<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.

In this dissertation, we focus on two research topics related to mixture models. The first topic is Adaptive Rejection Metropolis Simulated Annealing for Detecting Global Maximum Regions, and the second topic is Bayesian Model Selection for Nonlinear Mixed Effects Model. In the first topic, we consider a finite mixture model, which is used to fit the data from heterogeneous populations for many applications. An Expectation Maximization (EM) algorithm and Markov Chain Monte Carlo (MCMC) are two popular methods to estimate parameters in a finite mixture model. However, both of the methods may converge to local maximum regions rather than the global maximum when multiple local maxima exist. In this dissertation, we propose a new approach, Adaptive Rejection Metropolis Simulated Annealing (ARMS annealing), to improve the EM algorithm and MCMC methods. Combining simulated annealing (SA) and adaptive rejection metropolis sampling (ARMS), ARMS annealing generate a set of proper starting points which help to reach all possible modes. ARMS uses a piecewise linear envelope function for a proposal distribution. Under the SA framework, we start with a set of proposal distributions, which are constructed by ARMS, and this method finds a set of proper starting points, which help to detect separate modes. We refer to this approach as ARMS annealing. By combining together ARMS annealing with the EM algorithm and with the Bayesian approach, respectively, we have proposed two approaches: an EM ARMS annealing algorithm and a Bayesian ARMS annealing approach. EM ARMS annealing implement the EM algorithm by using a set of starting points proposed by ARMS annealing. ARMS annealing also helps MCMC approaches determine starting points. Both approaches capture the global maximum region and estimate the parameters accurately. An illustrative example uses a survey data on the number of charitable donations. The second topic is related to the nonlinear mixed effects model (NLME). Typically a parametric NLME model requires strong assumptions which make the model less flexible and often are not satisfied in real applications. To allow the NLME model to have more flexible assumptions, we present three semiparametric Bayesian NLME models, constructed with Dirichlet process (DP) priors. Dirichlet process models often refer to an infinite mixture model. We propose a unified approach, the penalized posterior Bayes factor, for the purpose of model comparison. Using simulation studies, we compare the performance of two of the three semiparametric hierarchical Bayesian approaches with that of the parametric Bayesian approach. Simulation results suggest that our penalized posterior Bayes factor is a robust method for comparing hierarchical parametric and semiparametric models. An application to gastric emptying studies is used to demonstrate the advantage of our estimation and evaluation approaches. / Ph. D.

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.

In HIV/AIDS studies, viral load (the number of copies of HIV-1 RNA) and CD4 cell counts are important biomarkers of the severity of viral infection, disease progression, and treatment evaluation. Recently, joint models, which have the capability on the bias reduction and estimates' efficiency improvement, have been developed to assess the longitudinal process, survival process, and the relationship between them simultaneously. However, the majority of the joint models are based on mean regression, which concentrates only on the mean effect of outcome variable conditional on certain covariates. In fact, in HIV/AIDS research, the mean effect may not always be of interest. Additionally, if obvious outliers or heavy tails exist, mean regression model may lead to non-robust results. Moreover, due to some data features, like left-censoring caused by the limit of detection (LOD), covariates with measurement errors and skewness, analysis of such complicated longitudinal and survival data still poses many challenges. Ignoring these data features may result in biased inference. Compared to the mean regression model, quantile regression (QR) model belongs to a robust model family, which can give a full scan of covariate effect at different quantiles of the response, and may be more robust to extreme values. Also, QR is more flexible, since the distribution of the outcome does not need to be strictly specified as certain parametric assumptions. These advantages make QR be receiving increasing attention in diverse areas. To the best of our knowledge, few study focuses on the QR-based joint models and applies to longitudinal-survival data with multiple features. Thus, in this dissertation research, we firstly developed three QR-based joint models via Bayesian inferential approach, including: (i) QR-based nonlinear mixed-effects joint models for longitudinal-survival data with multiple features; (ii) QR-based partially linear mixed-effects joint models for longitudinal data with multiple features; (iii) QR-based partially linear mixed-effects joint models for longitudinal-survival data with multiple features. The proposed joint models are applied to analyze the Multicenter AIDS Cohort Study (MACS) data. Simulation studies are also implemented to assess the performance of the proposed methods under different scenarios. Although this is a biostatistical methodology study, some interesting clinical findings are also discovered.

Le développement des méthodes de séquençage de nouvelle génération a permis d’approfondir les connaissances sur le rôle des communautés bactériennes commensales pour la santé de leur hôte, et l’impact négatif de la perturbation de leur équilibre. Les antibiotiques sont les principaux perturbateurs de cet équilibre, mais leur impact n’a pas été quantifié précisément.Nous avons quantifié la relation entre les concentrations fécales d’antibiotiques et la perturbation de la diversité bactérienne au sein du microbiote intestinal, et modélisé le lien entre la perte de diversité bactérienne et la probabilité de décès dans un modèle animal de colite à Clostridium difficile induite par les antibiotiques. Nous avons montré que l’indice de diversité de Shannon et la distance UniFac non pondérée étaient les indices de diversité qui étaient le plus prédictif du décès dans ce modèle d’infection.Chez des volontaires sains, nous avons développé un modèle mathématique semimécanistique de l’évolution de la diversité au sein du microbiote, mesurée par deux indices de diversité, après perturbation antibiotique, et quantifié la relation entre l’exposition individuelle plasmatique et fécale à un antibiotique, et son effet sur la perturbation de la diversité bactérienne au cours du temps. Nous avons également analysé le rôle de la voie d’élimination des antibiotiques pour la limitation de l’impact d’un antibiotique sur le microbiote. Ces travaux nous ont permis de montrer que le microbiote intestinal présente une grande sensibilité aux antibiotiques, et que la voie d’élimination ne semble de ce fait pas jouer un rôle prépondérant dans la perspective de limiter l’impact des antibiotiques sur le microbiote intestinal. / The development of next generation sequencing broadened our knowledge on the role of commensal bacterial communities on their host’s health, and the negative impact of their disruption. Antibiotics are the main disrupting factor, but their impact has not been precisely quantified.We quantified the relationship between antibiotic fecal concentrations and the loss of bacterial diversity in the intestinal microbiota, and modelled the link between the loss of diversity and mortality in a hamster model of antibiotic-induced Clostridium difficile infection. We showed that the Shannon diversity index and the unweighted UniFrac distance are the 2 indices that best predict mortality in this model. In healthy volunteers, we developed a semi-mechanistic model of the evolution over time of bacterial diversity – measured by two indices – after an antibiotic perturbation, and quantified the relationship between antibiotic concentrations in plasma and feces and the loss of bacterial diversity in the intestinal microbiota. We also analyzed the role of the antibiotic elimination pathway in the reduction of their impact on the microbiota. In this work, we showed that the intestinal microbiota is highly susceptible to antibiotics, and that the elimination route doesn’t have a major role, in the perspective of limiting antibiotics’ impact on the intestinal microbiota.

Reliability analysis plays an important role in keeping manufacturers in a competitive position. It can be applied in many areas such as warranty predictions, maintenance scheduling, spare parts provisioning, and risk assessment. This dissertation focuses on statistical modeling and predictions based on lifetime data, degradation data, and recurrent event data. The datasets used in this dissertation come from the field, and have complicated structures. The dissertation consists of three main chapters, in addition to Chapter 1 which is the introduction chapter, and Chapter 5 which is the general conclusion chapter. Chapter 2 consists of the traditional time-to-failure data analysis. We propose a statistical method to address the failure data from an appliance used at home with the consideration of retirement times and delayed reporting time. We also develop a prediction method based on the proposed model. Using the information of retirement-time distribution and delayed reporting time, the predictions are more accurate and useful in the decision making. In Chapter 3, we introduce a nonlinear mixed-effects general path model to incorporate dynamic covariates into degradation data analysis. Dynamic covariates include time-varying environmental variables and usage condition. The shapes of the effect functions of covariates may be constrained to be, for example, monotonically increasing (i.e., higher temperature is likely to cause more damage). Incorporating dynamic covariates with shape restrictions is challenging. A modified alternative algorithm and the corresponding prediction method are proposed. In Chapter 4, we introduce a multi-level trend-renewal process (MTRP) model to describe component-level events in multi-level repairable systems. In particular, we consider two-level repairable systems in which events can occur at the subsystem level, or the component (within the subsystem) level. The main goal is to develop a method for estimation of model parameters and a procedure for prediction of the future replacement events at component level with the consideration of the effects from the subsystem replacement events. To explain unit-to-unit variability, time-dependent covariates as well as random effects are introduced into the heterogeneous MTRP model (HMTRP). A Metropolis-within-Gibbs algorithm is used to estimate the unknown parameters in the HMTRP model. The proposed method is illustrated by a simulated dataset. / Ph. D.

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.