상세정보

Wide-Ranging Coverage of Parametric Modeling in Linear and Nonlinear Mixed Effects Models
Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools presents a rigorous framework for describing, implementing, and using mixed effects models. With these models, readers can perform parameter estimation and modeling across a whole population of individuals at the same time.

Easy-to-Use Techniques and Tools for Real-World Data Modeling
The book first shows how the framework allows model representation for different data types, including continuous, categorical, count, and time-to-event data. This leads to the use of generic methods, such as the stochastic approximation of the EM algorithm (SAEM), for modeling these diverse data types. The book also covers other essential methods, including Markov chain Monte Carlo (MCMC) and importance sampling techniques. The author uses publicly available software tools to illustrate modeling tasks. Methods are implemented in Monolix, and models are visually explored using Mlxplore and simulated using Simulx.

Careful Balance of Mathematical Representation and Practical Implementation
This book takes readers through the whole modeling process, from defining/creating a parametric model to performing tasks on the model using various mathematical methods. Statisticians and mathematicians will appreciate the rigorous representation of the models and theoretical properties of the methods while modelers will welcome the practical capabilities of the tools. The book is also useful for training and teaching in any field where population modeling occurs.

This book provides wide-ranging coverage of parametric modeling in linear and nonlinear mixed effects models. It presents a rigorous approach for describing, implementing, and using mixed effects models. With these models, readers can perform parameter estimation and modeling across a whole population of individuals at the same time. The book takes readers through the whole modeling process, from defining/creating a parametric model to performing tasks on the model using various mathematical methods. Numerous examples illustrate how to implement the models using the Monolix software.

정보제공 :

Introduction and Preliminary Concepts
Overview
The population approach 
About models 
Tasks, methods and tools 
Contents of the book 

Mixed Effects Models vs Hierarchical Models
From linear models to nonlinear mixed effects models .
From nonlinear mixed effects models to hierarchical models 
From generalized mixed models to hierarchical models

What Is a Model? A Joint Probability Distribution!
Introduction and notation 
An illustrative example 
Using a model for executing tasks 
Implementing hierarchical models with Mlxtran

Defining Models
Modeling Observations
Introduction 
Continuous data models 
Models for count data 
Models for categorical data 
Models for time-to-event data 
Joint models 

Modeling the Individual Parameters
Introduction 
Gaussian models 
Models with covariates 
Extensions to multivariate distributions 
Additional levels of variability 
Different mathematical representations and implementations of the same model 

Extensions
Mixture models 
Markov models 
Stochastic differential equation-based models 

Using Models
Tasks and Methods
Introduction 
Estimation 
Model evaluation 

Examples
Body weight curves in a toxicity study 
Joint PKPD modeling of warfarin data 
Gene expression in single cells 

Algorithms
Introduction 
The SAEM algorithm for estimating population parameters 
The Metropolis-Hastings algorithm for simulating the individual parameters 
Estimation of the observed Fisher information matrix 
Estimation of the log-likelihood 
Examples of calculating the log-likelihood and it derivatives 
Automatic construction of visual predictive checks 

Appendices
The Individual Approach
Some Useful Results
Introduction to Pharmacokinetics Modeling
Tools


Bibliography 
Glossary 
Index

정보제공 :