Este trabalho tem como objetivo aplicar a teoria de modelos mistos ao estudo do teor de nitrogênio e carbono no solo, em diversas profundidades. Devido a grande quantidade de matéria orgânica no solo, o teor de nitrogênio e carbono apresentam alta variabilidade nas primeiras profundidades, além de apresentar um comportamento não linear. Assim, fez-se necessário utilizar a abordagem de modelos não lineares mistos a dados longitudinais. A utilização desta abordagem proporciona um modelo que permite modelar dados não lineares, com heterogeneidade de variâncias, fornecendo uma curva para cada amostra. / This paper has as an objective to apply the theory of mixed models to the content of nitrogen and carbon in the soil at various depths. Due to the large amount of organic material in the soil, the content of nitrogen and carbon present high variability in the depths of soil surface, and present a nonlinear behavior. Thus, it was necessary to use the approach of nonlinear mixed models to longitudinal data analysis. The use of this approach provides a model that allows to model nonlinear data with heterogeneity of variances by providing a curve for each sample.

The cost of releasing a new drug on the market has increased rapidly in the last decade. The reasons for this increase vary with the drug, but the need to make correct decisions earlier in the drug development process and to maximize the information gained throughout the process is evident. Optimal experimental design (OD) describes the procedure of maximizing relevant information in drug development and drug treatment processes. While various optimization criteria can be considered in OD, the most common is to optimize the unknown model parameters for an upcoming study. To date, OD has mainly been used to optimize the independent variables, e.g. sample times, but it can be used for any design variable in a study. This thesis addresses the OD of multiple continuous or discrete design variables for nonlinear mixed effects models. The methodology for optimizing and the optimization of different types of models with either continuous or discrete data are presented and the benefits of OD for such models are shown. A software tool for optimizing these models in parallel is developed and three OD examples are demonstrated: 1) optimization of an intravenous glucose tolerance test resulting in a reduction in the number of samples by a third, 2) optimization of drug compound screening experiments resulting in the estimation of nonlinear kinetics and 3) an individual dose-finding study for the treatment of children with ciclosporin before kidney transplantation resulting in a reduction in the number of blood samples to ~27% of the original number and an 83% reduction in the study duration. This thesis uses examples and methodology to show that studies in drug development and drug treatment can be optimized using nonlinear mixed effects OD. This provides a tool than can lower the cost and increase the overall efficiency of drug development and drug treatment.

Este trabalho tem como objetivo aplicar a teoria de modelos mistos ao estudo do teor de nitrogênio e carbono no solo, em diversas profundidades. Devido a grande quantidade de matéria orgânica no solo, o teor de nitrogênio e carbono apresentam alta variabilidade nas primeiras profundidades, além de apresentar um comportamento não linear. Assim, fez-se necessário utilizar a abordagem de modelos não lineares mistos a dados longitudinais. A utilização desta abordagem proporciona um modelo que permite modelar dados não lineares, com heterogeneidade de variâncias, fornecendo uma curva para cada amostra. / This paper has as an objective to apply the theory of mixed models to the content of nitrogen and carbon in the soil at various depths. Due to the large amount of organic material in the soil, the content of nitrogen and carbon present high variability in the depths of soil surface, and present a nonlinear behavior. Thus, it was necessary to use the approach of nonlinear mixed models to longitudinal data analysis. The use of this approach provides a model that allows to model nonlinear data with heterogeneity of variances by providing a curve for each sample.

Despite the growing promise of pharmaceutical research, inferior experimentation or interpretation of data can inhibit breakthrough molecules from finding their way out of research institutions and reaching patients. This thesis provides evidence that better characterization of pre-clinical and clinical data can be accomplished using non-linear mixed effect modeling (NLMEM) and more effective experiments can be conducted using optimal design (OD).  To demonstrate applicability of NLMEM and OD in pre-clinical applications, in vitro ligand binding studies were examined. NLMEMs were used to evaluate precision and accuracy of ligand binding parameter estimation from different ligand binding experiments using sequential (NLR) and simultaneous non-linear regression (SNLR). SNLR provided superior resolution of parameter estimation in both precision and accuracy compared to NLR.  OD of these ligand binding experiments for one and two binding site systems including commonly encountered experimental errors was performed.  OD was employed using D- and ED-optimality.  OD demonstrated that reducing the number of samples, measurement times, and separate ligand concentrations provides robust parameter estimation and more efficient and cost effective experimentation. To demonstrate applicability of NLMEM and OD in clinical applications, a phase advanced sleep study formed the basis of this investigation. A mixed-effect Markov-chain model based on transition probabilities as multinomial logistic functions using polysomnography data in phase advanced subjects was developed and compared the sleep architecture between this population and insomniac patients. The NLMEM was sufficiently robust for describing the data characteristics in phase advanced subjects, and in contrast to aggregated clinical endpoints, which provide an overall assessment of sleep behavior over the night, described the dynamic behavior of the sleep process. OD of a dichotomous, non-homogeneous, Markov-chain phase advanced sleep NLMEM was performed using D-optimality by computing the Fisher Information Matrix for each Markov component.  The D-optimal designs improved the precision of parameter estimates leading to more efficient designs by optimizing the doses and the number of subjects in each dose group.  This thesis provides examples how studies in drug development can be optimized using NLMEM and OD. This provides a tool than can lower the cost and increase the overall efficiency of drug development. / <p>My name should be listed as "Charles Steven Ernest II" on cover.</p>

Tuberculosis (TB) is the world’s most deadly infectious disease and causes enormous public health problems. The comorbidity with HIV and the rise of multidrug-resistant TB strains impede successful therapy through drug-drug interactions and the lack of efficient second-line treatments. The aim of this thesis was to support the improvement of anti-TB therapy through development of pharmacometric models, specifically focusing on the novel drug bedaquiline, pharmacokinetic interactions and methods for pooled population analyses. A population pharmacokinetic model of bedaquiline and its metabolite M2, linked to semi-mechanistic models of body weight and albumin concentrations, was developed and used for exposure-response analysis. Treatment response was quantified by measurements of mycobacterial load and early bedaquiline exposure was found to significantly impact the half-life of bacterial clearance. The analysis represents the first successful characterization of a concentration-effect relationship for bedaquiline. Single-dose Phase I studies investigating potential interactions between bedaquiline and efavirenz, nevirapine, ritonavir-boosted lopinavir, rifampicin and rifapentine were analyzed with a model-based approach. Substantial effects were detected in several cases and dose-adjustments mitigating the impact were suggested after simulations. The interaction effects of nevirapine and ritonavir-boosted lopinavir were also confirmed in patients with multidrug-resistant TB on long-term treatment combining the antiretrovirals and bedaquiline. Furthermore, the outcomes from model-based analysis were compared to results from conventional non-compartmental analysis in a simulation study. Non-compartmental analysis was found to consistently underpredict the interaction effect when most of the concentration-time profile was not observed, as commonly is the case for compounds with very long terminal half-life such as bedaquiline. To facilitate pooled analyses of individual patient data from multiple sources a structured development procedure was outlined and a fast diagnostic tool for extensions of the stochastic model components was developed. Pooled analyses of nevirapine and rifabutin pharmacokinetics were performed; the latter generating comprehensive dosing recommendations for combined administration of rifabutin and antiretroviral protease inhibitors. The work presented in this thesis demonstrates the usefulness of pharmacometric techniques to improve treatment of TB and especially contributes evidence to inform optimized dosing regimens of new and old anti-TB drugs in various clinical contexts.

The costs of developing new pharmaceuticals have increased dramatically during the past decades. Contributing to these increased expenses are the increasingly extensive and more complex clinical trials required to generate sufficient evidence regarding the safety and efficacy of the drugs.  It is therefore of great importance to improve the effectiveness of the clinical phases by increasing the information gained throughout the process so the correct decision may be made as early as possible.   Optimal Design (OD) methodology using the Fisher Information Matrix (FIM) based on Nonlinear Mixed Effect Models (NLMEM) has been proven to serve as a useful tool for making more informed decisions throughout the clinical investigation. The calculation of the FIM for NLMEM does however lack an analytic solution and is commonly approximated by linearization of the NLMEM. Furthermore, two structural assumptions of the FIM is available; a full FIM and a block-diagonal FIM which assumes that the fixed effects are independent of the random effects in the NLMEM. Once the FIM has been derived, it can be transformed into a scalar optimality criterion for comparing designs. The optimality criterion may be considered local, if the criterion is based on singe point values of the parameters or global (robust), where the criterion is formed for a prior distribution of the parameters.  Regardless of design criterion, FIM approximation or structural assumption, the design will be based on the prior information regarding the model and parameters, and is thus sensitive to misspecification in the design stage.  Model based adaptive optimal design (MBAOD) has however been shown to be less sensitive to misspecification in the design stage.   The aim of this thesis is to further the understanding and practicality when performing standard and MBAOD. This is to be achieved by: (i) investigating how two common FIM approximations and the structural assumptions may affect the optimized design, (ii) reducing runtimes complex design optimization by implementing a low level parallelization of the FIM calculation, (iii) further develop and demonstrate a framework for performing MBAOD, (vi) and investigate the potential advantages of using a global optimality criterion in the already robust MBAOD.

Pharmacometric model-based analysis using nonlinear mixed-effects models (NLMEM) has to date mainly been applied to learning activities in drug development. However, such analyses can also serve as the primary analysis in confirmatory studies, which is expected to bring higher power than traditional analysis methods, among other advantages. Because of the high expertise in designing and interpreting confirmatory studies with other types of analyses and because of a number of unresolved uncertainties regarding the magnitude of potential gains and risks, pharmacometric analyses are traditionally not used as primary analysis in confirmatory trials. The aim of this thesis was to address current hurdles hampering the use of pharmacometric model-based analysis in confirmatory settings by developing strategies to increase model compliance to distributional assumptions regarding the residual error, to improve the quantification of parameter uncertainty and to enable model prespecification. A dynamic transform-both-sides approach capable of handling skewed and/or heteroscedastic residuals and a t-distribution approach allowing for symmetric heavy tails were developed and proved relevant tools to increase model compliance to distributional assumptions regarding the residual error. A diagnostic capable of assessing the appropriateness of parameter uncertainty distributions was developed, showing that currently used uncertainty methods such as bootstrap have limitations for NLMEM. A method based on sampling importance resampling (SIR) was thus proposed, which could provide parameter uncertainty in many situations where other methods fail such as with small datasets, highly nonlinear models or meta-analysis. SIR was successfully applied to predict the uncertainty in human plasma concentrations for the antibiotic colistin and its prodrug colistin methanesulfonate based on an interspecies whole-body physiologically based pharmacokinetic model. Lastly, strategies based on model-averaging were proposed to enable full model prespecification and proved to be valid alternatives to standard methodologies for studies assessing the QT prolongation potential of a drug and for phase III trials in rheumatoid arthritis. In conclusion, improved methods for handling residual error, parameter uncertainty and model uncertainty in NLMEM were successfully developed. As confirmatory trials are among the most demanding in terms of patient-participation, cost and time in drug development, allowing (some of) these trials to be analyzed with pharmacometric model-based methods will help improve the safety and efficiency of drug development.

<p>Forest quantification methods have evolved from a simple graphical approach to complex regression models with stochastic structural components. Currently, mixed effects models methodology is receiving attention in the forestry literature. However, the review work (Paper I) indicates a tendency to overlook appropriate covariance structures in the NLME modeling process.</p><p>A nonlinear mixed effects modeling process is demonstrated in Paper II using Cupressus lustanica tree merchantable volume data and compared several models with and without covariance structures. For simplicity and clarity of the nonlinear mixed effects modeling, four phases of modeling were introduced. The nonlinear mixed effects model for C. lustanica tree merchantable volume with the covariance structures for both the random effects and within group errors has shown a significant improvement over the model with simplified covariance matrix. However, this statistical significance has little to explain in the prediction performance of the model.</p><p>In Paper III, using several performance indicator statistics, tree taper models were compared in an effort to propose the best model for the forest management and planning purpose of the C. lustanica plantations. Kozak's (1988) tree taper model was found to be the best for estimating C. lustanica taper profile.</p><p>Based on the Kozak (1988) tree taper model, a Ds optimal experimental design study is carried out in Paper IV. In this study, a Ds-optimal (sub) replication free design is suggested for the Kozak (1988) tree taper model.</p>

Forest quantification methods have evolved from a simple graphical approach to complex regression models with stochastic structural components. Currently, mixed effects models methodology is receiving attention in the forestry literature. However, the review work (Paper I) indicates a tendency to overlook appropriate covariance structures in the NLME modeling process. A nonlinear mixed effects modeling process is demonstrated in Paper II using Cupressus lustanica tree merchantable volume data and compared several models with and without covariance structures. For simplicity and clarity of the nonlinear mixed effects modeling, four phases of modeling were introduced. The nonlinear mixed effects model for C. lustanica tree merchantable volume with the covariance structures for both the random effects and within group errors has shown a significant improvement over the model with simplified covariance matrix. However, this statistical significance has little to explain in the prediction performance of the model. In Paper III, using several performance indicator statistics, tree taper models were compared in an effort to propose the best model for the forest management and planning purpose of the C. lustanica plantations. Kozak's (1988) tree taper model was found to be the best for estimating C. lustanica taper profile. Based on the Kozak (1988) tree taper model, a Ds optimal experimental design study is carried out in Paper IV. In this study, a Ds-optimal (sub) replication free design is suggested for the Kozak (1988) tree taper model.

En dépit d’épidémies répétées, il n’existe pas à ce jour de thérapeutique ayant démontré son efficacité dans la maladie à virus Ebola. Sur la base d’expérimentations réalisées chez la souris et le macaque dans le cadre du consortium Reaction!, l’objectif de cette thèse visait à caractériser l’effet d’une molécule antivirale, le favipiravir, via l’implémentation de modèles mathématiques mécanistiques de l’infection et de la réponse immunitaire associée. L’approche utilisée pour construire ces modèles et en estimer les paramètres reposait sur les modèles non linéaires à effets mixtes. Un premier travail a permis d’explorer la relation concentration-effet sur la charge virale plasmatique chez la souris. Le second projet a conduit à caractériser la pharmacocinétique non linéaire dose et temps dépendante du favipiravir chez le macaque, en vue d’identifier les schémas posologiques pertinents pour la réalisation des études d’efficacité chez l’animal infecté. Au décours de leur réalisation, l’intégration des données virologiques et immunitaires générées au sein d’un modèle conjoint a permis de caractériser un effet modéré du favipiravir sur la réplication virale, mais suffisant pour limiter le développement d’une réaction inflammatoire délétère, et ainsi améliorer le taux de survie des animaux traités. Les simulations réalisées avec ce modèle ont pu souligner l’impact déterminant du délai d’initiation du traitement sur la survie. Ces résultats incitent à la poursuite de l’évaluation clinique du favipiravir, en favorisant des essais de prophylaxie ou post exposition. Enfin, un dernier travail a démontré l’absence de potentialisation du favipiravir par la ribavirine dans Ebola. / In spite of recurrent outbreaks, no therapeutics with demonstrated clinical efficacy are available in Ebola virus disease. Based on experimentations performed by Reaction! Consortium in mice and macaques, this thesis aimed to characterize the effect of an antiviral drug, favipiravir, using mechanistic mathematical models of the infection and associated immune response. The approach to build models and estimate parameters relied on nonlinear mixed effect models. The first project of this thesis explored the concentration-effect relationship on the viremia in mice. Then, a second project allowed to characterize the pharmacokinetics of favipiravir in macaques, underlying dose and time non linearity, and to identify relevant dosing regimen for efficacy experiments in infected animals. Once these experiments completed, the integration of the virological and immunological data into a mechanistic joint model shed light on the effect of favipiravir. The moderate inhibition of the viral replication resulting from the favipiravir plasma concentrations was enough to limit the development of a deleterious inflammatory response, and thus improve the survival rate of treated macaques. Simulations performed with this model underlined the crucial impact of the treatment initiation delay on survival. These results encourage the pursuit of the clinical evaluation of favipiravir in prophylaxis or post exposure trials. Finally, a last project demonstrated the lack of benefit of ribavirin addition to favipiravir in Ebola virus disease.