Chapman and Hall/CRC
383 pages | 147 B/W Illus.
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.
"Although there are many excellent books available on mixed linear models and generalized linear mixed models, few provide broad coverage of nonlinear models. The strength of this text is the extensive coverage of the modeling of nonlinear trajectories in a wide variety of forms." (Journal of the American Statistical Association)
"… the text contains much of interest to the applied statistician who may be working as a consultant. … I found the text useful to explain the difference between individual and population models so I have no hesitation in recommending this book for applied statisticians who may need a few well-developed examples from which to explain, and explore, statistical concepts and hierarchical modeling with non-statistical clients. In addition to model formulation and parameter estimation, the author addresses topics in model selection and diagnostic tools, too. … a valuable text that is well-worth reading …"
—International Statistical Review, 2015
"… it is very precise … I was pleasantly surprised at how readable it was … a very good addition to the books of Davidian and Giltinan and Bonate. … an essential companion to the Monolix software … I would highly recommend it to all practitioners of the population approach for the systematic and thorough way it presents the subject."
—CPT: Pharmacometrics & Systems Pharmacology, 2015"… the first combination of a 'how-to' framework for statisticians and mathematicians with a thorough description of the statistical and mathematical models for users with a clinical background. … an excellent book on how to model biopharmaceutical data with a very good structure and solid lecture materials."
—Julie Bertrand, Journal of Biopharmaceutical Statistics
Introduction and Preliminary Concepts
The population approach
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
Continuous data models
Models for count data
Models for categorical data
Models for time-to-event data
Modeling the Individual Parameters
Models with covariates
Extensions to multivariate distributions
Additional levels of variability
Different mathematical representations and implementations of the same model
Stochastic differential equation-based models
Tasks and Methods
Body weight curves in a toxicity study
Joint PKPD modeling of warfarin data
Gene expression in single cells
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
The Individual Approach
Some Useful Results
Introduction to Pharmacokinetics Modeling