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Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating the study-effectively reducing costs-or may benefit the general patient population by allowing early dissemination of its findings. Group sequential methods provide a means to balance the ethical and financial advantages of stopping a study early against the risk of an incorrect conclusion.

Group Sequential Methods with Applications to Clinical Trials describes group sequential stopping rules designed to reduce average study length and control Type I and II error probabilities. The authors present one-sided and two-sided tests, introduce several families of group sequential tests, and explain how to choose the most appropriate test and interim analysis schedule. Their topics include placebo-controlled randomized trials, bio-equivalence testing, crossover and longitudinal studies, and linear and generalized linear models.

Research in group sequential analysis has progressed rapidly over the past 20 years. Group Sequential Methods with Applications to Clinical Trials surveys and extends current methods for planning and conducting interim analyses. It provides straightforward descriptions of group sequential hypothesis tests in a form suited for direct application to a wide variety of clinical trials. Medical statisticians engaged in any investigations planned with interim analyses will find this book a useful and important tool.

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

Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating the study-effectively reducing costs-or may benefit the general patient population by allowing early dissemination of its findings. Group sequential methods provide a means to balance the ethical and financial advantages of stopping a study early against the risk of an incorrect conclusion.

Group Sequential Methods with Applications to Clinical Trials describes group sequential stopping rules designed to reduce average study length and control Type I and II error probabilities. The authors present one-sided and two-sided tests, introduce several families of group sequential tests, and explain how to choose the most appropriate test and interim analysis schedule. Their topics include placebo-controlled randomized trials, bio-equivalence testing, crossover and longitudinal studies, and linear and generalized linear models.

Research in group sequential analysis has progressed rapidly over the past 20 years. Group Sequential Methods with Applications to Clinical Trials surveys and extends current methods for planning and conducting interim analyses. It provides straightforward descriptions of group sequential hypothesis tests in a form suited for direct application to a wide variety of clinical trials. Medical statisticians engaged in any investigations planned with interim analyses will find this book a useful and important tool.

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

Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating the study-effectively reducing costs-or may benefit the general patient population by allowing early dissemination of its findings. Group sequential methods provide a means to balance the ethical and financial advantages of stopping a study early against the risk of an incorrect conclusion.

Group Sequential Methods with Applications to Clinical Trials describes group sequential stopping rules designed to reduce average study length and control Type I and II error probabilities. The authors present one-sided and two-sided tests, introduce several families of group sequential tests, and explain how to choose the most appropriate test and interim analysis schedule. Their topics include placebo-controlled randomized trials, bio-equivalence testing, crossover and longitudinal studies, and linear and generalized linear models.

Research in group sequential analysis has progressed rapidly over the past 20 years. Group Sequential Methods with Applications to Clinical Trials surveys and extends current methods for planning and conducting interim analyses. It provides straightforward descriptions of group sequential hypothesis tests in a form suited for direct application to a wide variety of clinical trials. Medical statisticians engaged in any investigations planned with interim analyses will find this book a useful and important tool.

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

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

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

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