Group Sequential Methods with Applications to Clinical Trials

TL;DR: A short history of sequential and group sequential methods can be found in this paper, where the authors present a road map for the application of two-sided tests for comparing two treatments with normal response of known variance.

Abstract: 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