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.

Statistical models have greatly improved our understanding of the pathogenesis of HIV-1 infection and guided for the treatment of AIDS patients and evaluation of antiretroviral (ARV) therapies. Although various statistical modeling and analysis methods have been applied for estimating the parameters of HIV dynamics via mixed-effects models, a common assumption of distribution is normal for random errors and random-effects. This assumption may lack the robustness against departures from normality so may lead misleading or biased inference. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. Bivariate clustered (correlated) data are also commonly encountered in HIV dynamic studies, in which the data set particularly exhibits skewness and heavy tails. In the literature, there has been considerable interest in, via tangible computation methods, comparing different proposed models related to HIV dynamics, accommodating skewness (in univariate) and covariate measurement errors, or considering skewness in multivariate outcomes observed in longitudinal studies. However, there have been limited studies that address these issues simultaneously. One way to incorporate skewness is to use a more general distribution family that can provide flexibility in distributional assumptions of random-effects and model random errors to produce robust parameter estimates. In this research, we developed Bayesian hierarchical models in which the skewness was incorporated by using skew-elliptical (SE) distribution and all of the inferences were carried out through Bayesian approach via Markov chain Monte Carlo (MCMC). Two real data set from HIV/AIDS clinical trial were used to illustrate the proposed models and methods. This dissertation explored three topics. First, with an SE distribution assumption, we compared models with different time-varying viral decay rate functions. The effect of skewness on the model fitting was also evaluated. The associations between the estimated decay rates based on the best fitted model and clinical related variables such as baseline HIV viral load, CD4 cell count and longterm response status were also evaluated. Second, by jointly modeling via a Bayesian approach, we simultaneously addressed the issues of outcome with skewness and a covariate process with measurement errors. We also investigated how estimated parameters were changed under linear, nonlinear and semiparametric mixed-effects models. Third, in order to accommodate individual clustering within subjects as well as the correlation between bivariate measurements such as CD4 and CD8 cell count measured during the ARV therapies, bivariate linear mixed-effects models with skewed distributions were investigated. Extended underlying normality assumption with SE distribution assumption was proposed. The impacts of different distributions in SE family on the model fit were also evaluated and compared. Real data sets from AIDS clinical trial studies were used to illustrate the proposed methodologies based on the three topics and compare various potential models with different distribution specifications. The results may be important for HIV/AIDS studies in providing guidance to better understand the virologic responses to antiretroviral treatment. Although this research is motivated by HIV/AIDS studies, the basic concepts of the methods developed here can have generally broader applications in other fields as long as the relevant technical specifications are met. In addition, the proposed methods can be easily implemented by using the publicly available WinBUGS package, and this makes our approach quite accessible to practicing statisticians in the fields.

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.

Criminology’s most recent theoretical tradition involves examination of the developmental onset, continuity, and desistance from offending behavior across the life course. A prominent life course perspective organized around social bonding was proffered by Robert J. Sampson and John H. Laub in dual volumes that include Crime in the Making: Pathways and Turning Points Through Life (1993), and Shared Beginnings, Divergent Lives (2003). Because Sampson and Laub’s age-graded theory is based on a sample of White males born in the 1920s and 1930s, and matured during a historical period of vast economic growth, the universal theoretical processes emphasized in their theory may be overstated. Such assumptions may not generalize to more heterogeneous samples that includes minorities and individuals that vary in their levels of offending. The present research evaluates the generalizability of the age-graded theory through examination of data collected from a representative and contemporary sample of adolescents followed into adulthood. In addition, this study seeks to examine an alternate turning point from deviant conduct, specifically religiosity/spirituality. Building on prior studies that explore the role of religiosity on change processes across race and ethnicity (Chu & Sung, 2009; Stansfield, 2017), the current investigation addresses open questions relating to the nature of the religion-desistance relationship. Multilevel mixed effects models are utilized to estimate over time the separate impact of religious behavior and religious beliefs on deviant conduct, to further assess a religious turning point effect across subgroups disaggregated by race/ethnicity, and to evaluate the influence of religiosity on change from deviant outcomes characterized as violations of secular and ascetic standards. Analyses of religiosity/spirituality on these differing forms of deviance across race/ethnicity are also conducted. In contrast to the hypothesized relationships, study findings reveal very little evidence of a religious/spiritual turning point effect in enacting change from deviant behaviors in the main models. Similar results indicate that religiosity indicates minimal differences in change from deviant conduct when the sample is disaggregated across race and ethnicity. Findings point to the nuances of the religion-desistance relationship, and depends upon processes that may involve attendance to church services or spiritual beliefs, and may be conditional on the type of deviance outcome examined—whether in violation of a secular or ascetic standard. Along with a discussion of these findings, limitations of the study, directions for future research, and implications for policy are provided.

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.

Substance use data such as alcohol drinking often contain a high proportion of zeros. In studies examining the alcohol consumption in college students, for instance, many students may not drink in the studied period, resulting in a number of zeros. Zero-inflated continuous data, also called semi continuous data, typically consist of a mixture of a degenerate distribution at the origin (zero) and a right-skewed, continuous distribution for the positive values. Ignoring the extreme non-normality in semi-continuous data may lead to substantially biased estimates and inference. Longitudinal or repeated measures of semi-continuous data present special challenges in statistical inference because of the correlation tangled in the repeated measures on the same subject. Linear mixed-eects models (LMM) with normality assumption that is routinely used to analyze correlated continuous outcomes are inapplicable for analyzing semi-continuous outcome. Data transformation such as log transformation is typically used to correct the non-normality in data. However, log-transformed data, after the addition of a small constant to handle zeros, may not successfully approximate the normal distribution due to the spike caused by the zeros in the original observations. In addition, the reasons that data transformation should be avoided include: (i) transforming usually provides reduced information on an underlying data generation mechanism; (ii) data transformation causes diculty in regard to interpretation of the transformed scale; and (iii) it may cause re-transformation bias. Two-part mixed-eects models with one component modeling the probability of being zero and one modeling the intensity of nonzero values have been developed over the last ten years to analyze the longitudinal semi-continuous data. However, log transformation is still needed for the right-skewed nonzero continuous values in the two-part modeling. In this research, we developed Bayesian hierarchical models in which the extreme non-normality in the longitudinal semi-continuous data caused by the spike at zero and right skewness was accommodated using skew-elliptical (SE) distribution and all of the inferences were carried out through Bayesian approach via Markov chain Monte Carlo (MCMC). The substance abuse/dependence data, including alcohol abuse/dependence symptoms (AADS) data and marijuana abuse/dependence symptoms (MADS) data from a longitudinal observational study, were used to illustrate the proposed models and methods. This dissertation explored three topics: First, we presented one-part LMM with skew-normal (SN) distribution under Bayesian framework and applied it to AADS data. The association between AADS and gene serotonin transporter polymorphism (5-HTTLPR) and baseline covariates was analyzed. The results from the proposed model were compared with those from LMMs with normal, Gamma and LN distributional assumptions. Simulation studies were conducted to evaluate the performance of the proposed models. We concluded that the LMM with SN distribution not only provides the best model t based on Deviance Information Criterion (DIC), but also offers more intuitive and convenient interpretation of results, because it models the original scale of response variable. Second, we proposed a flexible two-part mixed-effects model with skew distributions including skew-t (ST) and SN distributions for the right-skewed nonzero values in Part II of model under a Bayesian framework. The proposed model is illustrated with the longitudinal AADS data and the results from models with ST, SN and normal distributions were compared under different random-effects structures. Simulation studies are conducted to evaluate the performance of the proposed models. Third, multivariate (bivariate) correlated semi-continuous data are also commonly encountered in clinical research. For instance, the alcohol use and marijuana use may be observed in the same subject and there might be underlying common factors to cause the dependence of alcohol and marijuana uses. There is very limited literature on multivariate analysis of semi-continuous data. We proposed a Bayesian approach to analyze bivariate semi-continuous outcomes by jointly modeling a logistic mixed-effects model on zero-inflation in either response and a bivariate linear mixed-effects model (BLMM) on the positive values through a correlated random-effects structure. Multivariate skew distributions including ST and SN distributions were used to relax the normality assumption in BLMM. The proposed models were illustrated with an application to the longitudinal AADS and MADS data. A simulation study was conducted to evaluate the performance of the proposed models.

Un problème majeur du cancer est l'apparition de métastases, difficiles à détecter par l'imagerie médicale et qui peuvent progresser rapidement. Par le biais de la modélisation mathématique, nous espérons développer de nouveaux outils capables d'anticiper l'état métastatique d'un patient.Les deux premières parties de cette thèse sont dédiées au développement d'un tel outil, l'objectif étant sonutilisation chez l'animal voire en clinique. Dû aux variabilités intra- et inter-individuelles, nous sommes amenés à utiliser des modèles statistiques coûteux en temps de calcul.Dans la partie 1, nous étendons une approche introduite par Iwata et al. et développée dans l'équipe. Nousproposons une résolution numérique plus efficace basée sur la reformulation du modèle sous formed'équation intégrale de Volterra de type convolution, qui s'avère également utile pour montrer despropriétés théoriques du modèle. En outre, nous étudions une extension stochastique de ce modèle déterministe.Dans la partie 2, nous montrons que notre approche est adaptée à la description de données souris. Utilisant le cadre statistique des modèles nonlinéaires à effets mixtes, nous construisons un modèle métastatique identifiable à partir des données et nous interprétons les résultats biologiquement.La partie 3 regroupe des résultats issus de collaborations avec des biologistes. Nous avons commencé àmodéliser la croissance tumorale à partir d'observations par imagerie SPECT en utilisant un modèle deGyllenberg et Webb. D'autre part, afin d'améliorer la précision des observations SPECT, nous testons des techniques dedétection de contours via des méthodes volumes finis basées sur des schémas DDFV. / Metastasis is one of the major problems of cancer because metastases areoften difficult to detect by clinical imaging and may develop rapidly. With the help of mathematical modelling, we hope to developnew tools capable of anticipating the metastatic state of a patient.The first two parts of this thesis are dedicated to developing such a tool, destined for a preclinical oreven clinical use. As tumour growth dynamics vary strongly between individuals and since observations are often sparse andnoisy, we need to consider computationally expensive statistical tools.In the first part, we extend an approach introduced by Iwata et al. and developed by Barbolosi et al. In particular, wepropose a more efficient numerical resolution based on a model reformulation into a Volterra integral equation of convolutiontype. This reformulation also permits to prove theoretical model properties (regularity and identifiability). Moreover, we study a stochastic generalisation of this deterministic model.In the second part, we will show that our approach is suitable for the description of experimental data on tumour-bearing mice.Using the statistical framework of nonlinear mixed-effects modelling, we build a metastatic model that is identifiable fromour data. We then interpret the results biologically.The last part of this thesis contains several results obtained in collaboration with biologists. We have started to model tumourgrowth with data obtained from SPECT imaging, using a model by Gyllenberg and Webb. Also, in order to improve the precision ofSPECT data, we have tested contour detection methods via finite volume methods based on DDFV schemes.