Pharmacokinetic-Pharmacodynamic Modeling and Simulation shows, through theory and example, how to develop pharmacokinetic models, both at an individual and population level.

Each chapter builds upon previous chapters by first presenting the theory and then illustrating the theory using published data sets and actual data sets that were used in the development of new chemical entities.

The book provides an understanding of linear models and then builds to nonlinear models followed by linear mixed effects models and then ultimately nonlinear mixed effects models.

A key feature of the book is the process of modeling. In this book all examples are presented in an evolutionary manner.

Contents

1: The Art of Modeling

• What Is a Model and Why Are They Made?
• Modeling as Problem Solving
• Type of Models
• Properties of a Useful Model
• The Model Development Process
• Goodness of Fit Criteria
• Residuals and Residual Analysis
• Goodness of Fit Metrics
• Model Selection
• General Comments
• Choosing Compartmental Models
• Bias versus Variance Tradeoff
• Model Discrimination Criteria
• A Note on Inference
• Closing Notes
• Identifiability of Compartmental Models
• Model Validation
• The Importance of Effective Communication
• Good Plotting Practices
• Writing a Modeling Report
• Ethics in Modeling

2: Linear Models and Regression

• The Method of Least Squares and Simple Linear Regression
• The Concept of Ordinary Least Squares Applied to the Simple Linear Model
• Maximum Likelihood Estimation of Parameters in a Simple Linear Model
• Precision and Inference of the Parameter Estimates for the Simple Linear Model
• Regression Through the Origin Goodness of Fit Tests for the
• Simple Linear Model
• Prediction and Extrapolation in the Simple Linear Model
• Categorical Independent Variables
• Multiple Linear Regression
• Model Selection and Sequential Variable Selection
• Procedures in Multiple Linear Regression
• Collinearity and Ill-Conditioning
• Influence Diagnostics
• Influence in the X-direction
• Influence in the Y-direction
• Identification of Influential Observations
• So What Now?
• Example
• Conditional Models
• Error-in-Variables Regression
• Polynomial Regression
• Handling Missing Data
• Types of Missing Data and Definitions
• Methods for Handling Missing Data: Missing Dependent Variables
• Methods for Handling Missing Data: Missing Independent Variables

3: Nonlinear Models and Regression

• Nonlinear Least Squares
• Functions with One Variable
• Functions of Several Variables: The Gradient and Hessian
• Gradient Algorithms
• Newton or Newton-Raphson Based Methods
• Gauss-Newton Methods and Its Modifications
• Derivative Free Algorithms
• Convergence
• Inferences on the Parameter Estimates
• Functions of Model Parameters
• Obtaining Initial Parameter Estimates
• Ill-Conditioning and Near Singularity
• Constrained Optimization
• Influence Diagnostics
• Confidence Intervals for the Predicted Response
• Incorporating Prior Information into the Likelihood
• Error-in-Variables Nonlinear Regression
• Summarizing the Results: The 2-Stage Method
• Missing and Censored Data
• Fitting Discordant Models Among Individuals

Chapter 4: Variance Models, Weighting, and Transformations

• Residual Variance Models
• Testing for Heteroscedasticity
• Impact of Heteroscedasticity on OLS Estimates
• Impact of Heteroscedasticity on Parameter Inference
• Residual Variance Model Parameter Estimation Using Weighted Least-Squares
• Monte Carlo Comparison of the Methods
• Residual Variance Model Parameter Estimation Using Maximum Likelihood
• Model and/or Data Transformations to Normality or Linearity

5: Case Studies in Linear and Nonlinear Modeling

• Linear Regression Case Study: Allometric Scaling
• Linear Regression Case Study: Dose Proportionality
• Linear Regression Case Study: Limited Sampling Strategies
• Nonlinear Regression Case Study: Pharmacokinetic Modeling of Cocaine after Intravenous, Smoking Inhalation (‘‘Crack Cocaine’’) and Intranasal (‘‘Snorting’’) Administration
• Nonlinear Regression Case Study: Pharmacokinetic Modeling of a New Chemical Entity
• Nonlinear Regression Case Study: Assessing the Relationship Between Drug Concentrations and Adverse Events Using Logistic Regression

6: Linear Mixed Effects Models

• Fixed Effects, Random Effects, and Mixed Effects
• Sources of Variability
• A Two-Stage Analysis
• The General Linear Mixed Effects Model
• Estimation of the Mixed Effect Model Parameters
• Inference for the Fixed Effect Parameter Estimates
• Inference for the Variance Components
• Estimation of the Random Effects and Empirical Bayes Estimates
• Model Selection
• Sensitivity to the Model Assumptions
• Residual Analysis and Goodness of Fit
• Influence Analysis
• Handling Missing and Censored Data

7: Nonlinear Mixed Effects Models: Theory

• Application of PopPK in Drug Development
• The Nonlinear Mixed Effects Model
• The Structural or Base Model
• Modeling Random Effects
• Modeling Between-Subject Variability
• Modeling Interoccasion Variability
• Modeling Interstudy Variability
• Modeling Residual Variability
• Incorporating Fixed and Random Effects into the Structural Model
• Modeling Covariate Relationships (The Covariate Submodel)
• Mixture Models
• Estimation Methods
• Model Building Techniques
• Covariate Screening Methods
• Manual Covariate Screening Methods
• Direct Covariate Testing
• Automated Covariate Screening Methods
• Comparison of the Covariate Selection Methods
• Testing the Model Assumptions
• Precision of the Parameter Estimates and Confidence Intervals
• Model Misspecification and Violation of the Model Assumptions
• Misspecification of the Structural Model
• Misspecification of the Distribution of the Random Effects
• Interaction between the Structural and Covariate Submodel
• Misspecification of Sample Times
• Model Validation
• Influence Analysis
• More on Empirical Bayes Estimates

8: Nonlinear Mixed Effects Models: Practical Issues

• The Data Analysis Plan
• Choosing an Estimation Method
• Incorporating Concomitant Medications Into the Model
• Incorporating Laboratory Tests Into the Model
• Incorporating Weight and its Variants Into the Model
• Incorporating a Food Effect Into the Model
• Incorporating Patient Age Into the Model
• Incorporating Formulation Effects and Route of Administration Into the Model
• Incorporating Race Into the Model
• Incorporating Pharmacogenetics Into the Model
• Incorporating Prior Information into the Model
• Incorporating Lag-Times into the Model
• Experimental Design Issues in Phase 3
• Theory Based on Monte Carlo Simulation
• Review of Current Practice
• On the Detection of Subpopulations
• General Guidelines for Sample Collection
• Toxicokinetic Analyses with Destructive Sampling
• Handling Missing and Censored Data
• When the Dependent Variable is Missing
• When the Independent Variable is Missing
• Internal Validity Checks and Data Clean-Up
• Problems and Errors
• Consistency of Model Parameter Estimates Across Computer Platforms
• Regulatory Review of Population Analyses

9: Nonlinear Mixed Effects Models: Case Studies

• Pharmacodynamic Modeling of Acetylcholinesterase Inhibition
• Population Pharmacokinetics of Tobramycin

Appendices
Index

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