Orientador: Antônio Padilha Feltrin / Resumo: No presente trabalho tem-se como objetivo estimar o potencial fotovoltaico devido à instalação de sistemas fotovoltaicos em telhados de áreas residenciais. Na estimação desse potencial foram consideradas quatro grandezas: o nível de irradiação solar, a área aproveitável de telhado para a instalação dos sistemas fotovoltaicos, a eficiência de conversão dos sistemas fotovoltaicos e as probabilidades de instalação dos sistemas fotovoltaicos, que caracterizam as preferências dos habitantes à instalação desses sistemas. Um modelo hierárquico bayesiano foi proposto para o cálculo das probabilidades de instalação dos sistemas fotovoltaicos. Nesse modelo bayesiano é estabelecida uma relação entre as probabilidades de instalação, as variáveis socioeconômicas e as interações entre as subáreas, através de um modelo linear generalizado misto. O cálculo do valor esperado das probabilidades de instalação foi realizado usando o método de Monte Carlo via cadeias de Markov. Os resultados do potencial fotovoltaico são apresentados através de mapas temáticos, que permitem a visualização da distribuição espacial do seu valor esperado. Esta informação pode ajudar as concessionárias de distribuição no planejamento e expansão de suas redes elétricas em regiões com maior potencial de geração fotovoltaica. / Abstract: The present work aims to estimate the photovoltaic potential for installing solar panel on the rooftop of residential areas. The estimation of this potential considers four quantities: the solar radiation level, rooftop availability for installation of photovoltaic systems, conversion efficiency of the photovoltaic systems and the probabilities for the installation of photovoltaic systems that characterize the preferences of the inhabitants to the installation of such systems. A bayesian hierarchical model is proposed to calculate the installation probabilities of photovoltaic systems. This bayesian model establishes a relation among the installation probabilities, socioeconomic variables and interactions between subareas, through a generalized linear mixed model. The calculation of expected value of installation probabilities in each subarea is performed using the Markov Chain Monte Carlo method. Photovoltaic potential results are presented through thematic maps that allow the visualization of the spatial distribution of its expected value. This information can help to distribution utilities for planning and expansion of their networks in regions with the greatest potential for photovoltaic generation. / Mestre

In this work, we study the so-called combined models, generalized linear mixed models with extension to allow for overdispersion, in the context of genetics and breeding. Such flexible models accommodates cluster-induced correlation and overdispersion through two separate sets of random effects and contain as special cases the generalized linear mixed models (GLMM) on the one hand, and commonly known overdispersion models on the other. We use such models while obtaining heritability coefficients for non-Gaussian characters. Heritability is one of the many important concepts that are often quantified upon fitting a model to hierarchical data. It is often of importance in plant and animal breeding. Knowledge of this attribute is useful to quantify the magnitude of improvement in the population. For data where linear models can be used, this attribute is conveniently defined as a ratio of variance components. Matters are less simple for non-Gaussian outcomes. The focus is on time-to-event and count traits, where the Weibull-Gamma-Normal and Poisson-Gamma-Normal models are used. The resulting expressions are sufficiently simple and appealing, in particular in special cases, to be of practical value. The proposed methodologies are illustrated using data from animal and plant breeding. Furthermore, attention is given to the occurrence of negative estimates of variance components in the Poisson-Gamma-Normal model. The occurrence of negative variance components in linear mixed models (LMM) has received a certain amount of attention in the literature whereas almost no work has been done for GLMM. This phenomenon can be confusing at first sight because, by definition, variances themselves are non-negative quantities. However, this is a well understood phenomenon in the context of linear mixed modeling, where one will have to make a choice between a hierarchical and a marginal view. The variance components of the combined model for count outcomes are studied theoretically and the plant breeding study used as illustration underscores that this phenomenon can be common in applied research. We also call attention to the performance of different estimation methods, because not all available methods are capable of extending the parameter space of the variance components. Then, when there is a need for inference on such components and they are expected to be negative, the accuracy of the method is not the only characteristic to be considered. / Neste trabalho foram estudados os chamados modelos combinados, modelos lineares generalizados mistos com extensão para acomodar superdispersão, no contexto de genética e melhoramento. Esses modelos flexíveis acomodam correlação induzida por agrupamento e superdispersão por meio de dois conjuntos separados de efeitos aleatórios e contem como casos especiais os modelos lineares generalizados mistos (MLGM) e os modelos de superdispersão comumente conhecidos. Tais modelos são usados na obtenção do coeficiente de herdabilidade para caracteres não Gaussianos. Herdabilidade é um dos vários importantes conceitos que são frequentemente quantificados com o ajuste de um modelo a dados hierárquicos. Ela é usualmente importante no melhoramento vegetal e animal. Conhecer esse atributo é útil para quantificar a magnitude do ganho na população. Para dados em que modelos lineares podem ser usados, esse atributo é convenientemente definido como uma razão de componentes de variância. Os problemas são menos simples para respostas não Gaussianas. O foco aqui é em características do tipo tempo-até-evento e contagem, em que os modelosWeibull-Gama-Normal e Poisson-Gama-Normal são usados. As expressões resultantes são suficientemente simples e atrativas, em particular nos casos especiais, pelo valor prático. As metodologias propostas são ilustradas usando dados de melhoramento animal e vegetal. Além disso, a atenção é voltada à ocorrência de estimativas negativas de componentes de variância no modelo Poisson-Gama- Normal. A ocorrência de componentes de variância negativos em modelos lineares mistos (MLM) tem recebido certa atenção na literatura enquanto quase nenhum trabalho tem sido feito para MLGM. Esse fenômeno pode ser confuso a princípio porque, por definição, variâncias são quantidades não-negativas. Entretanto, este é um fenômeno bem compreendido no contexto de modelagem linear mista, em que a escolha deverá ser feita entre uma interpretação hierárquica ou marginal. Os componentes de variância do modelo combinado para respostas de contagem são estudados teoricamente e o estudo de melhoramento vegetal usado como ilustração confirma que esse fenômeno pode ser comum em pesquisas aplicadas. A atenção também é voltada ao desempenho de diferentes métodos de estimação, porque nem todos aqueles disponíveis são capazes de estender o espaço paramétrico dos componentes de variância. Então, quando há a necessidade de inferência de tais componentes e é esperado que eles sejam negativos, a acurácia do método de estimação não é a única característica a ser considerada.

Cette thèse avait pour but d'illustrer l'intérêt de méthodes statistiques avancées lorsqu'on s'in­ téresse aux associations entre différents facteurs et la progression de la maladie rénale chronique (MRC). Dans un premier temps, une revue de la littérature a été effectuée alin d'identifier les méthodes classiquement utilisées pour étudier les facteurs de progression de la MRC ; leurs limites et des méthodes permettant de mieux prendre en compte ces limites ont été discutées. Notre second travail s'est concentré sur les analyses de données de survie et la prise en compte de la censure par intervalle, qui survient lorsque l'évènement d'intérêt est la progression vers un stade spécifique de la MRC, et le risque compétitif avec le décès. Une comparaison entre des modèles de survie standards et le modêle illness-death pour données censurées par intervalle nous a permis d'illustrer l'impact de la modélisation choisie sur les estimations à la fois des effets des facteurs de risque et des probabilités d'évènements, à partir des données de la cohorte NephroTest. Les autres travaux ont porté sur les analyses de données longitudinales de la fonction rénale. Nous avons illustré l'intérêt du modèle linéaire mixte dans ce contexte et présenté son extension pour la prise en compte de sous-populations de trajectoires de la fonction rénale différentes. Nous avons ainsi identifier cinq classes, dont une avec un déclin très rapide et une autre avec une amélioration de la fonction rénale au cours du temps. Des perspectives de travaux liés à la prédiction permettent enfin de lier les deux types d'analyses présentées dans la thèse. / The objective of this thesis was to illustrate the benefit of using advanced statistical methods to study associations between risk factors and chrouic kidney disease (CKD) progression. In a first time, we conducted a literature review of statistical methods used to investigate risk factors of CKD progression, identified important methodological issues, and discussed solutions. In our sec­ ond work, we focused on survival analyses and issues with interval-censoring, which occurs when the event of interest is the progression to a specifie CKD stage, and competing risk with death. A comparison between standard survival models and the illness-death mode! for interval-censored data allowed us to illustrate the impact of modeling on the estimates of both the effects of risk factors and the probabilities of events, using data from the NephroTest cohort. Other works fo­ cused on analysis of longitudinal data on renal function. We illustrated the interest of linear mixed mode! in this context and presented its extension to account for sub-populations with different trajectories of renal function. We identified five classes, including one with a strong decline and one with an improvement of renal function over time. Severa! perspectives on predictions bind the two types of analyses presented in this thesis.

No description available.

Purpose In ophthalmology, data from both eyes of a person are frequently included in the statistical evaluation. This violates the requirement of data independence for classical statistical tests (e.g. t-Test or analysis of variance (ANOVA)) because it is correlated data. Linear mixed models (LMM) were used as a possibility to include the data of both eyes in the statistical evaluation. Methods The LMM is available for a variety of statistical software such as SPSS or R. The application was applied to a retrospective longitudinal analysis of an accelerated corneal cross-linking (ACXL (9*10)) treatment in progressive keratoconus (KC) with a follow-up period of 36 months. Forty eyes of 20 patients were included, whereas sequential bilateral CXL treatment was performed within 12 months. LMM and ANOVA for repeated measurements were used for statistical evaluation of topographical and tomographical data measured by Pentacam (Oculus, Wetzlar, Germany). Results Both eyes were classified into a worse and better eye concerning corneal topography. Visual acuity, keratometric values and minimal corneal thickness were statistically significant between them at baseline (p < 0.05). A significant correlation between worse and better eye was shown (p < 0.05). Therefore, analyzing the data at each follow-up visit using ANOVA partially led to an overestimation of the statistical effect that could be avoided by using LMM. After 36 months, ACXL has significantly improved BCVA and flattened the cornea. Conclusion The evaluation of data of both eyes without considering their correlation using classical statistical tests leads to an overestimation of the statistical effect, which can be avoided by using the LMM.

<p> The hydrological cycle is affected by land use variability. Land use spatial and temporal variability has the power to alter watershed runoff, water resource quantity and quality, ecosystems, and environmental sustainability. In recent decades, agriculture lands, pastures, plantations, and urban areas have increased, resulting in significant increases in energy, water, and fertilizer usage, as well as significant biodiversity losses. </p>

Cette thèse comporte trois articles dont un est publié et deux en préparation. Le sujet central de la thèse porte sur le traitement des valeurs aberrantes représentatives dans deux aspects importants des enquêtes que sont : l’estimation des petits domaines et l’imputation en présence de non-réponse partielle. En ce qui concerne les petits domaines, les estimateurs robustes dans le cadre des modèles au niveau des unités ont été étudiés. Sinha & Rao (2009) proposent une version robuste du meilleur prédicteur linéaire sans biais empirique pour la moyenne des petits domaines. Leur estimateur robuste est de type «plugin», et à la lumière des travaux de Chambers (1986), cet estimateur peut être biaisé dans certaines situations. Chambers et al. (2014) proposent un estimateur corrigé du biais. En outre, un estimateur de l’erreur quadratique moyenne a été associé à ces estimateurs ponctuels. Sinha & Rao (2009) proposent une procédure bootstrap paramétrique pour estimer l’erreur quadratique moyenne. Des méthodes analytiques sont proposées dans Chambers et al. (2014). Cependant, leur validité théorique n’a pas été établie et leurs performances empiriques ne sont pas pleinement satisfaisantes. Ici, nous examinons deux nouvelles approches pour obtenir une version robuste du meilleur prédicteur linéaire sans biais empirique : la première est fondée sur les travaux de Chambers (1986), et la deuxième est basée sur le concept de biais conditionnel comme mesure de l’influence d’une unité de la population. Ces deux classes d’estimateurs robustes des petits domaines incluent également un terme de correction pour le biais. Cependant, ils utilisent tous les deux l’information disponible dans tous les domaines contrairement à celui de Chambers et al. (2014) qui utilise uniquement l’information disponible dans le domaine d’intérêt. Dans certaines situations, un biais non négligeable est possible pour l’estimateur de Sinha & Rao (2009), alors que les estimateurs proposés exhibent un faible biais pour un choix approprié de la fonction d’influence et de la constante de robustesse. Les simulations Monte Carlo sont effectuées, et les comparaisons sont faites entre les estimateurs proposés et ceux de Sinha & Rao (2009) et de Chambers et al. (2014). Les résultats montrent que les estimateurs de Sinha & Rao (2009) et de Chambers et al. (2014) peuvent avoir un biais important, alors que les estimateurs proposés ont une meilleure performance en termes de biais et d’erreur quadratique moyenne. En outre, nous proposons une nouvelle procédure bootstrap pour l’estimation de l’erreur quadratique moyenne des estimateurs robustes des petits domaines. Contrairement aux procédures existantes, nous montrons formellement la validité asymptotique de la méthode bootstrap proposée. Par ailleurs, la méthode proposée est semi-paramétrique, c’est-à-dire, elle n’est pas assujettie à une hypothèse sur les distributions des erreurs ou des effets aléatoires. Ainsi, elle est particulièrement attrayante et plus largement applicable. Nous examinons les performances de notre procédure bootstrap avec les simulations Monte Carlo. Les résultats montrent que notre procédure performe bien et surtout performe mieux que tous les compétiteurs étudiés. Une application de la méthode proposée est illustrée en analysant les données réelles contenant des valeurs aberrantes de Battese, Harter & Fuller (1988). S’agissant de l’imputation en présence de non-réponse partielle, certaines formes d’imputation simple ont été étudiées. L’imputation par la régression déterministe entre les classes, qui inclut l’imputation par le ratio et l’imputation par la moyenne sont souvent utilisées dans les enquêtes. Ces méthodes d’imputation peuvent conduire à des estimateurs imputés biaisés si le modèle d’imputation ou le modèle de non-réponse n’est pas correctement spécifié. Des estimateurs doublement robustes ont été développés dans les années récentes. Ces estimateurs sont sans biais si l’un au moins des modèles d’imputation ou de non-réponse est bien spécifié. Cependant, en présence des valeurs aberrantes, les estimateurs imputés doublement robustes peuvent être très instables. En utilisant le concept de biais conditionnel, nous proposons une version robuste aux valeurs aberrantes de l’estimateur doublement robuste. Les résultats des études par simulations montrent que l’estimateur proposé performe bien pour un choix approprié de la constante de robustesse. / This thesis focuses on the treatment of representative outliers in two important aspects of surveys: small area estimation and imputation for item non-response. Concerning small area estimation, robust estimators in unit-level models have been studied. Sinha & Rao (2009) proposed estimation procedures designed for small area means, based on robustified maximum likelihood parameters estimates of linear mixed model and robust empirical best linear unbiased predictors of the random effect of the underlying model. Their robust methods for estimating area means are of the plug-in type, and in view of the results of Chambers (1986), the resulting robust estimators may be biased in some situations. Biascorrected estimators have been proposed by Chambers et al. (2014). In addition, these robust small area estimators were associated with the estimation of the Mean Square Error (MSE). Sinha & Rao (2009) proposed a parametric bootstrap procedure based on the robust estimates of the parameters of the underlying linear mixed model to estimate the MSE. Analytical procedures for the estimation of the MSE have been proposed in Chambers et al. (2014). However, their theoretical validity has not been formally established and their empirical performances are not fully satisfactorily. Here, we investigate two new approaches for the robust version the best empirical unbiased estimator: the first one relies on the work of Chambers (1986), while the second proposal uses the concept of conditional bias as an influence measure to assess the impact of units in the population. These two classes of robust small area estimators also include a correction term for the bias. However, they are both fully bias-corrected, in the sense that the correction term takes into account the potential impact of the other domains on the small area of interest unlike the one of Chambers et al. (2014) which focuses only on the domain of interest. Under certain conditions, non-negligible bias is expected for the Sinha-Rao method, while the proposed methods exhibit significant bias reduction, controlled by appropriate choices of the influence function and tuning constants. Monte Carlo simulations are conducted, and comparisons are made between: the new robust estimators, the Sinha-Rao estimator, and the bias-corrected estimator. Empirical results suggest that the Sinha-Rao method and the bias-adjusted estimator of Chambers et al (2014) may exhibit a large bias, while the new procedures offer often better performances in terms of bias and mean squared error. In addition, we propose a new bootstrap procedure for MSE estimation of robust small area predictors. Unlike existing approaches, we formally prove the asymptotic validity of the proposed bootstrap method. Moreover, the proposed method is semi-parametric, i.e., it does not rely on specific distributional assumptions about the errors and random effects of the unit-level model underlying the small-area estimation, thus it is particularly attractive and more widely applicable. We assess the finite sample performance of our bootstrap estimator through Monte Carlo simulations. The results show that our procedure performs satisfactorily well and outperforms existing ones. Application of the proposed method is illustrated by analyzing a well-known outlier-contaminated small county crops area data from North-Central Iowa farms and Landsat satellite images. Concerning imputation in the presence of item non-response, some single imputation methods have been studied. The deterministic regression imputation, which includes the ratio imputation and mean imputation are often used in surveys. These imputation methods may lead to biased imputed estimators if the imputation model or the non-response model is not properly specified. Recently, doubly robust imputed estimators have been developed. However, in the presence of outliers, the doubly robust imputed estimators can be very unstable. Using the concept of conditional bias as a measure of influence (Beaumont, Haziza and Ruiz-Gazen, 2013), we propose an outlier robust version of the doubly robust imputed estimator. Thus this estimator is denoted as a triple robust imputed estimator. The results of simulation studies show that the proposed estimator performs satisfactorily well for an appropriate choice of the tuning constant.

The purpose of this dissertation was to examine patterns of antenatal stressful life events (SLEs) experienced by women in the United States (U.S.) and their association with postpartum depression (PPD). It further explored the role of women's state-level socio-economic status (SES) on PPD; the racial/ethnic dispartites in SLE-PPD relationship; and the role of provider communication on perinatal depression. Data from 2009–11 Pregnancy Risk Assessment Monitoring System (PRAMS) and SES indicators published by the Institute of Women’s Policy Research (IWPR) were used. Latent class analysis (LCA) was performed to identify unobserved class membership based on antenatal SLEs. Multilevel generalized linear mixed models examined whether state-level SES moderated the antenatal SLE-PPD relationship. Of 116,595 respondents to the PRAMS 2009-11, the sample size for our analyses ranged from 78% to 99%. The majority (64%) of participants were in low-stress class. The illness/death related-stress class (13%) had a high prevalence of severe illness (77%) and death (63%) of a family member or someone very close to them, while those in the multiple-stress (22%) class endorsed most other SLEs. Eleven percent had PPD; women who experienced all types of stressors, had the highest odds (adjusted odds ratio [aOR]: 5.43; 95% confidence interval [CI]: 5.36, 5.51) of PPD. The odds of PPD decreased with increasing state-level social/economic autonomy index (aOR: 0.75; 95% CI: 0.64, 0.88), with significant cross-level interaction between stressors and state-level SES. Among non-Hispanic blacks and non-Hispanic whites, husband/partner not wanting the pregnancy (aOR: 1.47; 95% CI: 1.14, 1.90) and drug/drinking problems of someone close (aOR: 1.37; 95% CI: 1.21, 1.55) were respectively associated with PPD. Provider communication was protective. That 1 out of every 5 and 1 out of every 8 women were in the high- and emotional-stress classes suggests that SLEs are common among pregnant women. Our results suggest that screening for antenatal SLEs might help identify women at risk for PPD. The finding that the odds of PPD decrease with increasing social/economic autonomy, could have policy implications and motivate efforts to improve these indices. This study also indicates the benefits of antenatal health care provider communication on perinatal depression.

Cette thèse s’inscrit dans le contexte de l’analyse et de la classification de signaux électroencéphalogrammes (EEG) par des méthodes d’analyse discriminante. Ces signaux multi-capteurs qui sont, par nature, très fortement corrélés spatialement et temporellement sont considérés dans le plan temps-fréquence. En particulier, nous nous intéressons à des signaux de type potentiels évoqués qui sont bien représentés dans l’espace des ondelettes. Par la suite, nous considérons donc les signaux représentés par des coefficients multi-échelles et qui ont une structure matricielle électrodes × coefficients. Les signaux EEG sont considérés comme un mélange entre l’activité d’intérêt que l’on souhaite extraire et l’activité spontanée (ou "bruit de fond"), qui est largement prépondérante. La problématique principale est ici de distinguer des signaux issus de différentes conditions expérimentales (classes). Dans le cas binaire, nous nous focalisons sur l’approche probabiliste de l’analyse discriminante et des modèles de mélange gaussien sont considérés, décrivant dans chaque classe les signaux en termes de composantes fixes (moyenne) et aléatoires. Cette dernière, caractérisée par sa matrice de covariance, permet de modéliser différentes sources de variabilité. Essentielle à la mise en oeuvre de l’analyse discriminante, l’estimation de cette matrice (et de son inverse) peut être dégradée dans le cas de grandes dimensions et/ou de faibles échantillons d’apprentissage, cadre applicatif de cette thèse. Nous nous intéressons aux alternatives qui se basent sur la définition de modèle(s) de covariance(s) particulier(s) et qui permettent de réduire le nombre de paramètres à estimer. / The present thesis finds itself within the framework of analyzing and classifying electroencephalogram signals (EEG) using discriminant analysis. Those multi-sensor signals which are, by nature, highly correlated spatially and temporally are considered, in this work, in the timefrequency domain. In particular, we focus on low-frequency evoked-related potential-type signals (ERPs) that are well described in the wavelet domain. Thereafter, we will consider signals represented by multi-scale coefficients and that have a matrix structure electrodes × coefficients. Moreover, EEG signals are seen as a mixture between the signal of interest that we want to extract and spontaneous activity (also called "background noise") which is overriding. The main problematic is here to distinguish signals from different experimental conditions (class). In the binary case, we focus on the probabilistic approach of the discriminant analysis and Gaussian mixtures are used, describing in each class the signals in terms of fixed (mean) and random components. The latter, characterized by its covariance matrix, allow to model different variability sources. The estimation of this matrix (and of its inverse) is essential for the implementation of the discriminant analysis and can be deteriorated by high-dimensional data and/or by small learning samples, which is the application framework of this thesis. We are interested in alternatives that are based on specific covariance model(s) and that allow to decrease the number of parameters to estimate.

The raw data related to the second study of this thesis (Chapter 3) is available online in the section of supporting information at https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0232677. These files present the following data: S1 File. The pattern of foot orthosis depression/reformation for healthy subjects during walking with sport versus regular foot orthosis. S2 File. Raw data for the training session of sport foot orthosis. This Excel file consists three sheets in which the position of triad markers, the orientation of triad markers and the position of markers on plantar surface of foot orthosis are provided respectively. S3 File. Raw data for walking with sport foot orthosis. This Excel file consists two sheets in which the position of triad markers and the orientation of triad markers are provided respectively for subject 1. S4 File. The results of each participant during walking with sport foot orthosis. This .mat file includes “DispEachPoint” and “DispEachPointMean” which shows the displacement of each predicted marker on foot orthosis plantar surface during stance phase of walking relative to its corresponding position in static non weight-bearing for each trial and the average of trials respectively. In addition, “loc_stance” and “loc_meanstance” show the location of each predicted marker during stance phase of walking. “peaks” and “peaksMean” represent the minimum (depression) and maximum (reformation) value of displacement during walking S5 File. The results of each participant during walking with regular foot orthosis. This .mat file includes “DispEachPoint” and “DispEachPointMean” which shows the displacement of each predicted marker on foot orthosis plantar surface during stance phase of walking relative to its corresponding position in static non weight-bearing for each trial and the average of trials respectively. In addition, “loc_stance” and “loc_meanstance” show the location of each predicted marker during stance phase of walking. “peaks” and “peaksMean” represent the minimum (depression) and maximum (reformation) value of displacement during walking / Les orthèses plantaires (OP) sont des dispositifs médicaux fréquemment utilisés pour réduire les douleurs et blessures de surutilisation, notamment chez les personnes ayant les pieds plats. Le port d'OP permettrait de corriger les altérations biomécaniques attribuées à la déformation du pied plat, que sont la perte de l’arche longitudinale médiale et la pronation excessive du pied. Cependant, le manque de compréhension de la fonction des OP entraine une grande variabilité des OP prescrites en milieu clinique. L'objectif de cette thèse est d'approfondir les connaissances sur l’effet des OP sur la biomécanique, de quantifier les déformations des OP à la marche et de mettre en relation ces déformations avec la biomécanique du pied. La première étude a évalué la manière dont les différentes conceptions d'OP imposent des modifications dans le mouvement et le chargement appliqué sur le pied. Cet objectif a été atteint grâce à une revue systématique traitant des effets des OP sur la cinématique et la cinétique du membre inférieur pendant la marche chez des personnes ayant des pieds normaux. Les critères d'inclusion ont réduit les études à celles qui ont fait état des résultats pour les géométries les plus fréquentes des OP, à savoir les biseaux, les supports d’arche et les stabilisateurs de talon. La revue a mis en évidence que les orthèses avec un biseau médial peuvent réduire le moment d'éversion de la cheville. Aucune évidence significative n'a été trouvée dans notre méta-analyse sur l'efficacité des orthèses incluant des supports d’arche ou des stabilisateurs de talon. Les différents procédés et matériaux utilisés dans la conception des OP ainsi que les caractéristiques des pieds des participants pourraient expliquer la variabilité retrouvée au regard des effets des OP sur la biomécanique. La deuxième étude a apporté des informations précieuses et inédites sur le comportement dynamique des OP à la marche. La cinématique du contour des OP a été utilisée pour prédire la déformation de leur surface plantaire pendant la marche chez 13 individus ayant des pieds normaux en utilisant un réseau de neurones artificiels. Une erreur moyenne inférieure à 0,6 mm a été obtenue pour nos prédictions. En plus de la précision des prédictions, le modèle a été capable de différencier le patron de déformations pour deux OP de rigidités différentes et entre les participants inclus dans l’étude. Enfin, dans une troisième étude, nous avons identifié la relation entre la déformation des OP personnalisées et la biomécanique du pied à la marche chez 17 personnes avec des pieds plats. L'utilisation de modèles linéaires mixtes a permis d’exprimer les variations de la déformation des OP dans différentes régions en fonction des variables cinématiques du pied et de pressions plantaires. Cette étude a montré que l'interaction pied-OP varie selon les différentes régions de l’OP et les différentes phases du cycle de marche. Ainsi, des lignes directrices préliminaires ont été fournies afin de standardiser et optimiser la conception des OP. Dans l'ensemble, les résultats de cette thèse justifient l'importance d’'intégrer des caractéristiques dynamiques du pied de chaque individu dans la conception d'OP personnalisées. Des études futures pourraient étendre les modèles de prédiction de l'interaction pied-OP en incluant d'autres paramètres biomécaniques tels que les moments articulaires, les activations musculaires et la morphologie du pied. De tels modèles pourraient être utilisés pour développer des fonctions coût pour l'optimisation de la conception des OP par une approche itérative utilisant la simulation par les éléments finis. / Foot orthoses (FOs) are frequently used medical devices to manage overuse injuries and pain in flatfoot individuals. Wearing FOs can result in improving the biomechanical alterations attributed to flatfoot deformity such as the loss of medial longitudinal arch and excessive foot pronation. However, a lack of a clear understanding of the function of FOs contributes to the highly variable FOs prescribed in clinical practice. The objective of this thesis was to deepen the knowledge about the biomechanical outcomes of FOs and to formulate the dynamic behaviour of FOs as a function of foot biomechanics during gait. The primary study investigated how different designs of FOs impose alterations in foot motion and loading. This objective was achieved through a systematic review of all literature reporting the kinematics and kinetics of the lower body during walking with FOs in healthy individuals. The inclusion criteria narrowed the studies to the ones which reported the outcomes for common designs of FOs, namely posting, arch support, and heel support. The review identified some evidence that FOs with medial posting can decrease ankle eversion moment. No significant evidence was found in our meta-analysis for the efficiency of arch supported and heel supported FOs. The findings of this study revealed that differences in FO design and material as well as foot characteristics of participants could explain the variations in biomechanical outcomes of FOs. The second study provided valuable information on the dynamic behaviour of customized FOs. The kinematics of FO contour was used to predict the deformation of FO plantar surface in 13 healthy individuals during walking using an artificial intelligence approach. An average error below 0.6 mm was achieved for our predictions. In addition to the prediction accuracy, the model was capable to differentiate between different rigidities of FOs and between included participants in terms of range and pattern of deformation. Finally, the third study identified the relationship between the deformation of customized FOs and foot biomechanics in 17 flatfoot individuals during walking. The use of linear mixed models made it possible to identify the variables of foot kinematics and region-dependent plantar pressure that could explain the variations in FO deformation. This study showed that the foot-FO interaction changes over different regions of FO and different phases of gait cycle. In addition, some preliminary guidelines were provided to standardize and optimize the design of FOs. Overall, the results of this thesis justify the importance of incorporating the dynamic characteristics of each individual’s foot into the design of customized FOs. Future studies can extend the predictive models for foot-FO interactions by including other determinants of foot biomechanics such as joint moments, muscle activation, and foot morphology. Based on such extended models, the cost functions could be devised for optimizing the designs of customized 3D printed FOs through an iterative approach using finite element modeling.