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

Description

Statistical Methods for Survival Trial Design: With Applications to Cancer Clinical Trials Using Rprovides 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. Content: 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