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E-grāmata: Statistical Methods for Survival Trial Design: With Applications to Cancer Clinical Trials Using R

(University of Kentucky)
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Statistical Methods for Survival Trial Design: With Applications to Cancer Clinical Trials Using R provides a thorough presentation of the principles of designing and monitoring cancer clinical trials in which time-to-event is the primary endpoint. Traditional cancer trial designs with time-to-event endpoints are often limited to the exponential model or proportional hazards model. In practice, however, those model assumptions may not be satisfied for long-term survival trials.

This book is the first to cover comprehensively the many newly developed methodologies for survival trial design, including trial design under the Weibull survival models; extensions of the sample size calculations under the proportional hazard models; and trial design under mixture cure models, complex survival models, Cox regression models, and competing-risk models. A general sequential procedure based on the sequential conditional probability ratio test is also implemented for survival trial monitoring. All methodologies are presented with sufficient detail for interested researchers or graduate students. Real examples of cancer clinical trials are used to illustrate different trial designs and applications of the developed methodologies. R codes are provided for the benefit of readers who are interested in the sample size or power calculations but do not require details of the methodology. The book also discusses some practical issues in survival trial design and will be particularly useful to clinicians and biostatisticians who routinely design cancer clinical trials.

Jianrong (John) Wu is a Professor in the Division of Cancer Biostatistics, Biostatistics and Bioinformatics Shared Resource at the Markey Cancer Center, Department of Biostatistics, University of Kentucky.

Recenzijas

". . . this book provides a comprehensive introduction to statistical methods in cancer of sample size calculations and survival clinical trial designs from the classical techniques to the newly proposed formulae such as the mixture cure model and a group sequential trial design. This book has a vast list of citations and is an excellent reference for statisticians performing oncology research in the pharmaceutical industry or in other settings, and for graduate students in biostatistics or in related fields." ~ Journal of Biopharmaceutical Statistics

"I would recommend this book for those that are starting to work with this kind of trial design and would like to have a good overview and source of knowledge for some not so common methods for more complex cancer trial designs, including simple formulae to implement in R to calculate sample sizes." ~David Manteigas, ISCB Newsletter ". . . this book provides a comprehensive introduction to statistical methods in cancer of sample size calculations and survival clinical trial designs from the classical techniques to the newly proposed formulae such as the mixture cure model and a group sequential trial design. This book has a vast list of citations and is an excellent reference for statisticians performing oncology research in the pharmaceutical industry or in other settings, and for graduate students in biostatistics or in related fields." ~ Journal of Biopharmaceutical Statistics

"I would recommend this book for those that are starting to work with this kind of trial design and would like to have a good overview and source of knowledge for some not so common methods for more complex cancer trial designs, including simple formulae to implement in R to calculate sample sizes." ~David Manteigas, ISCB Newsletter

Preface ix
List of Figures
xi
List of Tables
xiii
1 Introduction to Cancer Clinical Trials
1(8)
1.1 General Aspects of Cancer Clinical Trial Design
2(1)
1.1.1 Study Objectives
2(1)
1.1.2 Treatment Plan
3(1)
1.1.3 Eligibility Criteria
3(1)
1.1.4 Statistical Considerations
3(1)
1.2 Statistical Aspects of Cancer Survival Trial Design
3(6)
1.2.1 Randomization
3(1)
1.2.2 Stratification
4(1)
1.2.3 Blinding
4(1)
1.2.4 Sample Size Calculation
5(4)
2 Survival Analysis
9(32)
2.1 Survival Distribution
9(12)
2.1.1 Exponential Distribution
11(3)
2.1.2 Weibull Distribution
14(1)
2.1.3 Gamma Distribution
14(2)
2.1.4 Gompertz Distribution
16(3)
2.1.5 Log-Normal Distribution
19(1)
2.1.6 Log-Logistic Distribution
19(2)
2.2 Survival Data
21(4)
2.3 Fitting the Parametric Survival Distribution
25(1)
2.4 Kaplan-Meier Estimates
26(4)
2.5 Median Survival Time
30(1)
2.6 Log-Rank Test
31(8)
2.7 Cox Regression Model
39(2)
3 Counting Process and Martingale
41(8)
3.1 Basic Convergence Concepts
41(1)
3.2 Counting Process Definition
42(1)
3.3 Filtration and Martingale
43(2)
3.4 Martingale Central Limit Theorem
45(1)
3.5 Counting Process Formulation of Censored Survival Data
46(3)
4 Survival Trial Design under the Parametric Model
49(12)
4.1 Introduction
49(1)
4.2 Weibull Model
50(2)
4.3 Test Statistic
52(1)
4.4 Distribution of the MLE test
53(1)
4.5 Sample Size Formula
54(1)
4.6 Sample Size Calculation
55(3)
4.7 Accrual Duration Calculation
58(1)
4.8 Example and R code
58(3)
5 Survival Trial Design under the Proportional Hazards Model
61(38)
5.1 Introduction
61(1)
5.2 Proportional Hazards Model
62(2)
5.3 Asymptotic Distribution of the Log-Rank Test
64(4)
5.4 Schoenfeld Formula
68(4)
5.5 Rubinstein Formula
72(2)
5.6 Freedman Formula
74(3)
5.7 Comparison
77(2)
5.8 Sample Size Calculation under Various Models
79(7)
5.9 Example
86(2)
5.10 Optimal Properties of the Log-Rank Test
88(2)
5.10.1 Optimal Sample Size Allocation
88(2)
5.10.2 Optimal Power
90(1)
5.11 Precise Formula
90(3)
5.12 Exact Formula
93(6)
6 Survival Trial Design under the Cox Regression Model
99(10)
6.1 Introduction
99(1)
6.2 Test Statistics
100(1)
6.3 Asymptotic Distribution of the Score Test
101(2)
6.4 Sample Size Formula
103(6)
7 Complex Survival Trial Design
109(32)
7.1 Extension of the Freedman Formula
111(6)
7.1.1 Example and R code
113(4)
7.2 Lakatos Formula
117(1)
7.3 Markov Chain Model with Simultaneous Entry
118(2)
7.4 Computation Formulae
120(2)
7.5 Markov Chain Model with Staggered Entry
122(3)
7.6 Examples and R code
125(16)
8 Survival Trial Design under the Mixture Cure Model
141(26)
8.1 Introduction
141(2)
8.2 Testing Differences in Cure Rates
143(11)
8.2.1 Mixture Cure Model
143(2)
8.2.2 Asymptotic Distribution
145(2)
8.2.3 Sample Size Formula
147(1)
8.2.4 Optimal Log-Rank Test
148(1)
8.2.5 Comparison
149(2)
8.2.6 Example and R code
151(3)
8.2.7 Conclusion
154(1)
8.3 Testing Differences in Short- and Long-Term Survival
154(13)
8.3.1 Hypothesis Testing
154(1)
8.3.2 Ewell and Ibrahim Formula
155(3)
8.3.3 Simulation
158(1)
8.3.4 Example and R code
159(5)
8.3.5 Conclusion
164(3)
9 A General Group Sequential Procedure
167(10)
9.1 Brownian Motion
167(1)
9.2 Sequential Conditional Probability Ratio Test
168(6)
9.3 Operating Characteristics
174(1)
9.4 Probability of Discordance
175(1)
9.5 SCPRT Design
175(2)
10 Sequential Survival Trial Design
177(22)
10.1 Introduction
177(1)
10.2 Sequential Procedure for the Parametric Model
177(8)
10.2.1 Sequential Wald Test
178(2)
10.2.2 SCPRT for the Parametric Model
180(5)
10.3 Sequential Procedure for the Proportional Hazard Model
185(14)
10.3.1 Sequential Log-Rank Test
185(4)
10.3.2 Information Time
189(2)
10.3.3 SCPRT for the PH Model
191(8)
11 Sequential Survival Trial Design Using Historical Controls
199(12)
11.1 Introduction
199(1)
11.2 Sequential Log-Rank Test with Historical Controls
200(8)
11.2.1 Sample Size Calculation
201(1)
11.2.2 Information Time
202(2)
11.2.3 Group Sequential Procedure
204(4)
11.3 Conclusion
208(3)
12 Some Practical Issues in Survival Trial Design
211(8)
12.1 Parametric vs. Nonparametric Model
211(1)
12.2 Nonproportional Hazards Model
212(1)
12.3 Accrual Patterns
212(1)
12.4 Mixed Populations
213(1)
12.5 Loss to Follow-Up
213(1)
12.6 Noncompliance and Drop-In
214(1)
12.7 Competing Risk
215(4)
A Likelihood Function for the Censored Data 219(2)
B Probability of Failure under Uniform Accrual 221(2)
C Verification of the Minimum Sample Size Conditions 223(2)
D R Codes for the Sample Size Calculations 225(6)
E Derivation of the Asymptotic Distribution 231(4)
F Derivation of Equations for
Chapter 8		 235(2)
Bibliography 237(10)
Index 247
Jianrong (John) Wu is a professor in the Division of Cancer Biostatistics, Department of Biostatistics, Markey Cancer Center, University of Kentucky. He has more than 15 years experience of designing and conducting cancer clinical trials at St. Jude Childrens Research Hospital and has developed several novel statistical methods for designing phase II and phase III survival trials.
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