Current excessive use and abuse of antibiotics has resulted in increasing bacterial resistance to common treatment options which is threatening to deprive us of a pillar of modern medicine. In this work methods to optimize the use of existing antibiotics and to help development of new antibiotics were developed and applied. Semi-mechanistic pharmacokinetic-pharmacodynamic (PKPD) models were developed to describe the time course of the dynamic effect and interaction of combinations of antibiotics. The models were applied to illustrate that colistin combined with a high dose of meropenem may overcome meropenem-resistant P. aeruginosa infections. The results from an in vivo dose finding study of meropenem was successfully predicted by the meropenem PKPD model in combination with a murine PK model, which supports model based dosage selection. However, the traditional PK/PD index based dose selection was predicted to have poor extrapolation properties from pre-clinical to clinical settings, and across patient populations. The precision of the model parameters, and hence the model predictions, is dependent on the experimental design. A limited study design is dictated by cost and, for in vivo studies, ethical reasons. In this work optimal design (OD) was demonstrated to be able to reduce the experimental effort in time-kill curve experiments and was utilized to suggest the experimental design for identification and estimation of an interaction between antibiotics. OD methods to handle inter occasion variability (IOV) in optimization of individual PK parameter estimates were proposed. The strategy was applied in the design of a sparse sampling schedule that aim to estimate individual exposures of colistin in a multi-centre clinical study. Plasma concentration samples from the first 100 patients have been analysed and indicate that the performance of the design is close to the predicted. The methods described in this thesis holds promise to facilitate the development of new antibiotics and to improve the use of existing antibiotics.

Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data. Biased inference can occur in linear mixed-effects modelling if subjects are drawn from a number of unknown sub-populations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a two-step approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially non-monotonic variance and correlation functions. Spatially explicit capture-recapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multi-occasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radio-tagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animal-level covariates.

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.

No description available.

In this thesis we develop methods for dealing with missing data in a univariate response variable when estimating regression parameters. Missing outcome data is a problem in a number of applications, one of which is follow-up studies. In follow-up studies data is collected at two (or more) occasions, and it is common that only some of the initial participants return at the second occasion. This is the case in Paper II, where we investigate predictors of decline in self reported health in older populations in Sweden, the Netherlands and Italy. In that study, around 50% of the study participants drop out. It is common that researchers rely on the assumption that the missingness is independent of the outcome given some observed covariates. This assumption is called data missing at random (MAR) or ignorable missingness mechanism. However, MAR cannot be tested from the data, and if it does not hold, the estimators based on this assumption are biased. In the study of Paper II, we suspect that some of the individuals drop out due to bad health. If this is the case the data is not MAR. One alternative to MAR, which we pursue, is to incorporate the uncertainty due to missing data into interval estimates instead of point estimates and uncertainty intervals instead of confidence intervals. An uncertainty interval is the analog of a confidence interval but wider due to a relaxation of assumptions on the missing data. These intervals can be used to visualize the consequences deviations from MAR have on the conclusions of the study. That is, they can be used to perform a sensitivity analysis of MAR. The thesis covers different types of linear regression. In Paper I and III we have a continuous outcome, in Paper II a binary outcome, and in Paper IV we allow for mixed effects with a continuous outcome. In Paper III we estimate the effect of a treatment, which can be seen as an example of missing outcome data.

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés. / We propose a method for analysing count or Poisson data based on the procedure called Poisson Regression Interactive Multilevel Modeling (PRIMM) introduced by Christiansen and Morris (1997). The Poisson regression in the PRIMM method has fixed effects only, whereas our model incorporates random effects. As well as Christiansen and Morris (1997), the model studied aims at doing inference based on adequate analytical approximations of posterior distributions of the parameters. This avoids the use of computationally expensive methods such as Markov chain Monte Carlo (MCMC) methods. The approximations are based on the Laplace's method and asymptotic theory. Estimates of Poisson mixed effects regression parameters are obtained through the maximization of their joint posterior density via the Newton-Raphson algorithm. This study also provides the first two posterior moments of the Poisson parameters involved. The posterior distributon of these parameters is approximated by a gamma distribution. Applications to two datasets show that our model can be somehow considered as a generalization of the PRIMM method since it also allows clustered count data. Finally, the model is applied to data involving many types of adverse events recorded by the participants of a drug clinical trial which involved a quadrivalent vaccine containing measles, mumps, rubella and varicella. The Poisson regression incorporates the fixed effect corresponding to the covariate treatment/control as well as a random effect associated with the biological system of the body affected by the adverse events.

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.

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés. / We propose a method for analysing count or Poisson data based on the procedure called Poisson Regression Interactive Multilevel Modeling (PRIMM) introduced by Christiansen and Morris (1997). The Poisson regression in the PRIMM method has fixed effects only, whereas our model incorporates random effects. As well as Christiansen and Morris (1997), the model studied aims at doing inference based on adequate analytical approximations of posterior distributions of the parameters. This avoids the use of computationally expensive methods such as Markov chain Monte Carlo (MCMC) methods. The approximations are based on the Laplace's method and asymptotic theory. Estimates of Poisson mixed effects regression parameters are obtained through the maximization of their joint posterior density via the Newton-Raphson algorithm. This study also provides the first two posterior moments of the Poisson parameters involved. The posterior distributon of these parameters is approximated by a gamma distribution. Applications to two datasets show that our model can be somehow considered as a generalization of the PRIMM method since it also allows clustered count data. Finally, the model is applied to data involving many types of adverse events recorded by the participants of a drug clinical trial which involved a quadrivalent vaccine containing measles, mumps, rubella and varicella. The Poisson regression incorporates the fixed effect corresponding to the covariate treatment/control as well as a random effect associated with the biological system of the body affected by the adverse events.