Statistical Thinking in Clinical Trials combines a relatively small number of key statistical principles and several instructive clinical trials to gently guide the reader through the statistical thinking needed in clinical trials. Randomization is the cornerstone of clinical trials and randomization-based inference is the cornerstone of this book. Read this book to learn the elegance and simplicity of re-randomization tests as the basis for statistical inference (the analyze as you randomize principle) and see how re-randomization tests can save a trial that required an unplanned, mid-course design change.
Other principles enable the reader to quickly and confidently check calculations without relying on computer programs. The `EZ’ principle says that a single sample size formula can be applied to a multitude of statistical tests. The `O minus E except after V’ principle provides a simple estimator of the log odds ratio that is ideally suited for stratified analysis with a binary outcome. The same principle can be used to estimate the log hazard ratio and facilitate stratified analysis in a survival setting. Learn these and other simple techniques that will make you an invaluable clinical trial statistician.
1. Evidence and Inference
Terminology and Paradigm of Inference
Classical Inference
Hypothesis Tests and P-Values
Confidence Intervals
Criticisms of Classical Methods
The Bayesian Approach
Large Sample Inference
Robust Methods Are Preferred in Clinical Trials
Summary
2. 2 × 2 Tables
Measures of Treatment Effect
Exact Tests and Confidence Intervals
Fisher’s Exact Test
Exact Confidence Interval for Odds Ratio
Oddities of Fisher’s Exact Test and Confidence Interval
Unconditional Tests As Alternatives to Fisher’s Exact Test
Appendix: P(X = x | S = s) in Table
Summary
3. Introduction to Clinical Trials
Summary
4. Design of Clinical Trials
Different Phases of Trials
Blinding
Baseline Variables
Controls
Regression to the Mean
Appropriate Control
Choice of Primary Endpoint
Reducing Variability
Replication and Averaging
Differencing
Stratification
Regression
Different Types of Trials
Superiority Versus Noninferiority
Parallel Arm Trials
Crossover Trials
Cluster-Randomized Trials
Multi-Arm Trials
Appendix: The Geometry of Stratification
Summary
5. Randomization/Allocation
Sanctity and Placement of Randomization
Simple Randomization
Permuted Block Randomization
Biased Coin Randomization
Stratified Randomization
Minimization and Covariate-Adaptive Randomization
Response-Adaptive Randomization
Adaptive Randomization And Temporal Trends
Summary
6. Randomization-Based Inference
Introduction
Paired Data
An Example
Control of Conditional Type Error Rate
Asymptotic Equivalence to a T-test
The Null Hypothesis and Generalizing
Does A Re-randomization Test Assume Independence?
Unpaired Data: Traditional Randomization
Introduction
Control of Conditional Type Error Rate
The Null Hypothesis and Generalizing
Does a Re-randomization Test Require Independence?
Asymptotic Equivalence to a t-Test
Protection Against Temporal Trends
Fisher’s Exact Test As a Re-Randomization Test
Unpaired Data: Covariate-Adaptive Randomization
Introduction
Control of Conditional Type Error Rate
Protection Against Temporal Trends
A More Rigorous Null Hypothesis
Unpaired Data: Response-Adaptive Randomization
Introduction
Re-randomization Tests & Strength of Randomized Evidence
Confidence Intervals
A Philosophical Criticism of Re-randomization Tests
Appendix: The Permutation Variance of ¯ YC − ¯ YT
Summary
7. Survival Analysis
Introduction to Survival Methods
Comparing Survival Across Arms
Comparing Survival At A Specific Time
The Logrank Test
The Hazard Rate and Cox Model
Competing Risk Analysis
Parametric Approaches
Conditional Binomial Procedure
Appendix: Partial Likelihood
Summary
8. Sample Size/Power
Introduction
The EZ Principle Illustrated through the -Sample t-Test
Important Takeaways from the EZ Principle
EZ Principle Applied More Generally
-Sample t-test
Test of Proportions
Logrank Test
Cluster-Randomized Trials
In a Nutshell
Nonzero Nulls
Practical Aspects of Sample Size Calculations
Test of Means
Test of Proportions
Specification of Treatment Effect
Exact Power
t-Tests
Exact Power for Fisher’s Exact Test
Adjusting for Noncompliance and Other Factors
Appendix: Other Sample Size Formulas for Two Proportions
Summary
9. Monitoring
Introduction
Efficacy Monitoring
A Brief History of Efficacy Boundaries
Z-scores, B-Values, and Information
Revisiting O’Brien-Fleming
Alpha Spending Functions
The Effect of Monitoring on Power
Small Sample Sizes
Futility Monitoring
What is Futility?
Conditional Power
Beta Spending Functions
Practical Aspects of Monitoring
Inference after A Monitored Trial
Statistical Contrast between Unmonitored and Monitored Trials
Defining A P-Value after a Monitored Trial
Defining A Confidence Interval after A Monitored Trial
Correcting Bias after A Monitored Trial
Bayesian Monitoring
Summary
10. M&Ms: Multiplicity & Missing Data
Introduction
Multiple Comparisons
The Debate
Control of Familywise Error Rate (FWER)
Showing Strong Control by Enumeration
Intuition Behind Multiple Comparison Procedures
Independent Comparisons
Closure Principle
The Dunnett Procedure And A Conditioning Technique
Missing Data
Definitions And An Example
Methods for Data That Are MAR
Sensitivity Analyses
Summary
11. Adaptive Methods
Introduction
Adaptive Sample Size Based on Nuisance Parameters
Continuous Outcomes
Binary Outcomes
Adaptive Sample Size Based on Treatment Effect
Introduction and Notation
Non-adaptive Two-Stage Setting
Adaptation Principle
Bauer-K¨ohne ()
Proschan and Hunsberger, ()
Criticisms of Adaptive Methods Based on The Treatment Effect
Unplanned Changes before Breaking the Blind
Summary
Index
Biography
Michael Proschan is a mathematical statistician and Fellow of the American Statistical Association with 32 years of clinical trial experience in cardiovascular and infectious diseases, including HIV/AIDS, Ebola virus disease, and COVID-19. He has expertise in statistical monitoring of clinical trials, having taught short courses and co-authored the book Statistical Monitoring of Clinical Trials: A Unified Approach with Gordon Lan and Janet Wittes. He co-authored, with Sally Hunsberger, one of the first papers on adaptive clinical trial methods using the observed treatment effect at an interim analysis. More recently, Dr. Proschan has written about the vital role re-randomization tests play in adaptive methods before breaking the treatment blind. He has recently been an adjunct faculty member at George Washington University and Johns Hopkins University’s Advanced Academic Programs.
"The goal of the book Statistical Thinking in Clinical Trials is to engender statistical intuition that can be used in different types of clinical trials, and author Michael A. Proschan brilliantly achieved the goal. The biggest part of the book is dedicated to re-randomization tests, which can be applied in a multitude of settings. The author shows their beauty and simplicity. To illustrate theoretical explanations, the author uses examples of real trials. There are not many examples of trials, but the author returns to them in different chapters and at the end of studying the book, readers become familiar with these examples. I think, it is a positive aspect of the book and provides a better understanding of the practical application of the techniques described in the book than the use of many different examples during the presentation of the material. It should be noted that author uses examples not only to show the correct methods used in trials, but also to show possible mistakes that may occur during the trial and how to avoid them. [...] I would recommend [this book] for biostatisticians who not only intent on deeper learning statistical techniques but are also interested in improvement of statistical intuition and using it in different types of clinical trials."
-Maria Ivanchuk, in ISCB News, June 2022
