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El. knyga: Dose Finding by the Continual Reassessment Method

(Columbia University)
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As clinicians begin to realize the important role of dose-finding in the drug development process, there is an increasing openness to "novel" methods proposed in the past two decades. In particular, the Continual Reassessment Method (CRM) and its variations have drawn much attention in the medical community, though it has yet to become a commonplace tool. To overcome the status quo in phase I clinical trials, statisticians must be able to design trials using the CRM in a timely and reproducible manner.

A self-contained theoretical framework of the CRM for researchers and graduate students who set out to learn and do research in the CRM and dose-finding methods in general, Dose Finding by the Continual Reassessment Method features:











Real clinical trial examples that illustrate the methods and techniques throughout the book Detailed calibration techniques that enable biostatisticians to design a CRM in timely manner Limitations of the CRM are outlined to aid in correct use of method

This book supplies practical, efficient dose-finding methods based on cutting edge statistical research. More than just a cookbook, it provides full, unified coverage of the CRM in addition to step-by-step guidelines to automation and parameterization of the methods used on a regular basis. A detailed exposition of the calibration of the CRM for applied statisticians working with dose-finding in phase I trials, the book focuses on the R package dfcrm for the CRM and its major variants.

The author recognizes clinicians skepticism of model-based designs, and addresses their concerns that the time, professional, and computational resources necessary for accurate model-based designs can be major bottlenecks to the widespread use of appropriate dose-finding methods in phase I practice. The theoretically- and empirically-based methods in Dose Finding by the Continual Reassessment Method will lessen the statisticians burden and encourage the continuing development and implementation of model-based dose-finding methods.

Recenzijos

"Overall, this book comprises a detailed and very useful description of a relatively novel and advanced method for designing dose-finding trials, which is starting to draw attention in the medical statistics community. The book focuses on the design (not analysis) of phase I and phase II dose-finding trials using the continual reassessment method (CRM) and its variants. The method is introduced alongside a description of the R package dfcrm, aiming to provide the reader with the skills to implement the method in R. ...This book aims to be a how-to book and although it seems to require only college algebra and basic calculus concepts, I did find it very technically advanced in terms of mathematical formulations and theories. However, it was also very thorough, containing plenty of practical examples and illustrations (and corresponding implementations in R), which helps its readability. Moreover, given the complexity behind the CRM design, it is difficult to imagine how it could be presented in a simplified manner and still satisfy the need for a deep understanding of the subject." -Rute Vieira, ISCB 2018

I Fundamentals
1(62)
1 Introduction
3(4)
2 Dose Finding in Clinical Trials
7(10)
2.1 The Maximum Tolerated Dose
7(3)
2.2 An Overview of Methodology
10(5)
2.3 Bibliographic Notes
15(1)
2.4 Exercises and Further Results
16(1)
3 The Continual Reassessment Method
17(16)
3.1 Introduction
17(1)
3.2 One-Stage Bayesian CRM
17(5)
3.2.1 General Setting and Notation
17(1)
3.2.2 Dose-Toxicity Model
17(1)
3.2.3 Dose Labels
18(2)
3.2.4 Model-Based MTD
20(1)
3.2.5 Normal Prior on β
21(1)
3.2.6 Implementation in R
21(1)
3.3 Two-Stage CRM
22(3)
3.3.1 Initial Design
22(1)
3.3.2 Maximum Likelihood CRM
23(2)
3.4 Simulating CRM Trials
25(2)
3.4.1 Numerical Illustrations
25(1)
3.4.2 Methods of Simulation
25(2)
3.5 Practical Modifications
27(4)
3.5.1 Dose Escalation Restrictions
27(1)
3.5.2 Group Accrual
28(2)
3.5.3 Stopping and Extension Criteria
30(1)
3.6 Bibliographic Notes
31(1)
3.7 Exercises and Further Results
31(2)
4 One-Parameter Dose-Toxicity Models
33(8)
4.1 Introduction
33(1)
4.2 ψ-Equivalent Models
33(3)
4.3 Model Assumptions†
36(4)
4.4 Proof of Theorem 4.1†
40(1)
4.5 Exercises and Further Results
40(1)
5 Theoretical Properties
41(16)
5.1 Introduction
41(1)
5.2 Coherence
41(5)
5.2.1 Motivation and Definitions
41(1)
5.2.2 Coherence Conditions of the CRM
42(1)
5.2.3 Compatibility
43(2)
5.2.4 Extensions
45(1)
5.3 Large-Sample Properties
46(8)
5.3.1 Consistency and Indifference Interval
46(2)
5.3.2 Consistency Conditions of the CRM
48(1)
5.3.2.1 Home Sets
48(1)
5.3.2.2 Least False Parameters
48(1)
5.3.2.3 Main Result
49(1)
5.3.2.4 A Relaxed Condition
49(2)
5.3.3 Model Sensitivity of the CRM
51(2)
5.3.4 Computing Model Sensitivity in R
53(1)
5.4 Proofs†
54(2)
5.4.1 Coherence of One-Stage CRM
54(1)
5.4.2 Consistency of the CRM
55(1)
5.5 Exercises and Further Results
56(1)
6 Empirical Properties
57(6)
6.1 Introduction
57(1)
6.2 Operating Characteristics
57(3)
6.2.1 Accuracy Index
57(2)
6.2.2 Overdose Number
59(1)
6.2.3 Average Toxicity Number
59(1)
6.3 A Nonparametric Optimal Benchmark
60(2)
6.4 Exercises and Further Results
62(1)
II Design Calibration
63(54)
7 Specifications of a CRM Design
65(10)
7.1 Introduction
65(1)
7.2 Specifying the Clinical Parameters
66(2)
7.2.1 Target Rate θ
66(1)
7.2.2 Number of Test Doses K
66(1)
7.2.3 Sample Size N
66(1)
7.2.4 Prior MTD v0 and Starting Dose x1
67(1)
7.3 A Roadmap for Choosing the Statistical Component
68(1)
7.4 The Trial-and-Error Approach: Two Case Studies
69(6)
7.4.1 The Bortezomib Trial
69(2)
7.4.2 NeuSTART
71(2)
7.4.3 The Case for an Automated Process
73(2)
8 Initial Guesses of Toxicity Probabilities
75(14)
8.1 Introduction
75(1)
8.2 Half-width (δ) of Indifferent Interval
75(2)
8.3 Calibration of δ
77(4)
8.3.1 Effects of δ on the Accuracy Index
77(1)
8.3.2 The Calibration Approach
78(1)
8.3.3 Optimal δ for the Logistic Model
79(2)
8.4 Case Study: The Bortezomib Trial
81(6)
8.5 Exercises and Further Results
87(2)
9 Least Informative Normal Prior
89(14)
9.1 Introduction
89(1)
9.2 Least Informative Prior
89(4)
9.2.1 Definitions
89(2)
9.2.2 Rules of Thumb
91(2)
9.3 Calibration of σβ
93(4)
9.3.1 Calibration Criteria
93(1)
9.3.2 An Application to the Choice of v0
93(2)
9.3.3 Optimality Near σLIβ
95(2)
9.4 Optimal Least Informative Model
97(2)
9.5 Revisiting the Bortezomib Trial
99(4)
10 Initial Design
103(14)
10.1 Introduction
103(1)
10.2 Ordering of Dose Sequences
103(3)
10.3 Building Reference Initial Designs
106(3)
10.3.1 Coherence-Based Criterion
106(1)
10.3.2 Calibrating Compatible Dose Sequences
107(2)
10.3.3 Reference Initial Designs for the Logistic Model
109(1)
10.4 Practical Issues
109(4)
10.4.1 Sample Size Constraint
109(3)
10.4.2 Dose Insertion†
112(1)
10.5 Case Study: NeuSTART
113(2)
10.6 Exercises and Further Results
115(2)
III CRM and Beyond
117(62)
11 The Time-to-Event CRM
119(20)
11.1 Introduction
119(1)
11.2 The Basic Approach
119(4)
11.2.1 A Weighted Likelihood
119(1)
11.2.2 Weight Functions
120(2)
11.2.3 Individual Toxicity Risks
122(1)
11.3 Numerical Illustration
123(2)
11.3.1 The Bortezomib Trial
123(1)
11.3.2 Implementation in R
124(1)
11.4 Enrollment Scheduling
125(4)
11.4.1 Patient Accrual
125(2)
11.4.2 Interim Suspensions
127(2)
11.5 Theoretical Properties†
129(2)
11.5.1 Real-Time Formulation
129(1)
11.5.2 Real-Time Coherence
129(1)
11.5.3 Consistency
130(1)
11.6 Two-Stage Design
131(4)
11.6.1 Waiting Window
131(1)
11.6.2 Case Study: The Poly E Trial
132(3)
11.7 Bibliographic Notes
135(1)
11.8 Exercises and Further Results
136(3)
12 CRM with Multiparameter Models
139(16)
12.1 Introduction
139(1)
12.2 Curve-Free Methods
139(7)
12.2.1 The Basic Approach
139(1)
12.2.2 Product-of-Beta Prior Distribution
140(3)
12.2.3 Dirichlet Prior Distribution
143(1)
12.2.4 Isotonic Design
144(2)
12.3 Rigidity
146(3)
12.3.1 Illustrations of the Problem
146(1)
12.3.2 Remedy 1: Increase m
147(1)
12.3.3 Remedy 2: Increase Prior Correlations
147(2)
12.4 Two-Parameter CRM†
149(5)
12.4.1 The Basic Approach
149(1)
12.4.2 A Rigid Two-Parameter CRM: Illustration
150(1)
12.4.3 Three-Stage Design
151(2)
12.4.4 Continuous Dosage
153(1)
12.5 Bibliographic Notes
154(1)
12.6 Exercise and Further Results
154(1)
13 When the CRM Fails
155(12)
13.1 Introduction
155(1)
13.2 Trade-Off Perspective of MTD
155(7)
13.2.1 Motivation
155(1)
13.2.2 Maximum Safe Dose and Multiple Testing
156(1)
13.2.3 A Sequential Stepwise Procedure
157(2)
13.2.4 Case Study: The ASCENT Trial
159(2)
13.2.5 Practical Notes
161(1)
13.3 Bivariate Dose Finding
162(5)
14 Stochastic Approximation
167(12)
14.1 Introduction
167(1)
14.2 The Past Literature
167(3)
14.2.1 The Robbins-Monro Procedure
167(1)
14.2.2 Maximum Likelihood Recursion
168(1)
14.2.3 Implications on the CRM
169(1)
14.3 The Present Relevance
170(6)
14.3.1 Practical Considerations
170(1)
14.3.2 Dichotomized Data
171(3)
14.3.3 Virtual Observations
174(1)
14.3.4 Quasi-Likelihood Recursion
175(1)
14.4 The Future Challenge
176(1)
14.5 Assumptions on M(x) and Y(x)+
177(1)
14.6 Exercises and Further Results
178(1)
References 179(8)
Index 187
Department of Biostatistics, Columbia University, USA
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