Made available in DSpace on 2016-06-02T20:06:09Z (GMT). No. of bitstreams: 1 6004.pdf: 835734 bytes, checksum: b9cae4e00b44525ff06f6dfea7cfe687 (MD5) Previous issue date: 2014-03-28 / Universidade Federal de Sao Carlos / Correlated data sets with nonlinear structure are common in many areas such as biostatistics, pharmacokinetics and longitudinal studies. Nonlinear mixed-effects models are useful tools to analyse those type of problems. In this dissertation, a generalization to this models is proposed, namely by semiparametric partially nonlinear mixed-effects model (MMSPNL), with a nonparametric function to model the mean of the response variable. It assumes that the mean of the interest variable is explained by a nonlinear function, which depends on fixed effects parameters and explanatory variables, and by a nonparametric function. Such nonparametic function is quite flexible, allowing a better adequacy to the functional form that underlies the data. The random effects are included linearly to the model, which simplify the expression of the response variable distribution and enables the model to take into account the within-group correlation structure. It is assumed that the random errors and the random effects jointly follow a multivariate normal distribution. Relate to the nonparametric function, it is deal with the P-splines smoothing technique. The methodology to obtain the parameters estimates is penalized maximum likelihood method. The random effects may be obtained by using the Empirical Bayes method. The goodness of the model and identification of potencial influent observation is verified with the local influence method and a residual analysis. The pharmacokinetic data set, in which the anti-asthmatic drug theophylline was administered to 12 subjects and serum concentrations were taken at 11 time points over the 25 hours (after being administered), was re-analysed with the proposed model, exemplifying its uses and properties. / Dados correlacionados com estrutura não linear são comuns em bioestatística, estudos farmacocinéticos e longitudinais. Modelos mistos não lineares são ferramentas úteis para se analisar esses tipos de problemas. Nesta dissertação, propõe-se uma generalização desses modelos, chamada de modelo misto semiparamétrico parcialmente não linear (MMSPNL), com uma função não paramétrica para se modelar a média da variável resposta. Assume-se que a média da variável de interesse é explicada por uma função não linear, que depende de parâmetros de efeitos fixos e variáveis explicativas, e por uma função não paramétrica. Tal função não paramétrica possui grande flexibilidade, permitindo uma melhor adequação à forma funcional que subjaz aos dados. Os efeitos aleatórios são incluídos linearmente ao modelo, o que simplifica a expressão da distribuição da variável resposta e permite considerar a estrutura de correlação intra grupo. É assumido que os erros aleatórios e efeitos aleatórios conjuntamente seguem uma distribuição normal multivariada. Em relação a função não paramétrica, utiliza-se a técnica de suavização com P-splines. A metodologia para se obterem as estimativas dos parâmetros é o método de máxima verossimilhança penalizada. Os efeitos aleatórios podem ser obtidos usando-se o método de Bayes empírico. A qualidade do modelo e a identificação de observações aberrantes é verificada pelo método de influência local e por análise de resíduos. O conjunto de dados farmacocinéticos, em que o antiasmático theophylline foi administrado a 12 sujeitos e concentrações séricas foram tomadas em 11 instantes de tempo durante as 25 horas (após ser administrado), foi reanalisado com o modelo proposto, exemplificando seu uso e propriedades.

Par delà les études transversales, étudier l'évolution temporelle de phénomènes connait un intérêt croissant. En effet, pour comprendre un phénomène, il semble plus adapté de comparer l'évolution des marqueurs de celui-ci au cours du temps plutôt que ceux-ci à un stade donné. Le suivi de maladies neuro-dégénératives s'effectue par exemple par le suivi de scores cognitifs au cours du temps. C'est également le cas pour le suivi de chimiothérapie : plus que par l'aspect ou le volume des tumeurs, les oncologues jugent que le traitement engagé est efficace dès lors qu'il induit une diminution du volume tumoral.L'étude de données longitudinales n'est pas cantonnée aux applications médicales et s'avère fructueuse dans des cadres d'applications variés tels que la vision par ordinateur, la détection automatique d'émotions sur un visage, les sciences sociales, etc.Les modèles à effets mixtes ont prouvé leur efficacité dans l'étude des données longitudinales, notamment dans le cadre d'applications médicales. Des travaux récent (Schiratti et al., 2015, 2017) ont permis l'étude de données complexes, telles que des données anatomiques. L'idée sous-jacente est de modéliser la progression temporelle d'un phénomène par des trajectoires continues dans un espace de mesures, que l'on suppose être une variété riemannienne. Sont alors estimées conjointement une trajectoire moyenne représentative de l'évolution globale de la population, à l'échelle macroscopique, et la variabilité inter-individuelle. Cependant, ces travaux supposent une progression unidirectionnelle et échouent à décrire des situations telles que la sclérose en plaques ou le suivi de chimiothérapie. En effet, pour ces pathologies, vont se succéder des phases de progression, de stabilisation et de remision de la maladie, induisant un changement de la dynamique d'évolution globale.Le but de cette thèse est de développer des outils méthodologiques et algorithmiques pour l’analyse de données longitudinales, dans le cas de phénomènes dont la dynamique d'évolution est multiple et d'appliquer ces nouveaux outils pour le suivi de chimiothérapie. Nous proposons un modèle non-linéaire à effets mixtes dans lequel les trajectoires d'évolution individuelles sont vues comme des déformations spatio-temporelles d'une trajectoire géodésique par morceaux et représentative de l'évolution de la population. Nous présentons ce modèle sous des hypothèses très génériques afin d'englober une grande classe de modèles plus spécifiques.L'estimation des paramètres du modèle géométrique est réalisée par un estimateur du maximum a posteriori dont nous démontrons l'existence et la consistance sous des hypothèses standards. Numériquement, du fait de la non-linéarité de notre modèle, l'estimation est réalisée par une approximation stochastique de l'algorithme EM, couplée à une méthode de Monte-Carlo par chaînes de Markov (MCMC-SAEM). La convergence du SAEM vers les maxima locaux de la vraisemblance observée ainsi que son efficacité numérique ont été démontrées. En dépit de cette performance, l'algorithme SAEM est très sensible à ses conditions initiales. Afin de palier ce problème, nous proposons une nouvelle classe d'algorithmes SAEM dont nous démontrons la convergence vers des minima locaux. Cette classe repose sur la simulation par une loi approchée de la vraie loi conditionnelle dans l'étape de simulation. Enfin, en se basant sur des techniques de recuit simulé, nous proposons une version tempérée de l'algorithme SAEM afin de favoriser sa convergence vers des minima globaux. / Beyond transversal studies, temporal evolution of phenomena is a field of growing interest. For the purpose of understanding a phenomenon, it appears more suitable to compare the evolution of its markers over time than to do so at a given stage. The follow-up of neurodegenerative disorders is carried out via the monitoring of cognitive scores over time. The same applies for chemotherapy monitoring: rather than tumors aspect or size, oncologists asses that a given treatment is efficient from the moment it results in a decrease of tumor volume. The study of longitudinal data is not restricted to medical applications and proves successful in various fields of application such as computer vision, automatic detection of facial emotions, social sciences, etc.Mixed effects models have proved their efficiency in the study of longitudinal data sets, especially for medical purposes. Recent works (Schiratti et al., 2015, 2017) allowed the study of complex data, such as anatomical data. The underlying idea is to model the temporal progression of a given phenomenon by continuous trajectories in a space of measurements, which is assumed to be a Riemannian manifold. Then, both a group-representative trajectory and inter-individual variability are estimated. However, these works assume an unidirectional dynamic and fail to encompass situations like multiple sclerosis or chemotherapy monitoring. Indeed, such diseases follow a chronic course, with phases of worsening, stabilization and improvement, inducing changes in the global dynamic.The thesis is devoted to the development of methodological tools and algorithms suited for the analysis of longitudinal data arising from phenomena that undergo multiple dynamics and to apply them to chemotherapy monitoring. We propose a nonlinear mixed effects model which allows to estimate a representative piecewise-geodesic trajectory of the global progression and together with spacial and temporal inter-individual variability. Particular attention is paid to estimation of the correlation between the different phases of the evolution. This model provides a generic and coherent framework for studying longitudinal manifold-valued data.Estimation is formulated as a well-defined maximum a posteriori problem which we prove to be consistent under mild assumptions. Numerically, due to the non-linearity of the proposed model, the estimation of the parameters is performed through a stochastic version of the EM algorithm, namely the Markov chain Monte-Carlo stochastic approximation EM (MCMC-SAEM). The convergence of the SAEM algorithm toward local maxima of the observed likelihood has been proved and its numerical efficiency has been demonstrated. However, despite appealing features, the limit position of this algorithm can strongly depend on its starting position. To cope with this issue, we propose a new version of the SAEM in which we do not sample from the exact distribution in the expectation phase of the procedure. We first prove the convergence of this algorithm toward local maxima of the observed likelihood. Then, with the thought of the simulated annealing, we propose an instantiation of this general procedure to favor convergence toward global maxima: the tempering-SAEM.

La vancomycine est l'un des antibiotiques les plus prescrits, principalement utilisé pour les infections suspectées et confirmées à Staphylococcus aureus résistant à la méthicilline (SARM). Les infections par des souches de SARM font peser une charge importante sur le système de santé, à laquelle s'ajoute l'incertitude qui demeure quant à la posologie optimale de la vancomycine. Les récentes lignes directrices révisées sur le suivi thérapeutique de la vancomycine, publiées en 2020, avalisent principalement l'estimation directe de l'aire sous la courbe de concentration en fonction du temps (AUC) par l'utilisation d'équations bayésiennes ou pharmacocinétiques (PK) de premier ordre pour le suivi thérapeutique. Pour mieux informer la posologie de la vancomycine, nous avons d'abord mis à jour une revue précédente des analyses pharmacocinétiques de population (PopPK) de la vancomycine publiées chez les adultes et les enfants. Pour ce faire, nous avons déterminé les caractéristiques des modèles pharmacocinétiques rapportés et identifié les diverses sources potentielles de variabilité observées dans différentes sous-populations particulières. Motivés par la controverse existante autour des nouvelles directives de surveillance thérapeutique de la vancomycine et par l'absence d'une étude approfondie des méthodes recommandées, nous avons recueilli des données hospitalières et construit un cadre de modélisation qui nous a permis d'évaluer les recommandations des directives sur les méthodes de surveillance, tout en considérant une variété de scénarios et d'hypothèses cliniques réalistes. Notre analyse a confirmé que la surveillance bayésienne est la méthode la plus rapide et la plus fiable, à condition qu'elle soit correctement mise en œuvre, la plus importante condition pour cela étant l'utilisation de modèles bayésiens a priori appropriés. De plus, nous avons montré que le suivi bayésien ne nécessite pas nécessairement des niveaux de concentration de types creux ou pic et peut en fait être réalisé en utilisant un niveau aléatoire. Aussi, nous avons démontré que l'utilisation correcte des équations pharmacocinétiques de premier ordre exigerait au moins deux mesures de concentration à l'état d'équilibre. L’utilisation de la méthode creux-seulement de la vancomycine à l'état d'équilibre peut être tout aussi efficace dans certaines situations que nous avons explorées ici. En considérant la larges étendue et la grande variabilité des populations traitées à la vancomycine en termes d'âge, de gravité de l'infection et de scénarios cliniques, cette thèse adopte un regard objectif pour évaluer quantitativement le gain potentiel de chaque méthode de surveillance de la vancomycine, en explorant leur adéquation en termes d'effort nécessaire, de disponibilité des ressources et de gain potentiel. Compte tenu des lignes directrices sur la vancomycine récemment publiées et de la controverse qui persiste, nous pensons que cette thèse a permis de démêler la variété et la complexité de l'utilisation de la vancomycine et a apporté un éclairage supplémentaire plus objectifvement informé vers un suivi thérapeutique optimal de la vancomycine. / Vancomycin is among the most prescribed antibiotics, mainly used for suspected and confirmed methicillin-resistant Staphylococcus aureus (MRSA) infections. Infections by MRSA strains carry a substantial burden on the health care system, supplemented by the uncertainty that remains regarding vancomycin optimal dosing. The recent revised vancomycin therapeutic monitoring guidelines published in 2020, endorsed primarily the direct estimation of area under the concentration-time curve (AUC) through the use of Bayesian or first-order pharmacokinetic (PK) equations monitoring. To better inform vancomycin dosing, we first updated a previous review of published vancomycin population pharmacokinetic (PopPK) analysis in both adults and children. This was accomplished by determining the characteristics of the reported pharmacokinetic models and identifying the potential various sources of variability observed in different special subpopulations. Motivated by the existing controversy around the new vancomycin therapeutic monitoring guidelines and the lack of a thorough investigation of the recommended methods, we collected hospital data and built a modeling framework that allowed us to assess the guideline recommendations of monitoring methods while considering a variety of realistic clinical scenarios and assumptions. Our analysis affirmed that Bayesian monitoring is the fastest and most reliable method, conditional on its proper implementation, the most important being the use of proper Bayesian priors. Moreover, we showed that Bayesian monitoring does not necessarily require trough or peak concentration levels and can in fact be performed using a random level. Proper use of first-order PK equations required at least two steady-state concentration measurements. Alternatively, simpler trough-only vancomycin monitoring near steady-state can be as effective in certain cases that we explored here. By considering the wide ranges and the high variability in populations treated with vancomycin in terms of age, the severity of infection, and clinical scenarios, this thesis takes an objective look to quantitatively assess the potential gain of each vancomycin drug monitoring method, by investigating their suitability in terms of the effort needed, the availability of resources and the resulting gain. Considering the recently released vancomycin guidelines and the ensuing controversies between well-established clinical teams, we believe that this dissertation helped untangle the variety and complexity of vancomycin use and brought additional insights towards a more objective and optimal vancomycin therapeutic monitoring.

Made available in DSpace on 2016-06-02T20:04:53Z (GMT). No. of bitstreams: 1 6714.pdf: 1130315 bytes, checksum: 4ce881df9c6c0f6451cae6908855d277 (MD5) Previous issue date: 2015-01-14 / Financiadora de Estudos e Projetos / We present a class of nonlinear truncated mixed-effects models where the truncation nature of the data is incorporated into the statistical model by assuming that the variable of interest, namely the truncated variable, follows a truncated distribution which, in turn, corresponds to a conditional distribution obtained by restricting the support of a given probability distribution function. The family of nonlinear truncated mixed-effects models for location and scale is constructed based on the perspective of nonlinear generalized mixed-effects models and by assuming that the distribution of response variable belongs to a truncated class of distributions indexed by a location and a scale parameter. The location parameter of the response variable is assumed to be associated with a continuous nonlinear function of covariates and unknown parameters and with unobserved random effects, and the scale parameter of the responses is assumed to be characterized by a continuous function of the covariates and unknown parameters. The proposed truncated nonlinear mixed-effects models are constructed assuming both random truncation limits; however, truncated nonlinear mixed-effects models with fixed known limits are readily obtained as particular cases of these models. For models constructed under the assumption of random truncation limits, the likelihood function of the observed data shall be a function both of the parameters of the truncated distribution of the truncated variable and of the parameters of the distribution of the truncation variables. For the particular case of fixed known truncation limits, the likelihood function of the observed data is a function only of the parameters of the truncated distribution assumed for the variable of interest. The likelihood equation resulting from the proposed truncated nonlinear regression models do not have analytical solutions and thus, under the frequentist inferential perspective, the model parameters are estimated by direct maximization of the log-likelihood using an iterative procedure. We also consider diagnostic analysis to check for model misspecification, outliers and influential observations using standardized residuals, and global and local influence metrics. Under the Bayesian perspective of statistical inference, parameter estimates are computed based on draws from the posterior distribution of parameters obtained using an Markov Chain Monte Carlo procedure. Posterior predictive checks, Bayesian standardized residuals and a Bayesian influence measures are considered to check for model adequacy, outliers and influential observations. As Bayesian model selection criteria, we consider the sum of log -CPO and a Bayesian model selection procedure using a Bayesian mixture model framework. To illustrate the proposed methodology, we analyze soil-water retention, which are used to construct soil-water characteristic curves and which are subject to truncation since soil-water content (the proportion of water in soil samples) is limited by the residual soil-water content and the saturated soil-water content. / Neste trabalho, apresentamos uma classe de modelos não lineares truncados mistos onde a característica de truncamento dos dados é incorporada ao modelo estatístico assumindo-se que a variável de interesse, isto é, a variável truncada, possui uma função de distribuição truncada que, por sua vez, corresponde a uma função de distribuição condicional obtida ao se restringir o suporte de alguma função de distribuição de probabilidade. A família de modelos não lineares truncados mistos para locação e escala é construída sob a perspectiva de modelos não lineares generalizados mistos e considerando uma classe de distribuições indexadas por parâmetros de locação e escala. Assumimos que o parâmetro de locação da variável resposta é associado a uma função não linear contínua de um conjunto de covariáveis e parâmetros desconhecidos e a efeitos aleatórios não observáveis, e que o parâmetro de escala das respostas pode ser caracterizado por uma função contínua das covariáveis e de parâmetros desconhecidos. Os modelos não lineares truncados mistos para locação e escala, aqui apresentados, são construídos supondo limites de truncamento aleatórios, porém, modelos não lineares truncados mistos com limites fixos e conhecidos são prontamente obtidos como casos particulares desses modelos. Nos modelos construídos sob a suposição de limites de truncamentos aleatórios, a função de verossimilhança é escrita em função dos parâmetros da distribuição da variável resposta truncada e dos parâmetros das distribuições das variáveis de truncamento. Para o caso particular de limites fixos e conhecidos, a função de verossimilhança será apenas uma função dos parâmetros da distribuição truncada assumida para a variável resposta de interesse. As equações de verossimilhança dos modelos, aqui propostos, não possuem soluções analíticas e, sob a perspectiva frequentista de inferência estatística, os parâmetros do modelo são estimados pela maximização direta da função de log-verossimilhança via um procedimento iterativo. Consideramos, também, uma análise de diagnóstico para verificar a adequação do modelo, observações discrepantes e/ou influentes, usando resíduos padronizados e medidas de influência global e influência local. Sob a perspectiva Bayesiana de inferência estatística, as estimativas dos parâmetros dos modelos propostos são definidas como as médias a posteriori de amostras obtidas via um algoritmo do tipo cadeia de Markov Monte Carlo das distribuições a posteriori dos parâmetros. Para a análise de diagnóstico Bayesiano do modelo, consideramos métricas de avaliação preditiva a posteriori, resíduos Bayesianos padronizados e a calibração de casos para diagnóstico de influência. Como critérios Bayesianos de seleção de modelos, consideramos a soma de log -CPO e um critério de seleção de modelos baseada na abordagem Bayesiana de mistura de modelos. Para ilustrar a metodologia proposta, analisamos dados de retenção de água em solo, que são usados para construir curvas de retenção de água em solo e que estão sujeitos a truncamento pois as medições de umidade de água (a proporção de água presente em amostras de solos) são limitadas pela umidade residual e pela umidade saturada do solo amostrado.

Emergency departments are fundamental for providing high-quality care, and their operations directly impact the logistics of the hospitals in their entirety. Poor emergency department performance leads to delays, prolonged hospitalization, and improper allocation of resources, reducing the quality of the provided care and increasing costs. Describing the variability embedded in real clinical data in a useful way is essential for improving the organization of hospitals in the near future. However, it is a challenging task due to clinical complexity and the lack of an established bridge between logistic systems and the clinical insights of the hospital. Therefore, this work aims to design and implement a simplified process model describing patient flow within an emergency department, which could allow the evaluation of the clinical impact of complex patient characteristics on the system's logistics. To achieve this, a novel nonlinear mixed-effects approach with hospital medical records was applied to design patient flow within the emergency department in the form of a multi-state Markov process. Four independent training data samples were extracted from the main dataset. For each of them, the set of covariates that could lead to the most significant improvement in the values of the employed likelihood indicators was selected. Through statistical tests, analysis of the outputs, and a validation process carried out on a fifth and independent dataset, it was possible to obtain a final model containing the most relevant and significant covariates for describing each of the modeled state transitions and confirming their clinical meaningfulness and relevance. The results achieved in this thesis can lead to future improvement of the healthcare logistics systems by extending the use of nonlinear mixed-effects approaches to the estimation of the covariate impact on emergency department flows. / Akutmottagningar är centrala för att tillhandahålla högkvalitativ vård. Deras verksamhet har en direkt inverkan på sjukhusens logistik i helhet. Undermålig prestation i en akutmottagning leder till förseningar, förlängd sjukhusvistelse för patienter och olämpliga resursfördelningar, som i sin tur försämrar kvaliteten på den erbjudna vården, samt ökar kostnader. Därför är det viktigt att beskriva den variabilitet som är inbäddad i kliniskt data för att kunna förbättra strukturen av sjukhus i den närmaste framtiden. Emellertid är det ett utmanande uppdrag på grund av den kliniska komplexiteten och bristen på en etablerad bro mellan logistiska system och insikter om den kliniska situationen på sjukhuset. Detta examensarbete ämnar därför designa och implementera en förenklad processmodel som beskriver patientflödet inom en akutmottagning, vilket skulle kunna tillåta evaluering av vad för klinisk inverkan patienters komplexa egenskaper har på systemets logistik. För att uppnå detta tillämpades ett nytt icke-linjärt tillvägagångssätt för blandade effekter med patientjournaler, med syfte att designa patientflöde inom akutmottagningen i form av en Markovprocess i flera tillstånd. Fyra oberoende urvalsgrupper med övningsdata extraherades från huvuddatasetet och för var och en av dem valdes den uppsättning kovariat som hade möjlighet att leda till den största förbättringen i de applicerade sannolikhetsindikatorerna. Genom statistiska test, analys av uteffekten och en valideringsprocess utförd på en femte oberoende urvalsgrupp, möjliggjordes framtagandet av en slutgiltig modell innehållande de mest relevanta och signifikanta kovariat för att beskriva var och en av de modellerade tillståndsövergångarna, och bekräfta dess kliniska betydelse och relevans. De resultat som uppnåddes i det här examensarbetet har potential att i framtiden leda till förbättring av sjukvårdens logistiksystem, genom att utvidga användningen av icke-linjära blandade effektmodeller för att uppskatta kovariatinverkan på akutmottagningsflöden.