bp mitochondrial cytochrome b gene (cytb) sequences was inferred by the maximum likelihood (ML) method. All 13 genera of extant Soricinae and two genera of Crocidurinae were included in the analyses. Anourosorex was phylogenetically distant from the main groupings within Soricinae and Crocidurinae in the ML tree. Thus, it could not be determined to which subfamily Anourosorex should be assigned: Soricinae, Crocidurinae or a new subfamily. Soricinae (excluding Anourosorex) should be divided into four tribes: Neomyini, Notiosoricini, Soricini and Blarinini. However, monophyly of Blarinini was not robust in the present data set. Also, branching orders among tribes of Soricinae and those among genera of Neomyini could not be determined because of insufficient phylogenetic information of the cytb sequences. For water shrews of Neomyini (Chimarrogale, Nectogale and Neomys), monophyly of Neomys and the Chimarrogale-Nectogale group could not be verified, which implies the possibility of multiple origins for the semi-aquatic mode of living among taxa within Neomyini. Episoriculus may contain several separate genera. Blarinella was included in Blarinini not Soricini, based on the cytb sequences, but the confidence level was rather low; hence more phylogenetic information is needed to determine its phylogenetic position. Furthermore, some specific problems of taxonomy of soricid shrews were clarified, for example phylogeny of local populations of Notiosorex crawfordi, Chimarrogale himalayica and Crocidura attenuata.

Associations of serum uric acid and SLC2A9 variant with depressive and anxiety disorders: a population-based study

Background: Limited information exists regarding the association between serum uric acid (SUA) and psychiatric disorders. We explored the relationship between SUA and subtypes of major depressive disorder (MDD) and specific anxiety disorders. Additionally, we examined the association of SLC2A9 rs6855911 variant with anxiety disorders. Methods: We conducted a cross-sectional analysis on 3,716 individuals aged 35-66 years previously selected for the population-based CoLaus survey and who agreed to undergo further psychiatric evaluation. SUA was measured using uricase-PAP method. The French translation of the semi-structured Diagnostic Interview for Genetic Studies was used to establish lifetime and current diagnoses of depression and anxiety disorders according to the DSM-IV criteria. Results: Men reported significantly higher levels of SUA compared to women (357}74 μmol/L vs. 263}64 μmol/L). The prevalence of lifetime and current MDD was 44% and 18% respectively while the corresponding estimates for any anxiety disorders were 18% and 10% respectively. A quadratic hockey-stick shaped curve explained the relationship between SUA and social phobia better than a linear trend. However, with regards to the other specific anxiety disorders and other subtypes of MDD, there was no consistent pattern of association. Further analyses using SLC2A9 rs6855911 variant, known to be strongly associated with SUA, supported the quadratic relationship observed between SUA phenotype and social phobia. Conclusions: A quadratic relationship between SUA and social phobia was observed consistent with a protective effect of moderately elevated SUA on social phobia, which disappears at higher concentrations. Further studies are needed to confirm our observations.