Introduction to Population Pharmacokinetic / Pharmacodynamic Analysis with Nonlinear Mixed Effects Models

Joel S. Owen is Professor of Pharmaceutics at Union University, Jackson, Tennessee and President and Principal Scientist of Joel S. Owen, LLC. He has led workshops on NONMEM and PK/PD modeling concepts and applications and served as Director PK/PD at Cognigen Corporation in Buffalo, New York. He has published 16 articles in research publications.Jill Fiedler-Kelly is Vice President and Chief Scientific Officer of Cognigen Corporation and Adjunct Associate Professor of Pharmaceutical Sciences at the University at Buffalo. She has been teaching workshops and graduate courses on population modeling for over 10 years and has published more than 20 articles and book chapters on pharmacokinetics and pharmacodynamics.

• Preface xiiiCHAPTER 1 The Practice of Pharmacometrics 11.1 Introduction 11.2 Applications of Sparse Data Analysis 21.3 Impact of Pharmacometrics 41.4 Clinical Example 5CHAPTER 2 Population Model Concepts and Terminology 92.1 Introduction 92.2 Model Elements 102.3 Individual Subject Models 112.4 Population Models 122.4.1 Fixed-Effect Parameters 132.4.2 Random-Effect Parameters 142.5 Models of Random Between-Subject Variability (L1) 172.5.1 Additive Variation 172.5.2 Constant Coefficient of Variation 182.5.3 Exponential Variation 182.5.4 Modeling Sources of Between-Subject Variation 192.6 Models of Random Variability in Observations (L2) 192.6.1 Additive Variation 202.6.2 Constant Coefficient of Variation 212.6.3 Additive Plus CCV Model 222.6.4 Log-Error Model 242.6.5 Relationship Between RV Expressions and Predicted Concentrations 242.6.6 Significance of the Magnitude of RV 252.7 Estimation Methods 262.8 Objective Function 262.9 Bayesian Estimation 27CHAPTER 3 NONMEM Overview and Writing an NM-TRAN Control Stream 283.1 Introduction 283.2 Components of the NONMEM System 283.3 General Rules 303.4 Required Control Stream Components 313.4.1 $PROBLEM Record 313.4.2 The $DATA Record 323.4.3 The $INPUT Record 353.5 Specifying the Model in NM-TRAN 353.5.1 Calling PREDPP Subroutines for Specific PK Models 353.5.2 Specifying the Model in the $PK Block 383.5.3 Specifying Residual Variability in the $ERROR Block 453.5.4 Specifying Models Using the $PRED Block 493.6 Specifying Initial Estimates with $THETA, $OMEGA, and $SIGMA 503.7 Requesting Estimation and Related Options 563.8 Requesting Estimates of the Precision of Parameter Estimates 623.9 Controlling the Output 63CHAPTER 4 Datasets 664.1 Introduction 664.2 Arrangement of the Dataset 684.3 Variables of the Dataset 714.3.1 TIME 714.3.2 DATE 714.3.3 ID 724.3.4 DV 744.3.5 MDV 744.3.6 CMT 744.3.7 EVID 754.3.8 AMT 764.3.9 RATE 774.3.10 ADDL 784.3.11 II 794.3.12 SS 804.4 Constructing Datasets with Flexibility to Apply Alternate Models 804.5 Examples of Event Records 814.5.1 Alternatives for Specifying Time 814.5.2 Infusions and Zero-Order Input 814.5.3 Using ADDL 824.5.4 Steady-State Approach 834.5.5 Samples Before and After Achieving Steady State 834.5.6 Unscheduled Doses in a Steady-State Regimen 844.5.7 Steady-State Dosing with an Irregular Dosing Interval 844.5.8 Multiple Routes of Administration 854.5.9 Modeling Multiple Dependent Variable Data Types 864.5.10 Dataset for $PRED 864.6 Beyond Doses and Observations 874.6.1 Other Data Items 874.6.2 Covariate Changes over Time 884.6.3 Inclusion of a Header Row 89CHAPTER 5 Model Building: Typical Process 905.1 Introduction 905.2 Analysis Planning 905.3 Analysis Dataset Creation 925.4 Dataset Quality Control 935.5 Exploratory Data Analysis 945.5.1 EDA: Population Description 955.5.2 EDA: Dose-Related Data 995.5.3 EDA: Concentration-Related Data 995.5.4 EDA: Considerations with Large Datasets 1115.5.5 EDA: Summary 1155.6 Base Model Development 1165.6.1 Standard Model Diagnostic Plots and Interpretation 1165.6.2 Estimation of Random Effects 1305.6.3 Precision of Parameter Estimates (Based on $COV Step) 1375.7 Covariate Evaluation 1385.7.1 Covariate Evaluation Methodologies 1405.7.2 Statistical Basis for Covariate Selection 1415.7.3 Diagnostic Plots to Illustrate Parameter-Covariate Relationships 1435.7.4 Typical Functional Forms for Covariate-Parameter Relationships 1485.7.5 Centering Covariate Effects 1565.7.6 Forward Selection Process 1605.7.7 Evaluation of the Full Multivariable Model 1675.7.8 Backward Elimination Process 1695.7.9 Other Covariate Evaluation Approaches 1715.8 Model Refinement 172CHAPTER 6 Interpreting the NONMEM Output 1786.1 Introduction 1786.2 Description of the Output Files 1786.3 The NONMEM Report File 1796.3.1 NONMEM-Related Output 1796.3.2 PREDPP-Related Output 1806.3.3 Output from Monitoring of the Search 1806.3.4 Minimum Value of the Objective Function and Final Parameter Estimates 1826.3.5 Covariance Step Output 1866.3.6 Additional Output 1876.4 Error Messages: Interpretation and Resolution 1886.4.1 NM-TRAN Errors 1886.4.2 $ESTIMATION Step Failures 1896.4.3 $COVARIANCE Step Failures 1906.4.4 PREDPP Errors 1916.4.5 Other Types of NONMEM Errors 1926.4.6 FORTRAN Compiler or Other Run-Time Errors 1936.5 General Suggestions for Diagnosing Problems 193CHAPTER 7 App lications Using Parameter Estimates from the Individual 1987.1 Introduction 1987.2 Bayes Theorem and Individual Parameter Estimates 2007.3 Obtaining Individual Parameter Estimates 2027.4 Applications of Individual Parameter Estimates 2047.4.1 Generating Subject-Specific Exposure Estimates 2047.4.2 Individual Exposure Estimates for Group Comparisons 210CHAPTER 8 Introduction to Model Evaluation 2128.1 Introduction 2128.2 Internal Validation 2128.3 External Validation 2138.4 Predictive Performance Assessment 2148.5 Objective Function Mapping 2178.6 Leverage Analysis 2208.7 Bootstrap Procedures 2228.8 Visual and Numerical Predictive Check Procedures 2238.8.1 The VPC Procedure 2238.8.2 Presentation of VPC Results 2258.8.3 The Numerical Predictive Check (NPC) Procedure 2298.9 Posterior Predictive Check Procedures 229CHAPTER 9 User-Written Models 2329.1 Introduction 2329.2 $MODEL 2359.3 $SUBROUTINES 2369.3.1 General Linear Models (ADVAN5 and ADVAN7) 2369.3.2 General Nonlinear Models (ADVAN6, ADVAN8, ADVAN9, and ADVAN13) 2389.3.3 $DES 2389.4 A Series of Examples 2409.4.1 Defined Fractions Absorbed by Zero- and First-Order Processes 2409.4.2 Sequential Absorption with First-Order Rates, without Defined Fractions 2429.4.3 Parallel Zero-Order and First-Order Absorption, without Defined Fractions 2439.4.4 Parallel First-Order Absorption Processes, without Defined Fractions 2459.4.5 Zero-Order Input into the Depot Compartment 2469.4.6 Parent and Metabolite Model: Differential Equations 247CHAPTER 10 PK/PD Models 25010.1 Introduction 25010.2 Implementation of PD Models in NONMEM 25110.3 $PRED 25210.3.1 Direct-Effect PK/PD Examples: PK Concentrations in the Dataset 25310.3.2 Direct-Effect PK/PD Example: PK from Computed Concentrations 25510.4 $PK 25610.4.1 Specific ADVANs (ADVAN1–ADVAN4 and ADVAN10–ADVAN12) 25610.4.2 General ADVANs (ADVAN5–ADVAN9 and ADVAN13) 25710.4.3 PREDPP: Effect Compartment Link Model Example (PD in $ERROR) 25710.4.4 PREDPP: Indirect Response Model Example: PD in $DES 25910.5 Odd-Type Data: Analysis of Noncontinuous Data 26110.6 PD Model Complexity 26210.7 Communication of Results 263CHAPTER 11 Simulation Basics 26511.1 Introduction 26511.2 The Simulation Plan 26511.2.1 Simulation Components 26611.2.2 The Input–Output Model 26611.2.3 The Covariate Distribution Model 27011.2.4 The Trial Execution Model 27311.2.5 Replication of the Study 27411.2.6 Analysis of the Simulated Data 27511.2.7 Decision Making Using Simulations 27511.3 Miscellaneous Other Simulation-Related Considerations 27611.3.1 The Seed Value 27611.3.2 Consideration of Parameter Uncertainty 27711.3.3 Constraining Random Effects or Responses 278CHAPTER 12 Quality Control 28512.1 Introduction 28512.2 QC of the Data Analysis Plan 28512.3 Analysis Dataset Creation 28612.3.1 Exploratory Data Analysis and Its Role in Dataset QC 28712.3.2 QC in Data Collection 28712.4 QC of Model Development 28812.4.1 QC of NM-TRAN Control Streams 28912.4.2 Model Diagnostic Plots and Model Evaluation Steps as QC 29012.5 Documentation of QC Efforts 29012.6 Summary 291References 292Index 293

“This book may make the “User Guide V experience” a story from the good old times for the next generation of pharmacometricians.”  (CPT: Pharmacometrics & Systems Pharmacology, 22 December 2014)