Statistical Thinking in Clinical Trials

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
1. Evidence and Inference
	1.1. Terminology and Paradigm of Inference
	1.2. Classical Inference
		1.2.1. Hypothesis Tests and P-Values
		1.2.2. Con dence Intervals
		1.2.3. Criticisms of Classical Methods
		1.2.4. Bayesian Approach
		1.2.5. Large Sample Inference
	1.3. Robust Methods Are Preferred in Clinical Trials
	1.4. Summary
2. 2 x 2 Tables
	2.1. Measures of Treatment Effect
	2.2. Exact Tests and Con dence Intervals
		2.2.1. Fisher's Exact Test
		2.2.2. Exact Con dence Interval for Odds Ratio
		2.2.3. Oddities of Fisher's Exact Test and Con dence Interval
		2.2.4. Unconditional Tests As Alternatives to Fisher's Exact Test
	2.3. Appendix: P(X1 = x1 | S = s) in Table 2.3
	2.4. Summary
3. Introduction to Clinical Trials
	3.1. Summary
4. Design of Clinical Trials
	4.1. Different Phases of Trials
	4.2. Blinding
	4.3. Baseline Variables
	4.4. Controls
		4.4.1. Regression to the Mean
		4.4.2. Appropriate Control
	4.5. Choice of Primary Endpoint
	4.6. Reducing Variability
		4.6.1. Replication and Averaging
		4.6.2. Differencing
		4.6.3. Stratification
		4.6.4. Regression
	4.7. Different Types of Trials
		4.7.1. Superiority Versus Noninferiority
		4.7.2. Parallel Arm Trials
		4.7.3. Crossover Trials
		4.7.4. Cluster-Randomized Trials
		4.7.5. Multi-Arm Trials
	4.8. Appendix: The Geometry of Stratification
	4.9. Summary
5. Randomization/Allocation
	5.1. Sanctity and Placement of Randomization
	5.2. Simple Randomization
	5.3. Permuted Block Randomization
	5.4. Biased Coin Randomization
	5.5. Stratified Randomization
	5.6. Minimization and Covariate-Adaptive Randomization
	5.7. Response-Adaptive Randomization
	5.8. Adaptive Randomization and Temporal Trends
	5.9. Summary
6. Randomization-Based Inference
	6.1. Introduction
	6.2. Paired Data
		6.2.1. An Example
		6.2.2. Control of Conditional Type I Error Rate
		6.2.3. Asymptotic Equivalence to a T-test
		6.2.4. Null Hypothesis and Generalizing
		6.2.5. Does a Re-randomization Test Assume Independence?
	6.3. Unpaired Data: Traditional Randomization
		6.3.1. Introduction
		6.3.2. Control of Conditional type I Error Rate
		6.3.3. The Null Hypothesis and Generalizing
		6.3.4. Does a Re-randomization Test Require Independence?
		6.3.5. Asymptotic Equivalence to a t-Test
		6.3.6. Protection Against Temporal Trends
		6.3.7. Fisher's Exact Test as a Re-Randomization Test
	6.4. Unpaired Data: Covariate-Adaptive Randomization
		6.4.1. Introduction
		6.4.2. Control of Conditional type I Error Rate
		6.4.3. Protection Against Temporal Trends
		6.4.4. More Rigorous Null Hypothesis
	6.5. Unpaired Data: Response-Adaptive Randomization
		6.5.1. Introduction
	6.6. Re-randomization Tests and Strength of Randomized Evidence
	6.7. Confidence Intervals
	6.8. Philosophical Criticism of Re-randomization Tests
	6.9. Appendix: The Permutation Variance of YC - YT
	6.10. Summary
7. Survival Analysis
	7.1. Introduction to Survival Methods
	7.2. Kaplan-Meier Survival Curve
	7.3. Comparing Survival Across Arms
		7.3.1. Comparing Survival at a Speci c Time
		7.3.2. Logrank Test
	7.4. Hazard Rate and Cox Model
	7.5. Competing Risk Analysis
	7.6. Parametric Approaches
		7.6.1. Conditional Binomial Procedure
	7.7. Appendix: Partial Likelihood
	7.8. Summary
8. Sample Size/Power
	8.1. Introduction
	8.2. EZ Principle Illustrated through the 2-Sample t-Test
		8.2.1. Important Takeaways from the EZ Principle
	8.3. EZ Principle Applied More Generally
		8.3.1. 1-Sample t-test
		8.3.2. Test of Proportions
		8.3.3. Logrank Test
		8.3.4. Cluster-Randomized Trials
		8.3.5. In a Nutshell
	8.4. Nonzero Nulls
	8.5. Practical Aspects of Sample Size Calculations
		8.5.1. Test of Means
		8.5.2. Test of Proportions
		8.5.3. Specification of Treatment Effect
	8.6. Exact Power
		8.6.1. t-Tests
		8.6.2. Exact Power for Fisher's Exact Test
	8.7. Adjusting for Noncompliance and Other Factors
	8.8. Appendix: Other Sample Size Formulas for Two Proportions
	8.9. Summary
9. Monitoring
	9.1. Introduction
	9.2. Efficacy Monitoring
		9.2.1. Brief History of Efficacy Boundaries
		9.2.2. Z-scores, B-Values, and Information
		9.2.3. Revisiting O'Brien-Fleming
		9.2.4. Alpha Spending Functions
		9.2.5. Effect of Monitoring on Power
	9.3. Small Sample Sizes
	9.4. Futility Monitoring
		9.4.1. What Is Futility?
		9.4.2. Conditional Power
		9.4.3. Beta Spending Functions
	9.5. Practical Aspects of Monitoring
	9.6. Inference after a Monitored Trial
		9.6.1. Statistical Contrast between Unmonitored and Monitored Trials
		9.6.2. Defining a P-Value after a Monitored Trial
		9.6.3. Defining a Confidence Interval after a Monitored Trial
		9.6.4. Correcting Bias after a Monitored Trial
	9.7. Bayesian Monitoring
	9.8. Summary
10. M&Ms: Multiplicity and Missing Data
	10.1. Introduction
	10.2. Multiple Comparisons
		10.2.1. The Debate
		10.2.2. Control of Familywise Error Rate
		10.2.3. Showing Strong Control by Enumeration
		10.2.4. Intuition Behind Multiple Comparison Procedures
		10.2.5. Independent Comparisons
		10.2.6. Closure Principle
	10.3. Dunnett Procedure and Conditioning Technique
	10.4. Missing Data
		10.4.1. Definitions and Example
		10.4.2. Methods for Data That Are MAR
		10.4.3. Sensitivity Analyses
	10.5. Summary
11. Adaptive Methods
	11.1. Introduction
	11.2. Adaptive Sample Size Based on Nuisance Parameters
		11.2.1. Continuous Outcomes
		11.2.2. Binary Outcomes
	11.3. Adaptive Sample Size Based on Treatment Effect
		11.3.1. Introduction and Notation
		11.3.2. Non-adaptive Two-Stage Setting
		11.3.3. Adaptation Principle
		11.3.4. Bauer-Köhne (1994)
		11.3.5. Proschan and Hunsberger (1995)
		11.3.6. Criticisms of Adaptive Methods Based on Treatment Effect
	11.4. Unplanned Changes before Breaking the Blind
	11.5. Summary
References
Index