The pharmacokinetics of rifampicin, isoniazid, pyrazinamide and ethambutol in TB/HIV coinfected patients recruited in two phase III clinical trials (61 patients in TB-HAART and 222 patients in RAFA study) were described using nonlinear mixed-effects modelling. Concentration-time data for rifampicin (TB-HAART study) was used to develop a semimechanistic pharmacokinetic model incorporating autoinduction and saturable pharmacokinetics. A model describing the pharmacokinetics of pyrazinamide (TB-HAART study) was developed and used to evaluate the 24-hour area under the concentration-time curve (AUC0–24), and maximum concentrations (Cmax) achieved with the currently recommended weight-adjusted doses for drug-susceptible and -resistant tuberculosis. Concentration-time data from the RAFA study were used to characterise the pharmacokinetics of the four drugs of the fixed dose combination (FDC) therapy including desacetyl-rifampicin, and acetyl-isoniazid. Binary recursive techniques were applied in the conditional inference framework to determine predictors including drug exposure of time-to-stable culture conversion and poor long-term treatment outcomes. The model describing the pharmacokinetics of rifampicin predicted that increasing the dose results in a more than proportional increase in exposure. Clearance of rifampicin increased by 90% from baseline to steady-state due to autoinduction and the process takes up to 21 days. Monte Carlo simulations showed that rifampicin doses of at least 25 mg/kg would be required to achieve an AUC0–24/MIC ratio of at least 271. Based on the model describing the pharmacokinetics of isoniazid, co-administration of isoniazid and efavirenz-based antiretroviral therapy results in a 54% reduction in isoniazid exposure only in fast acetylators. There were disparities in exposure across weight bands for all the four drugs: patients with lower weight had reduced exposure. To match drug exposure across the weight bands, we recommend the addition of one FDC tablet to patients with weight less than 55 kg. There is need to explore the use of fat-free mass-adjusted dosing since cumulative evidence shows its superiority over total body weight in driving exposure via allometric scaling for all first-line antituberculosis drugs. Individual drug exposures were not predictive of either time-to-stable culture conversion or long-term tuberculosis treatment outcomes. Baseline X-ray grading, HIV stage as TB diagnosis, and treatment arm were predictive of time-to-stable culture conversion while the presence of cavities, patient’s level of physical activity and CD4 count were the drivers of long-term treatment outcomes.

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.

abstract: Previous research has shown functional mixed-effects models and traditional mixed-effects models perform similarly when recovering mean and individual trajectories (Fine, Suk, & Grimm, 2019). However, Fine et al. (2019) showed traditional mixed-effects models were able to more accurately recover the underlying mean curves compared to functional mixed-effects models. That project generated data following a parametric structure. This paper extended previous work and aimed to compare nonlinear mixed-effects models and functional mixed-effects models on their ability to recover underlying trajectories which were generated from an inherently nonparametric process. This paper introduces readers to nonlinear mixed-effects models and functional mixed-effects models. A simulation study is then presented where the mean and random effects structure of the simulated data were generated using B-splines. The accuracy of recovered curves was examined under various conditions including sample size, number of time points per curve, and measurement design. Results showed the functional mixed-effects models recovered the underlying mean curve more accurately than the nonlinear mixed-effects models. In general, the functional mixed-effects models recovered the underlying individual curves more accurately than the nonlinear mixed-effects models. Progesterone cycle data from Brumback and Rice (1998) were then analyzed to demonstrate the utility of both models. Both models were shown to perform similarly when analyzing the progesterone data. / Dissertation/Thesis / Doctoral Dissertation Psychology 2019

Receptor occupancy assessed by Positron Emission Tomography (PET) can provide important translational information to help bridge information from one drug to another or from animal to man. The aim of this thesis was to develop nonlinear mixed effects methods for estimation of the relationship between drug exposure and receptor occupancy for the two mGluR5 antagonists AZD9272 and AZD2066 and for the 5HT1B receptor antagonist AZD3783. Also the optimal design for improved estimation of the relationship between drug exposure and receptor occupancy as well as for improved dose finding in neuropathic pain treatment, was investigated. Different modeling approaches were applied. For AZD9272, the radioligand kinetics and receptor occupancy was simultaneously estimated using arterial concentrations as input function and including two brain regions of interest. For AZD2066, a model was developed where brain/plasma partition coefficients from ten different brain regions were included simultaneously as observations. For AZD3783, the simplified reference tissue model was extended to allow different non-specific binding in the reference region and brain regions of interest and the possibility of using white matter as reference was also evaluated. The optimal dose-selection for improved precision of receptor occupancy as well as for improved precision of the minimum effective dose of a neuropathic pain treatment was assessed, using the D-optimal as well as the Ds-optimal criteria. Simultaneous modelling of radioligand and occupancy provided a means to avoid simplifications or approximations and provided the possibility to tests or to relax assumptions. Inclusion of several brain regions of different receptor density simultaneously in the analysis, markedly improved the precision of the affinity parameter. Higher precision was achieved in relevant parameters with designs based on the Ds compared to the D-optimal criterion. The optimal design for improved precision of the relationship between dose and receptor occupancy depended on the number of brain regions and the receptor density of these regions. In conclusion, this thesis presents novel non-linear mixed effects models estimating the relationship between drug exposure and receptor occupancy, providing useful translational information, allowing for a better informed drug-development.

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.