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E-raamat: Bayesian Analysis with R for Drug Development: Concepts, Algorithms, and Case Studies

, (MedImmune, LLC, Gaithersburg, Maryland, USA)
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Drug development is an iterative process. The recent publications of regulatory guidelines further entail a lifecycle approach. Blending data from disparate sources, the Bayesian approach provides a flexible framework for drug development. Despite its advantages, the uptake of Bayesian methodologies is lagging behind in the field of pharmaceutical development.

Written specifically for pharmaceutical practitioners, Bayesian Analysis with R for Drug Development: Concepts, Algorithms, and Case Studies, describes a wide range of Bayesian applications to problems throughout pre-clinical, clinical, and Chemistry, Manufacturing, and Control (CMC) development. Authored by two seasoned statisticians in the pharmaceutical industry, the book provides detailed Bayesian solutions to a broad array of pharmaceutical problems.

Features











Provides a single source of information on Bayesian statistics for drug development





Covers a wide spectrum of pre-clinical, clinical, and CMC topics





Demonstrates proper Bayesian applications using real-life examples





Includes easy-to-follow R code with Bayesian Markov Chain Monte Carlo performed in both JAGS and Stan Bayesian software platforms





Offers sufficient background for each problem and detailed description of solutions suitable for practitioners with limited Bayesian knowledge

Harry Yang, Ph.D., is Senior Director and Head of Statistical Sciences at AstraZeneca. He has 24 years of experience across all aspects of drug research and development and extensive global regulatory experiences. He has published 6 statistical books, 15 book chapters, and over 90 peer-reviewed papers on diverse scientific and statistical subjects, including 15 joint statistical works with Dr. Novick. He is a frequent invited speaker at national and international conferences. He also developed statistical courses and conducted training at the FDA and USP as well as Peking University.

Steven Novick, Ph.D., is Director of Statistical Sciences at AstraZeneca. He has extensively contributed statistical methods to the biopharmaceutical literature. Novick is a skilled Bayesian computer programmer and is frequently invited to speak at conferences, having developed and taught courses in several areas, including drug-combination analysis and Bayesian methods in clinical areas. Novick served on IPAC-RS and has chaired several national statistical conferences.
Preface xi
Authors xv
Section I Background
1 Bayesian Statistics in Drug Development
3(14)
1.1 Introduction
3(1)
1.2 Overview of Drug Development
3(6)
1.2.1 Basic Research
4(1)
1.2.2 Drug Discovery
5(1)
1.2.3 Formulation
5(1)
1.2.4 Laboratory Test Methods
6(1)
1.2.5 Pre-Clinical Studies
6(1)
1.2.6 Clinical Development
7(1)
1.2.6.1 Phase I Clinical Trial
7(1)
1.2.6.2 Phase II Clinical Trial
7(1)
1.2.6.3 Phase III Clinical Trial
8(1)
1.2.6.4 Phase IV Clinical Trial
8(1)
1.2.7 Translational Research
8(1)
1.2.8 Chemistry, Manufacturing, and Controls
8(1)
1.2.9 Regulatory Registration
9(1)
1.3 Statistics in Drug Research and Development
9(2)
1.4 Bayesian Statistics
11(1)
1.5 Opportunities of the Bayesian Approach
12(1)
1.5.1 Pre-Clinical Development
12(1)
1.5.2 CMC Development
12(1)
1.5.3 Clinical Trials
13(1)
1.6 Challenges of the Bayesian Approach
13(2)
1.6.1 Objection to Bayesian
13(1)
1.6.2 Regulatory Hurdles
14(1)
1.7 Concluding Remarks
15(2)
2 Basics of Bayesian Statistics
17(24)
2.1 Introduction
17(1)
2.2 Statistical Inferences
18(5)
2.2.1 Research Questions
18(1)
2.2.2 Probability Distribution
18(1)
2.2.3 Frequentist Methods
18(1)
2.2.4 Bayesian Inference
19(3)
2.2.4.1 Bayes' Theorem and Posterior Distribution
19(1)
2.2.4.2 Inference about Parameters
20(1)
2.2.4.3 Inference of Future Observations
21(1)
2.2.5 Selection of Priors
22(1)
2.3 Bayesian Computation
23(11)
2.3.1 Monte Carlo Simulation
23(1)
2.3.2 Example
24(4)
2.3.3 Rejection Sampling
28(1)
2.3.4 Markov Chain Monte Carlo
29(5)
2.3.4.1 Gibbs Sampling
29(2)
2.3.4.2 Metropolis-Hastings
31(3)
2.4 Computational Tools
34(5)
2.4.1 BUGS and JAGS
34(1)
2.4.2 SAS PROC MCMC
35(1)
2.4.3 Utility of JAGS
35(4)
2.5 Concluding Remarks
39(2)
3 Bayesian Estimation of Sample Size and Power
41(22)
3.1 Introduction
41(1)
3.2 Sample Size Determination
41(5)
3.2.1 Frequentist Methods
41(2)
3.2.2 Bayesian Considerations
43(2)
3.2.2.1 Prior Information
43(1)
3.2.2.2 Use of Historical Data
44(1)
3.2.3 Bayesian Approaches
45(1)
3.3 Power and Sample Size
46(8)
3.3.1 Phase II Study
47(7)
3.3.1.1 Test Procedure
47(1)
3.3.1.2 Sample Size Calculations
47(2)
3.3.1.3 Incorporation of Prior
49(2)
3.3.1.4 Proper Bayesian Procedure
51(1)
3.3.1.5 Two Prior Distributions
51(3)
3.4 Interim Analysis
54(1)
3.4.1 Futility and Sample Size
54(1)
3.5 Case Example
55(5)
3.5.1 Modeling of Overall Survival
55(1)
3.5.2 Maximum Likelihood Estimation
56(1)
3.5.3 Futility Analysis
56(4)
3.6 Concluding Remarks
60(3)
Section II Pre-Clinical and Clinical Research
4 Pre-Clinical Efficacy Studies
63(26)
4.1 Introduction
63(1)
4.2 Evaluation of Lab-Based Drugs in Combination
64(13)
4.2.1 Background
64(1)
4.2.2 Statistical Methods
64(1)
4.2.2.1 Loewe Additivity
64(1)
4.2.2.2 Bliss Independence
65(1)
4.2.3 Antiviral Combination
65(7)
4.2.3.1 Data
66(1)
4.2.3.2 Model
66(1)
4.2.3.3 Assessment of Drug Effect
67(4)
4.2.3.4 Use of Historical Data as Priors
71(1)
4.2.4 Evaluation of Fixed Dose Combination
72(5)
4.2.4.1 Follow-up Experiment
72(5)
4.3 Bayesian Survival Analysis
77(11)
4.3.1 Limitations of Animal Data
77(1)
4.3.2 Current Methods
78(1)
4.3.3 Bayesian Solution
79(4)
4.3.3.1 Survival Function
80(1)
4.3.3.2 Weibull Modeling
80(3)
4.3.4 Case Example
83(5)
4.4 Concluding Remarks
88(1)
5 Bayesian Adaptive Designs for Phase I Dose-Finding Studies
89(18)
5.1 Introduction
89(1)
5.2 Algorithm-Based Designs
89(3)
5.2.1 3 + 3 Design
89(1)
5.2.2 Alternate Algorithm-Based Designs
90(1)
5.2.3 Advantages and Disadvantages of Algorithm-Based Designs
91(1)
5.3 Model-Based Designs
92(14)
5.3.1 Continual Reassessment Method
92(2)
5.3.1.1 Models
92(1)
5.3.1.2 Procedure for Finding MTD
93(1)
5.3.2 CRM for Phase I Cancer Trials
94(4)
5.3.3 Escalation with Overdose Control
98(5)
5.3.4 Escalation Based on Toxicity Probability Intervals
103(5)
5.3.4.1 Toxicity Probability Intervals
103(1)
5.3.4.2 Model
103(1)
5.3.4.3 Method
104(1)
5.3.4.4 Method Implementation
105(1)
5.4 Concluding Remarks
106(1)
6 Design and Analysis of Phase II Dose-Ranging Studies
107(14)
6.1 Introduction
107(1)
6.2 Phase II Dose-Ranging Studies
108(2)
6.2.1 Criticisms of Traditional Methods
108(1)
6.2.2 Model-Based Approaches
109(1)
6.2.2.1 Modeling Dose-Response Curve
109(1)
6.2.2.2 Determination of Minimum Efficacy Dose
109(1)
6.3 Estimating Predictive Precision and Assurance for New Trial
110(8)
6.3.1 COPD Study
110(1)
6.3.2 Estimation Method
110(12)
6.3.2.1 Selection of Priors
112(2)
6.3.2.2 Estimation of Dose-Response Curve
114(1)
6.3.2.3 Estimation of Precision and Assurance
115(3)
6.4 Concluding Remarks
118(3)
7 Bayesian Multi-Stage Designs for Phase II Clinical Trials
121(20)
7.1 Introduction
121(1)
7.2 Phase II Clinical Trials
122(1)
7.3 Multi-stage Designs
122(6)
7.3.1 Frequentist Approaches
122(1)
7.3.2 Bayesian Methods
123(1)
7.3.3 Bayesian Single-Arm Trials
123(2)
7.3.3.1 Go or No-Go Criteria
124(1)
7.3.3.2 Predictive Probability
124(1)
7.3.4 Continuous Monitoring of Single-Arm Trials
125(1)
7.3.5 Comparative Phase II Studies
126(2)
7.3.5.1 Efficacy and Futility Based on Posterior Probability
126(1)
7.3.5.2 Efficacy and Futility Criteria Based on Predictive Probability
127(1)
7.4 Examples
128(9)
7.4.1 Oncology Trial
128(3)
7.4.2 Multi-Stage Bayesian Design
131(6)
7.5 Concluding Remarks
137(4)
Section III Chemistry, Manufacturing, and Control
8 Analytical Methods
141(22)
8.1 Introduction
141(1)
8.2 Method Validation
142(14)
8.2.1 Background
142(1)
8.2.2 Study Design for Validation of Accuracy and Precision
143(1)
8.2.2.1 Design Considerations
143(1)
8.2.3 Current Statistical Methods
144(1)
8.2.3.1 Definitions
144(1)
8.2.3.2 Methods
145(1)
8.2.4 Total Error Approach
145(1)
8.2.5 Bayesian Solutions
146(2)
8.2.6 Example
148(8)
8.2.6.1 Data
148(1)
8.2.6.2 Analysis
149(2)
8.2.6.3 Results
151(2)
8.2.6.4 Analysis Based on More Informative Priors
153(3)
8.3 Method Transfer
156(6)
8.3.1 Background
156(1)
8.3.2 Model
156(1)
8.3.3 Linear Response
157(1)
8.3.4 Case Example
158(4)
8.4 Concluding Remarks
162(1)
9 Process Development
163(32)
9.1 Introduction
163(1)
9.2 Quality by Design
164(1)
9.3 Critical Quality Attributes
165(8)
9.3.1 Risk of Oncogenicity
166(1)
9.3.2 Bayesian Risk Assessment
167(1)
9.3.3 Modeling Enzyme Cutting Efficiency
167(1)
9.3.4 Bayesian Solution
168(2)
9.3.5 Example
170(3)
9.4 Design Space
173(13)
9.4.1 Definition
173(2)
9.4.2 Statistical Methods for Design Space
175(3)
9.4.2.1 Overlapping Mean
175(1)
9.4.2.2 Desirability Method
175(2)
9.4.2.3 Criticisms of Current Methods
177(1)
9.4.3 Bayesian Design Space
178(3)
9.4.3.1 Regression Model
178(1)
9.4.3.2 Prior Information
179(1)
9.4.3.3 Posterior Predictive Probability and Design Space
179(2)
9.4.4 Example
181(5)
9.5 Process Validation
186(7)
9.5.1 Risk-Based Lifecycle Approach
186(1)
9.5.2 Method Based on Process Capability
187(2)
9.5.2.1 Frequentist Acceptance Criterion
187(1)
9.5.2.2 Bayesian Acceptance Criterion
188(1)
9.5.3 Method Based on Predictive Performance
189(2)
9.5.4 Determination of Number of PPQ Batches
191(2)
9.6 Concluding Remarks
193(2)
10 Stability
195(22)
10.1 Introduction
195(1)
10.2 Stability Study
196(1)
10.3 Shelf-Life Estimation
197(14)
10.3.1 Current Methods
197(1)
10.3.2 Bayesian Approaches
198(2)
10.3.3 Examples
200(7)
10.3.3.1 Shelf Life of Influenza Vaccine
200(7)
10.3.4 Selection of Stability Design
207(1)
10.3.5 Bayesian Criterion
208(3)
10.3.5.1 Design Options
208(1)
10.3.5.2 Results
209(2)
10.4 Setting Release Limit
211(4)
10.4.1 Background
211(4)
10.5 Concluding Remarks
215(2)
11 Process Control
217(30)
11.1 Introduction
217(1)
11.2 Quality Control and Improvement
218(1)
11.3 Control Charts
219(1)
11.4 Types of Control Charts
220(7)
11.4.1 Shewhart I-MR Charts
221(2)
11.4.2 EWMA Control Chart
223(2)
11.4.3 CUSUM Chart
225(1)
11.4.4 J-Chart
226(1)
11.4.5 Multivariate Control Chart
227(1)
11.5 Bayesian Control Charts
227(17)
11.5.1 Control Chart for Data with Censoring
227(2)
11.5.2 Control Chart for Discrete Data
229(5)
11.5.3 Control Limit for Aberrant Data
234(5)
11.5.3.1 Background
234(1)
11.5.3.2 Methods
235(4)
11.5.4 Product Quality Control Based on Safety Data from Surveillance
239(5)
11.5.4.1 Background
239(1)
11.5.4.2 Current Methods
239(2)
11.5.4.3 Zero-Inflated Models
241(1)
11.5.4.4 Alert Limit for AEs
242(2)
11.6 Concluding Remarks
244(3)
Appendix: Stan Computer Code 247(36)
References 283(18)
Index 301
Harry Yang is Senior Director and Head of Statistical Sciences at MedImmune. He has 24 years of experience across all aspects of drug research and development and extensive global regulatory experiences. He has published six statistical books, 15 book chapters, and over 90 peer-reviewed papers on diverse scientific and statistical subjects, including 15 joint statistical works with Dr. Novick. Dr. Yang is a frequent invited speaker at national and international conferences. He also developed statistical courses and conducted training at the FDA and USP as well as Peking University.

Steven Novick is Director of Statistical Sciences at MedImmune. He has extensively contributed statistical methods to the biopharmaceutical literature. Dr. Novick is a skilled Bayesian computer programmer and is frequently invited to speak at conferences, having developed and taught courses in several areas, including drug-combination analysis and Bayesian methods in clinical areas. He served on IPAC-RS and has chaired several national statistical conferences.