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Ribbing, Jakob. "Covariate Model Building in Nonlinear Mixed Effects Models." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7923.
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Gibiansky, Ekaterina. "Population pharmacokinetics : model-free approach and nonlinear mixed-effects modelling." Thesis, University of Greenwich, 1999. http://gala.gre.ac.uk/8654/.
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The work is devoted to the application and further development of modern statistical methods to study pharmacokinetics of drugs. Specifically, it deals with applications and development of repeated measures analysis, so called 'population approach' methods, in the field of pharmacokinetics. hi the first part of the thesis, a new, model-free approach is developed and tested. It introduces a model-free measure of patient's exposure to drugs, and then investigates the relationships between the exposure level and covariates using various statistical techniques. Classification tree models (CART) and regression analysis are used to study various subpopulations of interest. It is shown, via simulations, that the model-free method is capable to identify predictors of exposure in a wide range of variability in the data. The non-linear mixed effect modelling is used to confirm the results of the model-free investigation. Model-free approach is successfully applied to several drugs. Non-linear Mixed Effects population models developed for the same data agree with its results. Limits of the new method are also identified. Specifically, it does not allow the estimation of the variability: either the within-subject (intra-individual) variability in response, or between-subject (inter-individual) variability of the pharmacokinetic parameters in the population. The second part of the thesis is devoted to applications of the Non-linear Mixed Effect methodology to population pharmacokinetics and dose-response analysis. Population pharmacokinetic and dose-response models of several drugs are developed. Pharmacokinetic models allow for complete characterisation of the drug's pharmacokinetics and its relationships to safety and efficacy. The developed models are used to explore the relationships between the exposure (individual Bayes estimates) and demographic predictors of exposure, and safety and efficacy of the drug. Finally, the developed models are used in simulations to guide the design of new studies.
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Cole, James Jacob. "Assessing Nonlinear Relationships through Rich Stimulus Sampling in Repeated-Measures Designs." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1587.
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Explaining a phenomenon often requires identification of an underlying relationship between two variables. However, it is common practice in psychological research to sample only a few values of an independent variable. Young, Cole, and Sutherland (2012) showed that this practice can impair model selection in between-subject designs. The current study expands that line of research to within-subjects designs. In two Monte Carlo simulations, model discrimination under systematic sampling of 2, 3, or 4 levels of the IV was compared with that under random uniform sampling and sampling from a Halton sequence. The number of subjects, number of observations per subject, effect size, and between-subject parameter variance in the simulated experiments were also manipulated. Random sampling out-performed the other methods in model discrimination with only small, function-specific costs to parameter estimation. Halton sampling also produced good results but was less consistent. The systematic sampling methods were generally rank-ordered by the number of levels they sampled.
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Zhang, Huaiye. "Bayesian Approach Dealing with Mixture Model Problems." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/37681.
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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.
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Dosne, Anne-Gaëlle. "Improved Methods for Pharmacometric Model-Based Decision-Making in Clinical Drug Development." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-305697.
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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.
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Strömberg, Eric. "Applied Adaptive Optimal Design and Novel Optimization Algorithms for Practical Use." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-308452.
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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.
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Clewe, Oskar. "Novel Pharmacometric Methods for Informed Tuberculosis Drug Development." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-303872.
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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.
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Nagem, Mohamed O. "Diagnostics for Nonlinear Mixed-Effects Models." College Park, Md.: University of Maryland, 2009. http://hdl.handle.net/1903/9546.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2009.Thesis research directed by: Applied Mathematics & Statistics, and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Vong, Camille. "Model-Based Optimization of Clinical Trial Designs." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-233445.
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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.
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Barrowman, Nicholas J. "Nonlinear mixed effects models for meta-analysis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ57342.pdf.
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Mahbouba, Raid. "Nonlinear mixed effects models for longitudinal DATA." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120579.
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The main objectives of this master thesis are to explore the effectiveness of nonlinear mixed effects model for longitudinal data. Mixed effect models allow to investigate the nature of relationship between the time-varying covariates and the response while also capturing the variations of subjects. I investigate the robustness of the longitudinal models by building up the complexity of the models starting from multiple linear models and ending up with additive nonlinear mixed models. I use a dataset where firms’ leverage are explained by four explanatory variables in addition to a grouping factor that is the firm factor. The models are compared using comparison statistics such as AIC, BIC and by a visual inspection of residuals. Likelihood ratio test has been used in some nested models only. The models are estimated by maximum likelihood and restricted maximum likelihood estimation. The most efficient model is the nonlinear mixed effects model which has lowest AIC and BIC. The multiple linear regression model failed to explain the relation and produced unrealistic statistics
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Xu, Zhibing. "Statistical Modeling and Predictions Based on Field Data and Dynamic Covariates." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/51130.
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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.
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Johansson, Åsa M. "Methodology for Handling Missing Data in Nonlinear Mixed Effects Modelling." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-224098.
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To obtain a better understanding of the pharmacokinetic and/or pharmacodynamic characteristics of an investigated treatment, clinical data is often analysed with nonlinear mixed effects modelling. The developed models can be used to design future clinical trials or to guide individualised drug treatment. Missing data is a frequently encountered problem in analyses of clinical data, and to not venture the predictability of the developed model, it is of great importance that the method chosen to handle the missing data is adequate for its purpose. The overall aim of this thesis was to develop methods for handling missing data in the context of nonlinear mixed effects models and to compare strategies for handling missing data in order to provide guidance for efficient handling and consequences of inappropriate handling of missing data. In accordance with missing data theory, all missing data can be divided into three categories; missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). When data are MCAR, the underlying missing data mechanism does not depend on any observed or unobserved data; when data are MAR, the underlying missing data mechanism depends on observed data but not on unobserved data; when data are MNAR, the underlying missing data mechanism depends on the unobserved data itself. Strategies and methods for handling missing observation data and missing covariate data were evaluated. These evaluations showed that the most frequently used estimation algorithm in nonlinear mixed effects modelling (first-order conditional estimation), resulted in biased parameter estimates independent on missing data mechanism. However, expectation maximization (EM) algorithms (e.g. importance sampling) resulted in unbiased and precise parameter estimates as long as data were MCAR or MAR. When the observation data are MNAR, a proper method for handling the missing data has to be applied to obtain unbiased and precise parameter estimates, independent on estimation algorithm. The evaluation of different methods for handling missing covariate data showed that a correctly implemented multiple imputations method and full maximum likelihood modelling methods resulted in unbiased and precise parameter estimates when covariate data were MCAR or MAR. When the covariate data were MNAR, the only method resulting in unbiased and precise parameter estimates was a full maximum likelihood modelling method where an extra parameter was estimated, correcting for the unknown missing data mechanism's dependence on the missing data. This thesis presents new insight to the dynamics of missing data in nonlinear mixed effects modelling. Strategies for handling different types of missing data have been developed and compared in order to provide guidance for efficient handling and consequences of inappropriate handling of missing data.
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Nyberg, Joakim. "Practical Optimal Experimental Design in Drug Development and Drug Treatment using Nonlinear Mixed Effects Models." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-160481.
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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.
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Ernest, II Charles. "Benefits of Non-Linear Mixed Effect Modeling and Optimal Design : Pre-Clinical and Clinical Study Applications." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-209247.
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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.My name should be listed as "Charles Steven Ernest II" on cover.
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Wang, Liangliang. "Estimating nonlinear mixed-effects models by the generalized profiling method and its application to pharmacokinetics." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18424.
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Several methods with software tools have been developed to estimate nonlinear mixed-effects models. However, fewer have addressed the issue when nonlinear mixed-effects models are implicitly expressed as a set of ordinary differential equations (ODE's) while these ODE's have no closed-form solutions. The main objective of this thesis is to solve this problem based on the framework of the generalized profiling method proposed by Ramsay, Hooker, Campbell, and Cao (2007). Four types of parameters are identified and estimated in a cascaded way by a multiple-level nested optimization. In the outermost level, the smoothing parameter is selected by the criterion of generalized cross-validation (GCV). In the outer level, the structural parameters, including the fixed effects, the variance-covariance matrix for random effects, and the residual variance, are optimized by a criterion based on a first-order Taylor expansion of the nonlinear function. In the middle level, the random effects are optimized by the penalized nonlinear least squares. In the inner level, the coefficients of basis function expansions are optimized by penalized smoothing with the penalty defined by ODE's. Consequently, some types of parameters are expressed as explicit or implicit functions of other parameters. The dimensionality of the parameter space is reduced, and the optimization surface becomes smoother. The Newton-Raphson algorithm is applied to estimate parameters for each level of optimization with gradients and Hessian matrices worked out analytically with the Implicit Function Theorem. Our method, along with MATLAB codes, is tested by estimating several compartment models in pharmacokinetics from both simulated and real data sets. Results are compared with the true values or estimates obtained by the package nlme in R, and it turns out that the generalized profiling method can achieve reasonable estimates without solving ODE's directly.Il n'y a aucune solution de exacte pour beaucoup de modèles non-linéaires à effets mixtes (NLME) exprimés comme un ensemble d'équations ordinaires (ODE) en modèles de compartiment. Cette thèse passe en revue plusieurs méthodes et outils courants de logiciel pour NLME, et explore une nouvelle manière d'estimer des effets mixtes non-linéaires en modèles de compartiment basée sur le cadre de la méthode de profilage généralisée proposée par Ramsay, Hooker, Campbell, et Cao (2007). Quatre types de paramètres sont identifiés et estimés d'en cascade par une optimisation de multiple-niveau: le paramètre regularisateur est choisi par le critère de la contre-vérification généralisée (GCV); les paramètres structuraux, y compris les effets fixes, la matrice de variance-covariance pour les effets aléatoires, et la variance résiduelle sont optimisés par un critère basé sur une expansion de premier ordre de Taylor de fonction non-linéaire ; les effets aléatoires sont optimisés par une methode des moindres carrés non-linéaires pénalisés ; et les coefficients d'expansions de fonction de base sont optimisés par un lissage pénalisé avec la pénalité définie par l'equation differentielle. En conséquence, certains des paramètres sont exprimés en tant que fonctions explicites ou implicites d'autres paramètres. La dimensionnalité de l'espace des paramètres est réduite, et la surface d'optimisation devient plus lisse. L'algorithme de Newton-Raphson est appliqué aux paramètres d'évaluation pour chaque niveau d'optimisation, où le théorème des fonctions implicites est employé couramment pour établir les gradients et les matrices de Hessiennes de facon analytiques. La méthode proposée et des codes de MATLAB sont examinés par des applications à plusieurs modèles de compartiment en pharmacocinétique sur des donnees simulées et vraies. Des résultats sont comparés aux valeurs ou aux évaluations vraies obtenues pa
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Zhang, Hanze. "Bayesian inference on quantile regression-based mixed-effects joint models for longitudinal-survival data from AIDS studies." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7456.
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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.
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Wang, Tao. "Multivariate one-sided tests for multivariate normal and nonlinear mixed effects models with complete and incomplete data." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/32764.
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Multivariate one-sided hypotheses testing problems arise frequently in practice. Various tests haven been developed for multivariate normal data. However only limited literatures are available for multivariate one-sided testing problems in regression models. In particular, one-sided tests for nonlinear mixed effects (NLME) models, which
are popular in many longitudinal studies, have not been studied yet, even in the cases of complete data. In practice, there are often missing values in multivariate data and longitudinal data. In this case, standard testing procedures based on complete data may not be applicable or may perform poorly if the observations that contain missing data are discarded. In this thesis, we propose testing methods for multivariate one-sided testing problems in multivariate normal distributions with missing data and for NLME models with complete and incomplete data. In the missing data case, testing methods are based on multiple imputations. Some theoretical results are presented. The proposed
methods are evaluated using simulations. Real data examples are presented to illustrate the methods.
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Galarza, Morales Christian Eduardo 1988. "Quantile regression for mixed-effects models = Regressão quantílica para modelos de efeitos mistos." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306681.
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Orientador: Víctor Hugo Lachos DávilaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Os dados longitudinais são frequentemente analisados usando modelos de efeitos mistos normais. Além disso, os métodos de estimação tradicionais baseiam-se em regressão na média da distribuição considerada, o que leva a estimação de parâmetros não robusta quando a distribuição do erro não é normal. Em comparação com a abordagem de regressão na média convencional, a regressão quantílica (RQ) pode caracterizar toda a distribuição condicional da variável de resposta e é mais robusta na presença de outliers e especificações erradas da distribuição do erro. Esta tese desenvolve uma abordagem baseada em verossimilhança para analisar modelos de RQ para dados longitudinais contínuos correlacionados através da distribuição Laplace assimétrica (DLA). Explorando a conveniente representação hierárquica da DLA, a nossa abordagem clássica segue a aproximação estocástica do algoritmo EM (SAEM) para derivar estimativas de máxima verossimilhança (MV) exatas dos efeitos fixos e componentes de variância em modelos lineares e não lineares de efeitos mistos. Nós avaliamos o desempenho do algoritmo em amostras finitas e as propriedades assintóticas das estimativas de MV através de experimentos empíricos e aplicações para quatro conjuntos de dados reais. Os algoritmos SAEMs propostos são implementados nos pacotes do R qrLMM() e qrNLMM() respectivamente
Abstract: Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation for non-normal error distributions. Compared to the conventional mean regression approach, quantile regression (QR) can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. This thesis develops a likelihood-based approach to analyzing QR models for correlated continuous longitudinal data via the asymmetric Laplace distribution (ALD). Exploiting the nice hierarchical representation of the ALD, our classical approach follows the stochastic Approximation of the EM (SAEM) algorithm for deriving exact maximum likelihood (ML) estimates of the fixed-effects and variance components in linear and nonlinear mixed effects models. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to four real life datasets. The proposed SAEMs algorithms are implemented in the R packages qrLMM() and qrNLMM() respectively
Mestrado
Estatistica
Mestre em Estatística
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Mello, Marcello Neiva de. "Modelo não linear misto aplicado a análise de dados longitudinais em um solo localizado em Paragominas, PA." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-17032014-101144/.
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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.
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Mielke, Tobias [Verfasser], and Rainer [Akademischer Betreuer] Schwabe. "Approximations of the Fisher information for the construction of efficient experimental designs in nonlinear mixed effects models / Tobias Mielke. Betreuer: Rainer Schwabe." Magdeburg : Universitätsbibliothek, 2011. http://d-nb.info/1051445477/34.
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Berhe, Leakemariam. "Statistical modeling and design in forestry : The case of single tree models." Doctoral thesis, Umeå : Umeå University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1663.
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El, Halimi Rachid. "Nonlinear Mixed-effects Models and Nonparametric Inference. A Method Based on Bootstrap for the Analysis of Non-normal Repeated Measures Data in Biostatistical Practice." Doctoral thesis, Universitat de Barcelona, 2005. http://hdl.handle.net/10803/1556.
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En la presente investigacion se presenta un "taller" de análisis avanzado de datos en el contexto de los modelos mixtos, con matrices estructuradas de varianzas-covarianzas de los efectos aleatorios y/o de los residuos. El ajuste de dichos modelos ha permitiedo poner de manifiesto ciertas preocupaciones por la sensibilidad de las inferencias respecto de las suposiciones del modelo, especialmente cuando no cumplen las hipótesis habituales sobre normalidad de residuos y de factores aleatorios. El propósito principal del trabajo ha sido el estudio de la validez del empleo de modelos mixtos no lineales para analizar datos de medidas repetidas y discutir la robustez del enfoque inferencial paramétrico basado en la aproximación propuesta por Lindstrom y Bates (1990), y proponer y evaluar posibles alternativas al mismo, basadas en la metodología bootstrap. Se discute además el mejor procedimiento para generar las muestras bootstrap a partir de datos longitudinales bajo modelos mixtos, y se realiza una adaptación de la metodología bootstrap a métodos de ajuste en dos etapas, como STS (Standard two-stage) y GTS (Global two-stage).
Los resultados de simulación confirman que la aproximación paramétrica basada en la hipótesis de normalidad no es fiable cuando la distribución de la variable estudiada se aparta seriamente de la normal. En concreto, los intervalos de confianza aproximados basados en una aproximación lineal, y en general en los resultados asintóticos de la máxima verosimilitud, no son robustos frente a la desviación de la hipótesis de normalidad de los datos, incluso para tamaños muéstrales relativamente grandes.
El método "bootstrap" proporciona un estimador de los parámetros, en términos de amplitud del intervalo y de su cobertura relativamente más adecuado que el método clásico, basado en la hipótesis de normalidad de la variable estudiada.
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Diabaté, Modibo. "Modélisation stochastique et estimation de la croissance tumorale." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAM040.
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Cette thèse porte sur la modélisation mathématique de la dynamique du cancer ; elle se divise en deux projets de recherche.Dans le premier projet, nous estimons les paramètres de la limite déterministe d'un processus stochastique modélisant la dynamique du mélanome (cancer de la peau) traité par immunothérapie. L'estimation est réalisée à l'aide d'un modèle statistique non-linéaire à effets mixtes et l'algorithme SAEM, à partir des données réelles de taille tumorale mesurée au cours du temps chez plusieurs patients. Avec ce modèle mathématique qui ajuste bien les données, nous évaluons la probabilité de rechute du mélanome (à l'aide de l'algorithme Importance Splitting), et proposons une optimisation du protocole de traitement (doses et instants du traitement).Nous proposons dans le second projet, une méthode d'approximation de vraisemblance basée sur une approximation de l'algorithme Belief Propagation à l'aide de l'algorithme Expectation-Propagation, pour une approximation diffusion du modèle stochastique de mélanome observée chez un seul individu avec du bruit gaussien. Cette approximation diffusion (définie par une équation différentielle stochastique) n'ayant pas de solution analytique, nous faisons recours à une méthode d'Euler pour approcher sa solution (après avoir testé la méthode d'Euler sur le processus de diffusion d'Ornstein Uhlenbeck). Par ailleurs, nous utilisons une méthode d'approximation de moments pour faire face à la multidimensionnalité et la non-linéarité de notre modèle. A l'aide de la méthode d'approximation de vraisemblance, nous abordons l'estimation de paramètres dans des Modèles de Markov CachésThis thesis is about mathematical modeling of cancer dynamics ; it is divided into two research projects.In the first project, we estimate the parameters of the deterministic limit of a stochastic process modeling the dynamics of melanoma (skin cancer) treated by immunotherapy. The estimation is carried out with a nonlinear mixed-effect statistical model and the SAEM algorithm, using real data of tumor size. With this mathematical model that fits the data well, we evaluate the relapse probability of melanoma (using the Importance Splitting algorithm), and we optimize the treatment protocol (doses and injection times).We propose in the second project, a likelihood approximation method based on an approximation of the Belief Propagation algorithm by the Expectation-Propagation algorithm, for a diffusion approximation of the melanoma stochastic model, noisily observed in a single individual. This diffusion approximation (defined by a stochastic differential equation) having no analytical solution, we approximate its solution by using an Euler method (after testing the Euler method on the Ornstein Uhlenbeck diffusion process). Moreover, a moment approximation method is used to manage the multidimensionality and the non-linearity of the melanoma mathematical model. With the likelihood approximation method, we tackle the problem of parameter estimation in Hidden Markov Models
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Madelain, Vincent. "Modélisation de l’effet du favipiravir sur la dynamique viro-immunologique de la maladie à virus Ebola et implications pour son évaluation clinique." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC049.
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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 EbolaIn 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
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Novakovic, Ana M. "Longitudinal Models for Quantifying Disease and Therapeutic Response in Multiple Sclerosis." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-316562.
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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.
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Chevallier, Juliette. "Statistical models and stochastic algorithms for the analysis of longitudinal Riemanian manifold valued data with multiple dynamic." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX059/document.
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Par delà les études transversales, étudier l'évolution temporelle de phénomènes connait un intérêt croissant. En effet, pour comprendre un phénomène, il semble plus adapté de comparer l'évolution des marqueurs de celui-ci au cours du temps plutôt que ceux-ci à un stade donné. Le suivi de maladies neuro-dégénératives s'effectue par exemple par le suivi de scores cognitifs au cours du temps. C'est également le cas pour le suivi de chimiothérapie : plus que par l'aspect ou le volume des tumeurs, les oncologues jugent que le traitement engagé est efficace dès lors qu'il induit une diminution du volume tumoral.L'étude de données longitudinales n'est pas cantonnée aux applications médicales et s'avère fructueuse dans des cadres d'applications variés tels que la vision par ordinateur, la détection automatique d'émotions sur un visage, les sciences sociales, etc.Les modèles à effets mixtes ont prouvé leur efficacité dans l'étude des données longitudinales, notamment dans le cadre d'applications médicales. Des travaux récent (Schiratti et al., 2015, 2017) ont permis l'étude de données complexes, telles que des données anatomiques. L'idée sous-jacente est de modéliser la progression temporelle d'un phénomène par des trajectoires continues dans un espace de mesures, que l'on suppose être une variété riemannienne. Sont alors estimées conjointement une trajectoire moyenne représentative de l'évolution globale de la population, à l'échelle macroscopique, et la variabilité inter-individuelle. Cependant, ces travaux supposent une progression unidirectionnelle et échouent à décrire des situations telles que la sclérose en plaques ou le suivi de chimiothérapie. En effet, pour ces pathologies, vont se succéder des phases de progression, de stabilisation et de remision de la maladie, induisant un changement de la dynamique d'évolution globale.Le but de cette thèse est de développer des outils méthodologiques et algorithmiques pour l’analyse de données longitudinales, dans le cas de phénomènes dont la dynamique d'évolution est multiple et d'appliquer ces nouveaux outils pour le suivi de chimiothérapie. Nous proposons un modèle non-linéaire à effets mixtes dans lequel les trajectoires d'évolution individuelles sont vues comme des déformations spatio-temporelles d'une trajectoire géodésique par morceaux et représentative de l'évolution de la population. Nous présentons ce modèle sous des hypothèses très génériques afin d'englober une grande classe de modèles plus spécifiques.L'estimation des paramètres du modèle géométrique est réalisée par un estimateur du maximum a posteriori dont nous démontrons l'existence et la consistance sous des hypothèses standards. Numériquement, du fait de la non-linéarité de notre modèle, l'estimation est réalisée par une approximation stochastique de l'algorithme EM, couplée à une méthode de Monte-Carlo par chaînes de Markov (MCMC-SAEM). La convergence du SAEM vers les maxima locaux de la vraisemblance observée ainsi que son efficacité numérique ont été démontrées. En dépit de cette performance, l'algorithme SAEM est très sensible à ses conditions initiales. Afin de palier ce problème, nous proposons une nouvelle classe d'algorithmes SAEM dont nous démontrons la convergence vers des minima locaux. Cette classe repose sur la simulation par une loi approchée de la vraie loi conditionnelle dans l'étape de simulation. Enfin, en se basant sur des techniques de recuit simulé, nous proposons une version tempérée de l'algorithme SAEM afin de favoriser sa convergence vers des minima globauxBeyond transversal studies, temporal evolution of phenomena is a field of growing interest. For the purpose of understanding a phenomenon, it appears more suitable to compare the evolution of its markers over time than to do so at a given stage. The follow-up of neurodegenerative disorders is carried out via the monitoring of cognitive scores over time. The same applies for chemotherapy monitoring: rather than tumors aspect or size, oncologists asses that a given treatment is efficient from the moment it results in a decrease of tumor volume. The study of longitudinal data is not restricted to medical applications and proves successful in various fields of application such as computer vision, automatic detection of facial emotions, social sciences, etc.Mixed effects models have proved their efficiency in the study of longitudinal data sets, especially for medical purposes. Recent works (Schiratti et al., 2015, 2017) allowed the study of complex data, such as anatomical data. The underlying idea is to model the temporal progression of a given phenomenon by continuous trajectories in a space of measurements, which is assumed to be a Riemannian manifold. Then, both a group-representative trajectory and inter-individual variability are estimated. However, these works assume an unidirectional dynamic and fail to encompass situations like multiple sclerosis or chemotherapy monitoring. Indeed, such diseases follow a chronic course, with phases of worsening, stabilization and improvement, inducing changes in the global dynamic.The thesis is devoted to the development of methodological tools and algorithms suited for the analysis of longitudinal data arising from phenomena that undergo multiple dynamics and to apply them to chemotherapy monitoring. We propose a nonlinear mixed effects model which allows to estimate a representative piecewise-geodesic trajectory of the global progression and together with spacial and temporal inter-individual variability. Particular attention is paid to estimation of the correlation between the different phases of the evolution. This model provides a generic and coherent framework for studying longitudinal manifold-valued data.Estimation is formulated as a well-defined maximum a posteriori problem which we prove to be consistent under mild assumptions. Numerically, due to the non-linearity of the proposed model, the estimation of the parameters is performed through a stochastic version of the EM algorithm, namely the Markov chain Monte-Carlo stochastic approximation EM (MCMC-SAEM). The convergence of the SAEM algorithm toward local maxima of the observed likelihood has been proved and its numerical efficiency has been demonstrated. However, despite appealing features, the limit position of this algorithm can strongly depend on its starting position. To cope with this issue, we propose a new version of the SAEM in which we do not sample from the exact distribution in the expectation phase of the procedure. We first prove the convergence of this algorithm toward local maxima of the observed likelihood. Then, with the thought of the simulated annealing, we propose an instantiation of this general procedure to favor convergence toward global maxima: the tempering-SAEM
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Machado, Robson José Mariano. "Modelos mistos semiparamétricos parcialmente não lineares." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/4582.
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Previous issue date: 2014-03-28Universidade Federal de Sao Carlos
Correlated data sets with nonlinear structure are common in many areas such as biostatistics, pharmacokinetics and longitudinal studies. Nonlinear mixed-effects models are useful tools to analyse those type of problems. In this dissertation, a generalization to this models is proposed, namely by semiparametric partially nonlinear mixed-effects model (MMSPNL), with a nonparametric function to model the mean of the response variable. It assumes that the mean of the interest variable is explained by a nonlinear function, which depends on fixed effects parameters and explanatory variables, and by a nonparametric function. Such nonparametic function is quite flexible, allowing a better adequacy to the functional form that underlies the data. The random effects are included linearly to the model, which simplify the expression of the response variable distribution and enables the model to take into account the within-group correlation structure. It is assumed that the random errors and the random effects jointly follow a multivariate normal distribution. Relate to the nonparametric function, it is deal with the P-splines smoothing technique. The methodology to obtain the parameters estimates is penalized maximum likelihood method. The random effects may be obtained by using the Empirical Bayes method. The goodness of the model and identification of potencial influent observation is verified with the local influence method and a residual analysis. The pharmacokinetic data set, in which the anti-asthmatic drug theophylline was administered to 12 subjects and serum concentrations were taken at 11 time points over the 25 hours (after being administered), was re-analysed with the proposed model, exemplifying its uses and properties.
Dados correlacionados com estrutura não linear são comuns em bioestatística, estudos farmacocinéticos e longitudinais. Modelos mistos não lineares são ferramentas úteis para se analisar esses tipos de problemas. Nesta dissertação, propõe-se uma generalização desses modelos, chamada de modelo misto semiparamétrico parcialmente não linear (MMSPNL), com uma função não paramétrica para se modelar a média da variável resposta. Assume-se que a média da variável de interesse é explicada por uma função não linear, que depende de parâmetros de efeitos fixos e variáveis explicativas, e por uma função não paramétrica. Tal função não paramétrica possui grande flexibilidade, permitindo uma melhor adequação à forma funcional que subjaz aos dados. Os efeitos aleatórios são incluídos linearmente ao modelo, o que simplifica a expressão da distribuição da variável resposta e permite considerar a estrutura de correlação intra grupo. É assumido que os erros aleatórios e efeitos aleatórios conjuntamente seguem uma distribuição normal multivariada. Em relação a função não paramétrica, utiliza-se a técnica de suavização com P-splines. A metodologia para se obterem as estimativas dos parâmetros é o método de máxima verossimilhança penalizada. Os efeitos aleatórios podem ser obtidos usando-se o método de Bayes empírico. A qualidade do modelo e a identificação de observações aberrantes é verificada pelo método de influência local e por análise de resíduos. O conjunto de dados farmacocinéticos, em que o antiasmático theophylline foi administrado a 12 sujeitos e concentrações séricas foram tomadas em 11 instantes de tempo durante as 25 horas (após ser administrado), foi reanalisado com o modelo proposto, exemplificando seu uso e propriedades.
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Paraiba, Carolina Costa Mota. "Modelos não lineares truncados mistos para locação e escala." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/4497.
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Previous issue date: 2015-01-14Financiadora de Estudos e Projetos
We present a class of nonlinear truncated mixed-effects models where the truncation nature of the data is incorporated into the statistical model by assuming that the variable of interest, namely the truncated variable, follows a truncated distribution which, in turn, corresponds to a conditional distribution obtained by restricting the support of a given probability distribution function. The family of nonlinear truncated mixed-effects models for location and scale is constructed based on the perspective of nonlinear generalized mixed-effects models and by assuming that the distribution of response variable belongs to a truncated class of distributions indexed by a location and a scale parameter. The location parameter of the response variable is assumed to be associated with a continuous nonlinear function of covariates and unknown parameters and with unobserved random effects, and the scale parameter of the responses is assumed to be characterized by a continuous function of the covariates and unknown parameters. The proposed truncated nonlinear mixed-effects models are constructed assuming both random truncation limits; however, truncated nonlinear mixed-effects models with fixed known limits are readily obtained as particular cases of these models. For models constructed under the assumption of random truncation limits, the likelihood function of the observed data shall be a function both of the parameters of the truncated distribution of the truncated variable and of the parameters of the distribution of the truncation variables. For the particular case of fixed known truncation limits, the likelihood function of the observed data is a function only of the parameters of the truncated distribution assumed for the variable of interest. The likelihood equation resulting from the proposed truncated nonlinear regression models do not have analytical solutions and thus, under the frequentist inferential perspective, the model parameters are estimated by direct maximization of the log-likelihood using an iterative procedure. We also consider diagnostic analysis to check for model misspecification, outliers and influential observations using standardized residuals, and global and local influence metrics. Under the Bayesian perspective of statistical inference, parameter estimates are computed based on draws from the posterior distribution of parameters obtained using an Markov Chain Monte Carlo procedure. Posterior predictive checks, Bayesian standardized residuals and a Bayesian influence measures are considered to check for model adequacy, outliers and influential observations. As Bayesian model selection criteria, we consider the sum of log -CPO and a Bayesian model selection procedure using a Bayesian mixture model framework. To illustrate the proposed methodology, we analyze soil-water retention, which are used to construct soil-water characteristic curves and which are subject to truncation since soil-water content (the proportion of water in soil samples) is limited by the residual soil-water content and the saturated soil-water content.
Neste trabalho, apresentamos uma classe de modelos não lineares truncados mistos onde a característica de truncamento dos dados é incorporada ao modelo estatístico assumindo-se que a variável de interesse, isto é, a variável truncada, possui uma função de distribuição truncada que, por sua vez, corresponde a uma função de distribuição condicional obtida ao se restringir o suporte de alguma função de distribuição de probabilidade. A família de modelos não lineares truncados mistos para locação e escala é construída sob a perspectiva de modelos não lineares generalizados mistos e considerando uma classe de distribuições indexadas por parâmetros de locação e escala. Assumimos que o parâmetro de locação da variável resposta é associado a uma função não linear contínua de um conjunto de covariáveis e parâmetros desconhecidos e a efeitos aleatórios não observáveis, e que o parâmetro de escala das respostas pode ser caracterizado por uma função contínua das covariáveis e de parâmetros desconhecidos. Os modelos não lineares truncados mistos para locação e escala, aqui apresentados, são construídos supondo limites de truncamento aleatórios, porém, modelos não lineares truncados mistos com limites fixos e conhecidos são prontamente obtidos como casos particulares desses modelos. Nos modelos construídos sob a suposição de limites de truncamentos aleatórios, a função de verossimilhança é escrita em função dos parâmetros da distribuição da variável resposta truncada e dos parâmetros das distribuições das variáveis de truncamento. Para o caso particular de limites fixos e conhecidos, a função de verossimilhança será apenas uma função dos parâmetros da distribuição truncada assumida para a variável resposta de interesse. As equações de verossimilhança dos modelos, aqui propostos, não possuem soluções analíticas e, sob a perspectiva frequentista de inferência estatística, os parâmetros do modelo são estimados pela maximização direta da função de log-verossimilhança via um procedimento iterativo. Consideramos, também, uma análise de diagnóstico para verificar a adequação do modelo, observações discrepantes e/ou influentes, usando resíduos padronizados e medidas de influência global e influência local. Sob a perspectiva Bayesiana de inferência estatística, as estimativas dos parâmetros dos modelos propostos são definidas como as médias a posteriori de amostras obtidas via um algoritmo do tipo cadeia de Markov Monte Carlo das distribuições a posteriori dos parâmetros. Para a análise de diagnóstico Bayesiano do modelo, consideramos métricas de avaliação preditiva a posteriori, resíduos Bayesianos padronizados e a calibração de casos para diagnóstico de influência. Como critérios Bayesianos de seleção de modelos, consideramos a soma de log -CPO e um critério de seleção de modelos baseada na abordagem Bayesiana de mistura de modelos. Para ilustrar a metodologia proposta, analisamos dados de retenção de água em solo, que são usados para construir curvas de retenção de água em solo e que estão sujeitos a truncamento pois as medições de umidade de água (a proporção de água presente em amostras de solos) são limitadas pela umidade residual e pela umidade saturada do solo amostrado.
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Chiswell, Karen Elizabeth. "Model diagnostics for the nonlinear mixed effects model with balanced longitudinal data." 2007. http://www.lib.ncsu.edu/theses/available/etd-09042007-214316/unrestricted/etd.pdf.
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"Examination of Mixed-Effects Models with Nonparametrically Generated Data." Doctoral diss., 2019. http://hdl.handle.net/2286/R.I.53768.
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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
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Wang, Hui-Ching, and 王繪情. "Analyzing data in ovarian cancer study using extended Cox proportional hazards model (including time-varying coefficients) and nonlinear mixed-effects model." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/2a43re.
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碩士國立中山大學
應用數學系研究所
103
Ovarian cancer is not the most common tumor in gynecology department, but it is the most lethal gynecologic malignancy. The first part is to find the important variates between different cell types. We use Kaplan-Meier curve to analysis the survival curves with different cell types, and test whether the curves are different by log-rank test. The second part, we were interested in the correlation of the risk factors and survival. The traditional Cox proportional hazards model has been used to identify independent risk factors without considering time effect. The objective of this study was to explore whether the risk factors in ovarian cancer had time-varying effects on survival. We shared the R package on internet for download. The final section is to model patients'' CA125 by time. We can roughly classify patients into two types with the tendency of CA125. After treatment, the perform of CA125 will keep stable continuously or get rise eventually. Therefore, we use nonlinear mixed-effects model with Bayesian hierarchical framework to analysis the longitudinal data. Data used in this study was from Kaohsiung Veteran''s General Hospital from 1995 to end of 2011.
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Wang, Li-pei, and 王莉珮. "Bayesian inference for a piecewise nonlinear mixed-effects model with skewed distribution and heteroscedasticity with application to an ovarian cancer study." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/4qd8n7.
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碩士國立中山大學
應用數學系研究所
105
In ovarian cancer studies, cancer antigen 125 (CA125) is an important tumor marker which is repeatedly measured over time. We aim to model the CA125 trajectories that can help us understand patients’ prognosis. In longitudinal studies, nonlinear mixed-effects (NLME) models are often used to model patients’ trajectories. The random effects and random errors of NLME are often assumed to be normally distributed and in addition, errors are assumed to be homogeneous. However, these assumption may not be satisfied when modeling the CA125 trajectories. In this paper, we propose a general nonlinear mixed-effects model with random effects being skewed and errors being skewed, heteroskedastic and possibly heavy tailed. We applied the proposed model to the CA125 trajectories and compared the fitting of our model to those with other models. Moreover, we conducted a simulation study to study the effects of skewness, heteroskedasticity and heavy tail on the fitting.
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TSAI, YI-SHIUAN, and 蔡宜軒. "Maximum Likelihood Estimation for Multivariate Nonlinear Mixed-effects Models." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/8f5s94.
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碩士逢甲大學
統計學系統計與精算碩士班
102
Multivariate nonlinear mixed-effects models (MNLMM) have recently received a great deal of attention in the statistical literature due to the flexibility for analyzing a broad range of multi-outcome longitudinal data especially following nonlinear profiles. In this thesis, we aim at providing five different methods for maximum likelihood (ML) estimation of the parameters in the MNLMM. The five approximation methods include the penalized nonlinear least squares coupled with multivariate linear mixed effects (PNLS-MLME) approximation, Laplacian approximation, pseudodata ECM algorithm, Monte Carlo EM algorithm, and importance sampling approximation. A somewhat complex numerical issue for ML estimation in the MNLMM is the evaluation of the observed log-likelihood function because it involves evaluating a multiple integral that, in most cases, does not show a closed-form expression. Thus, we also offer several approximations to the observed log-likelihood function and an information-based method to calculate the standard errors of parameters estimates under large sample properties. A comparison of the computational performance for the proposed methods is investigated through a simulation study and an application to a real dataset.
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Zhou, Meijian. "Fully exponential Laplace approximation EM algorithm for nonlinear mixed effects models." 2009. http://proquest.umi.com/pqdweb?did=1933939851&sid=8&Fmt=2&clientId=14215&RQT=309&VName=PQD.
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Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009.Title from title screen (site viewed February 25, 2010). PDF text: x, 193 p. ; 3 Mb. UMI publication number: AAT 3386609. Includes bibliographical references. Also available in microfilm and microfiche formats.
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Calegario, Natalino. "Modeling Eucalyptus stand growth based on linear and nonlinear mixed-effects models." 2002. http://purl.galileo.usg.edu/uga%5Fetd/calegario%5Fnatalino%5F200205%5Fphd.
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Wang, Jing. "An optimization approach for the parameter estimation of the nonlinear mixed effects models." 2004. http://www.lib.ncsu.edu/theses/available/etd-07282004-165624/unrestricted/etd.pdf.
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Chen, Yakuan. "Methods for functional regression and nonlinear mixed-effects models with applications to PET data." Thesis, 2017. https://doi.org/10.7916/D87W6QJ9.
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The overall theme of this thesis focuses on methods for functional regression and nonlinear mixed-effects models with applications to PET data.
The first part considers the problem of variable selection in regression models with functional responses and scalar predictors. We pose the function-on-scalar model as a multivariate regression problem and use group-MCP for variable selection. We account for residual covariance by "pre-whitening" using an estimate of the covariance matrix, and establish theoretical properties for the resulting estimator. We further develop an iterative algorithm that alternately updates the spline coefficients and covariance. Our method is illustrated by the application to two-dimensional planar reaching motions in a study of the effects of stroke severity on motor control.
The second part introduces a functional data analytic approach for the estimation of the IRF, which is necessary for describing the binding behavior of the radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject's IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which shrinkage and roughness penalties are incorporated to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and non-negativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data.
The third part discusses a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a compartment model. The traditional NLS estimators of the population parameters are applied in a two-stage analysis, which brings instability issue and neglects the variation in rate parameters. In contrast, we propose to estimate the rate parameters by fitting nonlinear mixed-effects (NLME) models, in which all the subjects are modeled simultaneously by allowing rate parameters to have random effects and population parameters can be estimated directly from the joint model. Simulations are conducted to compare the power of detecting group effect in both rate parameters and summarized measures of tests based on both NLS and NLME models. We apply our NLME approach to clinical PET data to illustrate the model building procedure.
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HUANG, YAN-LING, and 黃彥菱. "Analysis of Longitudinal Data with Censored and Missing Values via Nonlinear Mixed-effects Models." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/23267683758841290881.
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碩士逢甲大學
統計學系
105
Repeated measures from clinical trials or biomedical research are usually collected and shown to be nonlinear profiles, the nonlinear mixed-effects model (NLMM) has become a popular modelling tool for analyzing such kind of data. However, censored and missing data often occur in longitudinal studies due to limitations of the measuring technology, missed visits, loss to follow-up, and so on. This thesis formulates the nonlinear mixed-effects model with censored and missing responses (NLMM-CM), which allows the analysts to model longitudinal data in the presence of censored and missing values simultaneously. The nonlinear mixed-effects model with censored values (NLMM-C), nonlinear mixed-effects model with missing values (NLMM-M) and nonlinear mixed-effects model (NLMM), which are treated as special cases of the NLMM-CM, are also presented and compared to the proposed NLMM-CM in simulation sudies. To carry out maximum likelihood estimation of model parameters, we provide an efficient expectation conditional maximization (ECM) algorithm. This method is developed under the complete pseudo-data likelihood function, which is derived by using first-order Taylor expansion around individual-specific parameters. Real-data examples and simulation studies are used to demonstrate the performance of our proposed methods.
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Song, Shijun. "Nonlinear mixed effects models with dropout and missing covariates when the dropout depends on the random effects." Thesis, 2005. http://hdl.handle.net/2429/16692.
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Nonlinear mixed effects models (NLMEs) are very popular in many longitudinal
studies such as HIV viral dynamic studies, pharmacokinetics analyses, and studies
of growth and decay. In these studies, however, missing data problems often arise,
which make some statistical analyses complicated. In this thesis, we proposed an
exact method and an approximate method for NLMEs with random-effects based informative
dropouts and missing covariates, and propose methods for simultaneous
inference. Monte Carlo E M algorithms are used in both methods. The approximate
method, which is based on a Taylor series expansion, avoids sampling the random
effects in the E-step and thus reduces the computation burden substantially. To illustrate
the proposed methods, we analyze two real datasets. The exact method is
applied to a dataset with covariates and a dataset without covariates. The approximate
method is applied to the dataset without covariates. The result shows that, for
both datasets, dropouts may be correlated with individual random effects. Ignoring
the missingness or assuming ignorable missingness may lead to unreliable inferences.
A simulation study is performed to evaluate the two proposed methods under various
situations.Science, Faculty of
Statistics, Department of
Graduate
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Li, He. "A simulation study of the second-order least squares estimators for nonlinear mixed effects models." 2006. http://hdl.handle.net/1993/20816.
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Rodriguez-Zas, Sandra Luisa. "Bayesian analysis of somatic cell score lactation patterns in Holstein cows using nonlinear mixed effects models." 1998. http://catalog.hathitrust.org/api/volumes/oclc/40952874.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1998.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 392-426).
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Liu, Wei. "The theory and methods for measurement errors and missing data problems in semiparametric nonlinear mixed-effects models." Thesis, 2006. http://hdl.handle.net/2429/18520.
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Semiparametric nonlinear mixed-effects (NLME) models are flexible for modelling complex longitudinal data. Covariates are usually introduced in the models to partially explain inter-individual variations. Some covariates, however, may be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. In this thesis, we develop approximate maximum likelihood inference in the following three problems: (1) semiparametric NLME models with measurement errors and missing data in time-varying covariates; (2) semiparametric NLME models with covariate measurement errors and outcome-based informative missing responses; (3) semiparametric NLME models with covariate measurement errors and random-effect-based informative missing responses. Measurement errors, dropouts, and missing data are addressed simultaneously in a unified way. For each problem, we propose two joint model methods to simultaneously obtain approximate maximum likelihood estimates (MLEs) of all model parameters. Some asymptotic properties of the estimates are discussed. The proposed methods are illustrated in a HIV data example. Simulation results show that all proposed methods perform better than the commonly used two-step method and the naive method.Science, Faculty of
Statistics, Department of
Graduate
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Chen, Chi-Chung, and 陳吉重. "Bayesian analysis for mixture nonlinear mixed-effects models with skewed random effects and errors with application to an ovarian cancer study." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/51744864893611079506.
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碩士國立中山大學
應用數學系研究所
104
It is common to analyze longitudinal data using nonlinear mixed-effects (NLME) model. And we often use NLME model with normality and homogeneity assumption. However, this assumption may be unrealistic in practice. Our aim is to model the longitu- dinal profiles of CA125, a tumor marker, in an ovarian cancer study. When fitting these profiles using NLME model, we observed that the distribution of the random effects and errors are skewed. Hence we propose an NLME model with skewed normal random effects and skewed-t errors. Moreover, we observed that errors and some of the random effects are heterogeneous due to early and late cancer stage. Therefore, we apply the Bayesian hierarchical framework using the heterogeneity and skewness information to construct our new NLME model. Most importantly, we hope that this model can be helpful for doctors during the clinical treatments. In the second part, we provide a more generalized Cox proportional hazard (Cox PH) model. The traditional Cox PH model has been used to identify the risk factors without considering time-varying effects. A generalized Cox PH model must satisfy the proportional hazard assumption, even though the risk factors are time-dependent. Wang (2015) has provided a more generalized Cox PH model by considering the risk factors which have time-varying effects and shared the R package. Here we extended the model even more. Some of the risk factors which are time-dependent can have time-varying effects simultaneously. We use spline function to approximate the time-varying coefficients and also provide an R function.
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Svensson, Elin M. "Pharmacometric Models to Improve Treatment of Tuberculosis." Doctoral thesis, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-282139.
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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.