With approximately nine million new cases and the attributable cause of death of an estimated two millions people every year there is an urgent need for new and effective drugs and treatment regimens targeting tuberculosis. The tuberculosis drug development pathway is however not ideal, containing non-predictive model systems and unanswered questions that may increase the risk of failure during late-phase drug development. The aim of this thesis was hence to develop pharmacometric tools in order to optimize the development of new anti-tuberculosis drugs and treatment regimens. The General Pulmonary Distribution model was developed allowing for prediction of both rate and extent of distribution from plasma to pulmonary tissue. A distribution characterization that is of high importance as most current used anti-tuberculosis drugs were introduced into clinical use without considering the pharmacokinetic properties influencing drug distribution to the site of action. The developed optimized bronchoalveolar lavage sampling design provides a simplistic but informative approach to gathering of the data needed to allow for a model based characterization of both rate and extent of pulmonary distribution using as little as one sample per subject. The developed Multistate Tuberculosis Pharmacometric model provides predictions over time for a fast-, slow- and non-multiplying bacterial state with and without drug effect. The Multistate Tuberculosis Pharmacometric model was further used to quantify the in vitro growth of different strains of Mycobacterium tuberculosis and the exposure-response relationships of three first line anti-tuberculosis drugs. The General Pharmacodynamic Interaction model was successfully used to characterize the pharmacodynamic interactions of three first line anti-tuberculosis drugs, showing the possibility of distinguishing drug A’s interaction with drug B from drug B’s interaction with drug A. The successful separation of all three drugs effect on each other is a necessity for future work focusing on optimizing the selection of anti-tuberculosis combination regimens. With a focus on pharmacokinetics and pharmacodynamics, the work included in this thesis provides multiple new methods and approaches that individually, but maybe more important the combination of, has the potential to inform development of new but also to provide additional information of the existing anti-tuberculosis drugs and drug regimen.

Treatment of patients with multiple sclerosis (MS) and development of new therapies have been challenging due to the disease complexity and slow progression, and the limited sensitivity of available clinical outcomes. Modeling and simulation has become an increasingly important component in drug development and in post-marketing optimization of use of medication. This thesis focuses on development of pharmacometric models for characterization and quantification of the relationships between drug exposure, biomarkers and clinical endpoints in relapse-remitting MS (RRMS) following cladribine treatment. A population pharmacokinetic model of cladribine and its main metabolite, 2-chloroadenine, was developed using plasma and urine data. The renal clearance of cladribine was close to half of total elimination, and was found to be a linear function of creatinine clearance (CRCL). Exposure-response models could quantify a clear effect of cladribine tablets on absolute lymphocyte count (ALC), burden of disease (BoD), expanded disability status scale (EDSS) and relapse rate (RR) endpoints. Moreover, they gave insight into disease progression of RRMS. This thesis further demonstrates how integrated modeling framework allows an understanding of the interplay between ALC and clinical efficacy endpoints. ALC was found to be a promising predictor of RR. Moreover, ALC and BoD were identified as predictors of EDSS time-course. This enables the understanding of the behavior of the key outcomes necessary for the successful development of long-awaited MS therapies, as well as how these outcomes correlate with each other. The item response theory (IRT) methodology, an alternative approach for analysing composite scores, enabled to quantify the information content of the individual EDSS components, which could help improve this scale. In addition, IRT also proved capable of increasing the detection power of potential drug effects in clinical trials, which may enhance drug development efficiency. The developed nonlinear mixed-effects models offer a platform for the quantitative understanding of the biomarker(s)/clinical endpoint relationship, disease progression and therapeutic response in RRMS by integrating a significant amount of knowledge and data.

General attrition rates in drug development pipeline have been recognized as a necessity to shift gears towards new methodologies that allow earlier and correct decisions, and the optimal use of all information accrued throughout the process. The quantitative science of pharmacometrics using pharmacokinetic-pharmacodynamic models was identified as one of the strategies core to this renaissance. Coupled with Optimal Design (OD), they constitute together an attractive toolkit to usher more rapidly and successfully new agents to marketing approval. The general aim of this thesis was to investigate how the use of novel pharmacometric methodologies can improve the design and analysis of clinical trials within drug development. The implementation of a Monte-Carlo Mapped power method permitted to rapidly generate multiple hypotheses and to adequately compute the corresponding sample size within 1% of the time usually necessary in more traditional model-based power assessment. Allowing statistical inference across all data available and the integration of mechanistic interpretation of the models, the performance of this new methodology in proof-of-concept and dose-finding trials highlighted the possibility to reduce drastically the number of healthy volunteers and patients exposed to experimental drugs. This thesis furthermore addressed the benefits of OD in planning trials with bio analytical limits and toxicity constraints, through the development of novel optimality criteria that foremost pinpoint information and safety aspects. The use of these methodologies showed better estimation properties and robustness for the ensuing data analysis and reduced the number of patients exposed to severe toxicity by 7-fold.  Finally, predictive tools for maximum tolerated dose selection in Phase I oncology trials were explored for a combination therapy characterized by main dose-limiting hematological toxicity. In this example, Bayesian and model-based approaches provided the incentive to a paradigm change away from the traditional rule-based “3+3” design algorithm. Throughout this thesis several examples have shown the possibility of streamlining clinical trials with more model-based design and analysis supports. Ultimately, efficient use of the data can elevate the probability of a successful trial and increase paramount ethical conduct.

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.

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.