Group Sequential Methods with Applications to Clinical Trials

INTRODUCTION
About This Book
Why Sequential Methods
A Short History of Sequential and Group Sequential Methods
Chapter Organization: A Roadmap
Bibliography and Notes
TWO-SIDED TESTS: INTRODUCTION
Two-Sided Tests for Comparing Two Treatments with Normal Response of Known Variance
A Fixed Sample Test
Group Sequential Tests
Pocock's Test
O'Brien and Fleming's Test
Properties of Pocock and O'Brien and Fleming Tests
Other Tests
Conclusions
TWO-SIDED TESTS: GENERAL APPLICATIONS
A Unified Formulation
Applying the Tests with Equal Group Sizes
Applying the Tests with Unequal Increments in Information
Normal Linear Models
Other Parametric Models
Binary Data: Group Sequential Tests for Proportions
The Group Sequential Log-Rank Test for Survival Data
Group Sequential t-Tests
ONE-SIDED TESTS
Introduction
The Power Family of One-Sided Group Sequential Tests
Adapting Power Family Tests to Unequal Increments in Information
Group Sequential One-Sided t-Tests
Whitehead's Triangular Test
TWO-SIDED TESTS WITH EARLY STOPPING UNDER THE NULL HYPOTHESIS
Introduction
The Power Family of Two-Sided, Inner Wedge Tests
Whitehead's Double Triangular Test
EQUIVALENCE TESTS
Introduction
One-Sided Tests of Equivalence
Two-Sided Tests of Equivalence: Application to Comparative Bioavailability Studies
Individual Bioequivalence: A One-Sided Test for Proportions
Bibliography and Notes
FLEXIBLE MONITORING: THE ERROR SPENDING APPROACH
Unpredictable Information Sequences
Two-Sided Tests
One-Sided Tests
Data Dependent Timing of Analyses
Computations for Error Spending Tests
ANALYSIS FOLLOWING A SEQUENTIAL TEST
Introduction
Distribution Theory
Point Estimation
P-Values
Confidence intervals
REPEATED CONFIDENCE INTERVALS
Introduction
Example: Difference of Normal Means
Derived Tests: Use of RCIs to Aid Early Stopping Decisions
Repeated P-Values
Discussion
STOCHASTIC CURTAILMENT
Introduction
Conditional Power Approach
Predictive Power Approach
A Parameter-Free Approach
A Case Study with Survival Data
Bibliography and Notes
GENERAL GROUP SEQUENTIAL DISTRIBUTION THEORY
Introduction
A Standard Joint Distribution for Successive Estimates of a Parameter Vector
Normal Linear Models
Normal Linear Models with Unknown Variance: Group Sequential t-Tests
Example: An Exact One-Sample Group Sequential t-Test
General Parametric Models: Generalized Linear Models
Connection with Survival Analysis
BINARY DATA
A Single Bernoulli Probability
Two Bernoulli Probabilities
The Odds Ratio and Multiple 2 x 2 Tables
Case-Control and Matched Pair Analysis
Logistic Regression: Adjusting for Covariates
Bibliography and Notes
SURVIVAL DATA
Introduction
The Log Rank Test
The Stratified Log-Rank Test
Group Sequential Methods for Survival Data with Covariates
Repeated Confidence Intervals for a Hazard Ratio
Example: A Clinical Trial for Carcinoma of the Oropharynx
Survival Probabilities and Quantiles
Bibliography and Notes
INTERNAL PILOT STUDIES: SAMPLE SIZE RE-ESTIMATION
The Role of an Internal Pilot Phase
Sample Size Re-estimation for a Fixed Sample Test
Sample Size Re-estimation in Group Sequential Tests
MULTIPLE ENDPOINTS
Introduction
The Bonferroni Procedure
A Group Sequential Hotelling Test
A Group Sequential Version of O'Brien's Test
Tests Based on other Global Statistics
Tests Based on Marginal Criteria
Bibliography and Notes
MULTI-ARMED TRIALS
Introduction
Global Tests
Monitoring Pairwise Comparisons
Bibliography and Notes
ADAPTIVE TREATMENT ASSIGNMENT
A Multi-Stage Adaptive Design
A Multi-Stage Adaptive Design with Time Trends
Validity of Adaptive Multi-Stage Procedures
Bibliography and Notes
BAYESIAN APPROACHES
The Bayesian Paradigm
Stopping Rules
Choice of Prior Distribution
Discussion
NUMERICAL COMPUTATIONS FOR GROUP SEQUENTIAL TESTS
Introduction
The Basic Calculation
Error Probabilities and Sample Size Distributions
Tests Defined by Error Spending Functions
Analysis Following a Group Sequential Test
Further Applications of Numerical Computation
Computer Software

"This book represents a comprehensive presentation of group sequential methods. Written by active researchers in this area, it provides an ideal source for those wishing an introduction to the area and for those who desire a clear outline of specific topics or methods. It should quickly become a standard reference both for those wishing to apply the methods and for researchers in the area…The extent of coverage of various topics broadly reflects current usage…the discussion of each topic appears to be well balanced…All in all, this is a very welcome book."
- Short Book Reviews of the ISI

"The statistical methodology for sequential trials is complicated. This book provides an excellent presentation of it. It succeeds as both a training text and as a reference source. I liked the progression of the book…any statistician involved in designing or analysing sequential trials should have a copy."
--Tim Auton, Protherics, Macclesfield