Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools

ISBN-13: 9781032477350 / Angielski / Miękka / 2023 / 384 str.

Marc Lavielle

Opis

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.

Spis treści

Introduction and Preliminary Concepts: Overview. Mixed Effects Models vs Hierarchical Models. What Is a Model? A Joint Probability Distribution! Defining Models: Modeling Observations. Modeling the Individual Parameters. Extensions. Using Models: Tasks and Methods. Examples. Algorithms. Appendices: The Individual Approach. Some Useful Results. Introduction to Pharmacokinetics Modeling. Tools. Bibliography. Glossary. Index.

O autorze

Marc Lavielle is a statistician specializing in computational statistics and healthcare applications. He holds a Ph.D. in statistics from University Paris-Sud, Orsay. He was named professor at Paris Descartes University and joined Inria as research director in 2007. Creator of the Monolix software, he led the Monolix software development project at Inria between 2009 and 2011. He created the CNRS Research Group "Statistics and Health" in 2007. Since 2009, Dr. Lavielle has been a member of the French High Council of Biotechnologies, where he promotes the use of sound statistical methods to evaluate health and environmental risks related to genetically modified organisms (GMOs).