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Statistical Methods for Survival Trial Design - 
      Jianrong Wu

Statistical Methods for Survival Trial Design

With Applications to Cancer Clinical Trials Using R

«<p>". . . 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." <em>~ Journal of Biopharmaceutical Statistics</em></p> <p>"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<br />for some not so common methods for more complex cancer trial designs, including simple formulae to implement in R to calculate sample sizes."<br /><em>~David Manteigas, ISCB Newsletter</em></p> <p> </p>»

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. Les mer
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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.
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Utgitt:
Forlag: CRC Press
Innbinding: Innbundet
Språk: Engelsk
Sider: 257
ISBN: 9781138033221
Format: 23 x 16 cm
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Preface





List of Figures





List of Tables





1. Introduction to Cancer Clinical Trials


General Aspects of Cancer Clinical Trial Design


Study Objectives


Treatment Plan


Eligibility Criteria


Statistical Considerations


Statistical Aspects of Cancer Survival Trial Design


Randomization


Stratification


Blinding


Sample Size Calculation





2. Survival Analysis


Survival Distribution


Exponential Distribution


Weibull Distribution


Gamma Distribution


Gompertz Distribution


Log-Normal Distribution


Log-Logistic Distribution


Survival Data


Fitting the Parametric Survival Distribution


Kaplan-Meier Estimates


Median Survival Time


Log-Rank Test


Cox Regression Model





3. Counting Process and Martingale_


Basic Convergence Concepts


Counting Process Definition


Martingale Central Limit Theorem


Counting Process Formulation of Censored Survival Data





4. Survival Trial Design Under the Parametric Model


Introduction


Weibull Model


Test Statistic


Distribution of the MLE test


Sample Size Formula


Sample Size Calculation


Accrual Duration Calculation


Example and R code





5. Survival Trial Design Under the Proportional Hazards Model


Introduction


Proportional Hazards Model


Asymptotic Distribution of the Log-rank Test


Schoenfeld Formula


Rubinstein Formula


Freedman Formula


Comparison


Sample Size Calculation Under Various Models


Example


Optimal Properties of the Log-Rank Test_


Optimal Sample Size Allocation


Optimal Power


Precise Formula


Exact Formula





6. Survival Trial Design Under the Cox Regression Model


Introduction


Test Statistics


Asymptotic Distribution of the Score Test_


Sample Size Formula





7. Complex Survival Trial Design


Extension of the Freedman Formula


Example and R code


Lakatos Formula


Markov Chain Model with Simultaneous Entry


Computation Formulae


Markov Chain Model with Staggered Entry


Examples and R code





8. Survival Trial Design Under the Mixture Cure Model


Introduction


Testing Differences in Cure Rates


Mixture Cure Model


Asymptotic Distribution


Sample Size Formula


Optimal Log-Rank Test


Comparison


Example and R code


Conclusion


Testing Differences in Short- and Long-Term Survival


Hypothesis Testing


Ewell and Ibrahim Formula


Simulation


Example and R code


Conclusion





9. A General Group Sequential Procedure


Brownian Motion


Sequential Conditional Probability Ratio Test


Operating Characteristics


Probability of Discordance


SCPRT Design





10. Sequential Survival Trial Design


Introduction


Sequential Procedure for the Parametric Model


Sequential Wald Test


SCPRT for the Parametric Model


Sequential Procedure for the Proportional Hazard Model


Sequential Log-Rank Test


Information Time


SCPRT for the PH Model





11. Sequential Survival Trial Design Using Historical Controls


Introduction


Sequential Log-Rank Test with Historical Controls


Sample Size Calculation


Information Time


Group Sequential Procedure


Conclusion





12. Some Practical Issues in Survival Trial Design


Parametric vs Nonparametric Model


Nonproportional Hazards Model


Accrual Patterns


Mixed Populations


Loss to Follow-Up


Noncompliance and Drop-In


Competing Risk





A Likelihood Function For the Censored Data


B Probability of Failure Under Uniform Accrual


C Verification of the Minimum Sample Size Conditions


D R Codes for the Sample Size Calculations


E Derivation of the Asymptotic Distribution


F Derivation of Equations for Chapter





Bibliography





Index
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 Children’s Research Hospital and has developed several novel statistical methods for designing phase II and phase III survival trials.