The concern of this thesis is to discuss classification of different objects based on longitudinal observations. In the first instance the reader is introduced to a linear mixed-effects model which is useful for longitudinal data modeling. Description of discriminant analysis methods follows. These methods ares usually used for classification based on longitudinal observations. Individual methods are introduced in the theoretic aspect. Random effects approach is generalized to continuous time. Subsequently the methods and features of the linear mixed-effects model are applied to real data. Finally features of the methods are studied with help of simulations.

The main idea of this thesis is studying the importance of the carry-over effects and interaction effects in statistical models. To investigate it, a hand-milking experiment in Burkina Faso was studied. In many no electricity access countries, such as Burkina Faso, the amount of milk and milk compositions are still highly  relying on hand-milking techniques and milkers. Moreover, the time effects also plays a important role in stockbreeding system. Therefore, falling all effects, carry-over effects and interaction effects into a linear mixed effects model, it is concluded that the carry-over effects of milker and hand-milking techniques cannot be neglected, and the interaction effects among hand-milking techniques, different milkers, days and periods can be substantial.

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.

Contrast agents are of great importance in clinical applications of Magnetic Resonance Imaging (MRI) to improve the contrast of internal body structures and to obtain tissue-specific image. However, current approved contrast agents still have limitations including low relaxivity, low specificity and uncontrolled blood circulation time, which motivated researchers to develop novel contrast agents with higher relaxivity, improved targeting abilities and optimal retention time. This thesis uses animal experimental data from Dr. Jenny J. Yang’s lab at the Department of Chemistry in Georgia State University to study effects of a class of newly designed protein-based MRI contrast agents (ProCAs). Models for the longitudinal data on MRI intensity are constructed to evaluate the efficiency of different MRI contrast agents. Statistically significant results suggest that ProCA1B14 has the great potential to be a tumor specific contrast agent and ProCA32 could be a promising MRI contrast agent for the liver imaging in clinical applications.

The minimum description length (MDL) principle originated from data compression literature and has been considered for deriving statistical model selection procedures. Most existing methods utilizing the MDL principle focus on models consisting of independent data, particularly in the context of linear regression. The data considered in this thesis are in the form of repeated measurements, and the exploration of MDL principle begins with classical linear mixed-effects models. We distinct two kinds of research focuses: one concerns the population parameters and the other concerns the cluster/subject parameters. When the research interest is on the population level, we propose a class of MDL procedures which incorporate the dependence structure within individual or cluster with data-adaptive penalties and enjoy the advantages of Bayesian information criteria. When the number of covariates is large, the penalty term is adjusted by data-adaptive structure to diminish the under selection issue in BIC and try to mimic the behaviour of AIC. Theoretical justifications are provided from both data compression and statistical perspectives. Extensions to categorical response modelled by generalized estimating equations and functional data modelled by functional principle components are illustrated. When the interest is on the cluster level, we use group LASSO to set up a class of candidate models. Then we derive a MDL criterion for this LASSO technique in a group manner to selection the final model via the tuning parameters. Extensive numerical experiments are conducted to demonstrate the usefulness of the proposed MDL procedures on both population level and cluster level.

The minimum description length (MDL) principle originated from data compression literature and has been considered for deriving statistical model selection procedures. Most existing methods utilizing the MDL principle focus on models consisting of independent data, particularly in the context of linear regression. The data considered in this thesis are in the form of repeated measurements, and the exploration of MDL principle begins with classical linear mixed-effects models. We distinct two kinds of research focuses: one concerns the population parameters and the other concerns the cluster/subject parameters. When the research interest is on the population level, we propose a class of MDL procedures which incorporate the dependence structure within individual or cluster with data-adaptive penalties and enjoy the advantages of Bayesian information criteria. When the number of covariates is large, the penalty term is adjusted by data-adaptive structure to diminish the under selection issue in BIC and try to mimic the behaviour of AIC. Theoretical justifications are provided from both data compression and statistical perspectives. Extensions to categorical response modelled by generalized estimating equations and functional data modelled by functional principle components are illustrated. When the interest is on the cluster level, we use group LASSO to set up a class of candidate models. Then we derive a MDL criterion for this LASSO technique in a group manner to selection the final model via the tuning parameters. Extensive numerical experiments are conducted to demonstrate the usefulness of the proposed MDL procedures on both population level and cluster level.

Longitudinal assessments are crucial in evaluating the disease state and trajectory in patients of neurodegenerative diseases. Neuropsychological outcomes measured over time often have a non-linear trajectory with autocorrelated residuals and skewed distributions. Due to these issues, statistical analysis and interpretation involving longitudinal cognitive outcomes can be a difficult and controversial task, thus hindering most convenient transformations (e.g. logarithmic) to avoid the assumption violations of common statistical modelling techniques. We propose the Adjusted Local Linear Trend (ALLT) model, an extended state space model in lieu of the commonly-used linear mixed-effects model (LMEM) in modeling longitudinal neuropsychological outcomes. Our contributed model has the capability to utilize information from the stochasticity of the data while accounting for subject-specific trajectories with the inclusion of covariates and unequally-spaced time intervals. The first step of model fitting involves a likelihood maximization step to estimate the unknown variances in the model before parsing these values into the Kalman Filter and Kalman Smoother recursive algorithms. Results from simulation studies showed that the ALLT model is able to attain lower bias, lower standard errors and high power, particularly in short longitudinal studies with equally-spaced time intervals, as compared to the LMEM. The ALLT model also outperforms the LMEM when data is missing completely at random (MCAR), missing at random (MAR) and, in certain cases, even in data with missing not at random (MNAR). In terms of model selection, likelihood-based inference is applicable for the ALLT model. Although a Chi-Square distribution with k degrees of freedom, where k is the number of parameter lost during estimation, was not the asymptotic distribution in the case of ALLT, we were able to derive an asymptotic distribution approximation of the likelihood ratio test statistics using the power transformation method for the utility of a Gaussian distribution to facilitate model selections for ALLT. In light of these findings, we believe that our proposed model will shed light into longitudinal data analysis not only in the neuropsychological data realm but also on a broader scale for statistical analysis of longitudinal data. / 2023-10-05T00:00:00Z

Tuberculosis is one the leading causes of death globally and was before the COVID-19 pandemic the leading cause of death from a single infectious agent. Developing active tuberculosis is life threatening and therefore is the rise of drug-resistant tuberculosis alarming as this risk causing current treatments to become ineffective. Linezolid is a promising drug for treatment of drug-resistant pulmonary tuberculosis, but the effect of linezolid treatment for pulmonary tuberculosis subjects is still not understood well enough and the World Health Organization has requested this knowledge gap to be filled. In this project we support the closing of this knowledge gap by describing the pharmacokinetics of linezolid for treatment of pulmonary tuberculosis using data collected from a phase two clinical trial in a South African population. This was done by creating a pop-PK model and resulted in the PK of linezolid in pulmonary tuberculosis patients from South Africa was best described using a one-compartment model, with first-order absorption process preceded by a series of transit compartments and saturable elimination. However, the diagnostics of the model still show that there are room for improvements and future work is necessary to further optimize the model.

No description available.

<p>Hypercholesterolemia is the presence of high levels of cholesterol in the blood, and it is one of the major factors for the development of long-term complications in T1D patients.</p> <p>In the thesis, we studied 1303 Caucasians with type 1 diabetes in the Diabetes Control and Complications Trial (DCCT). With the experience of diabetes study, many factors are associated with diabetes complications, they are age, gender, cohort, treatment, diabetes duration, body mass index (BMI), exercise, insulin dose, etc. We mainly focus on which factors are associated with total cholesterol (CHL) analysis in the thesis.</p> <p>Many measures were collected monthly, quarterly or yearly for average 6.5 years from 1983 to 1993. We used annually lipid measures of DCCT because of their values are sufficient and complete, and they belong to longitudinal data.</p> <p>Different methods are discussed in the study, and linear mixed effect models are the appropriate approach to the study. The details of model selection with CHL model analysis are shown, which includes fixed effect selection, random effects selection, and residual correlation structure selection. Then the SNPs were added on three models individually in GWAS. We found locus (rs7412) is not only genome-wide associated with CHL, but also genome-wide associated with LDL.</p> <p>We will assess whether these SNPs are diabetes-specific in the future, and we will add dietary data in the three models to identify locus are associated with the interaction of diet and SNPs.</p> / Master of Science (MSc)