Statistical Thinking in Clinical Trials  book cover
1st Edition

Statistical Thinking in Clinical Trials

ISBN 9781138058590
Published November 24, 2021 by Chapman and Hall/CRC
264 Pages 4 Color & 38 B/W Illustrations

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Book Description

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.

Table of Contents


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


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


3. Introduction to Clinical Trials


4. Design of Clinical Trials

Different Phases of Trials


Baseline Variables


Regression to the Mean

Appropriate Control

Choice of Primary Endpoint

Reducing Variability

Replication and Averaging




Different Types of Trials

Superiority Versus Noninferiority

Parallel Arm Trials

Crossover Trials

Cluster-Randomized Trials

Multi-Arm Trials

Appendix: The Geometry of Stratification


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


6. Randomization-Based Inference


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


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


Control of Conditional Type Error Rate

Protection Against Temporal Trends

A More Rigorous Null Hypothesis

Unpaired Data: Response-Adaptive Randomization


Re-randomization Tests & Strength of Randomized Evidence

Confidence Intervals

A Philosophical Criticism of Re-randomization Tests

Appendix: The Permutation Variance of ¯ YC − ¯ YT


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


8. Sample Size/Power


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


Exact Power for Fisher’s Exact Test

Adjusting for Noncompliance and Other Factors

Appendix: Other Sample Size Formulas for Two Proportions


9. Monitoring


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


10. M&Ms: Multiplicity & Missing Data


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


11. Adaptive Methods


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




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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.