Design and Analysis of Cross-Over Trials is concerned with a specific kind of comparative trial known as the cross-over trial, in which subjects receive different sequences of treatments. Such trials are widely used in clinical and medical research, and in other diverse areas such as veterinary science, psychology, sports science, and agriculture.
The first edition of this book was the first to be wholly devoted to the subject. The second edition was revised to mirror growth and development in areas where the design remained in widespread use and new areas where it had grown in importance. This new Third Edition:
- Contains seven new chapters written in the form of short case studies that address re-estimating sample size when testing for average bioequivalence, fitting a nonlinear dose response function, estimating a dose to take forward from phase two to phase three, establishing proof of concept, and recalculating the sample size using conditional power
- Employs the R package Crossover, specially created to accompany the book and provide a graphical user interface for locating designs in a large catalog and for searching for new designs
- Includes updates regarding the use of period baselines and the analysis of data from very small trials
- Reflects the availability of new procedures in SAS, particularly proc glimmix
- Presents the SAS procedure proc mcmc as an alternative to WinBUGS for Bayesian analysis
Complete with real data and downloadable SAS code, Design and Analysis of Cross-Over Trials, Third Edition provides a practical understanding of the latest methods along with the necessary tools for implementation.
Table of Contents
List of Figures
List of Tables
Preface to the Third Edition
What Is a Cross-Over Trial?
With Which Sort of Cross-Over Trial Are We Concerned?
Why Do Cross-Over Trials Need Special Consideration?
A Brief History
Notation, Models, and Analysis
Aims of This Book
Structure of the Book
The 2×2 Cross-Over Trial
Plotting the Data
Analysis Using T-Tests
Sample Size Calculations
Analysis of Variance
Aliasing of Effects
Consequences of Preliminary Testing
Analyzing the Residuals
A Bayesian Analysis of the 2×2 Trial
Bayes Using Approximations
Bayes Using Gibbs Sampling
Use of Baseline Measurements
Use of Covariates
Testing λ1 =λ2
Testing t1 =t2, Given that λ1 =λ2
Testing π1 =π2, Given that λ1 =λ2
Obtaining the Exact Version of the Wilcoxon Ranksum Test Using Tables
Point Estimate and Confidence Interval for Δ =t1 −t2
A More General Approach to Nonparametric Testing
Nonparametric Analysis of Ordinal Data
Analysis of a Multicenter Trial
Tests Based on Nonparametric Measures of Association
The Mainland–Gart Test
Fisher’s Exact Version of the Mainland–Gart Test
Higher-Order Designs for Two Treatments
Balaam’s Design for Two Treatments
Effect of Preliminary Testing in Balaam’s Design
Three-Period Designs with Two Sequences
Three-Period Designs with Four Sequences
A Three-Period Six-Sequence Design
Which Three-Period Design to Use?
Four-Period Designs with Two Sequences
Four-Period Designs with Four Sequences
Four-Period Designs with Six Sequences
Which Four-Period Design to Use?
Which Two-Treatment Design to Use?
Designing Cross-Over Trials
Designs with p = t
Designs with p < t
Designs with p > t
Designs with Many Periods
Optimality Results for Cross-Over Designs
Which Variance-Balanced Design to Use?
Partially Balanced Designs
Comparing Test Treatments to a Control
Factorial Treatment Combinations
Extending the Simple Model for Carry-Over Effects
Computer Search Algorithms
Analysis of Continuous Data
Example: INNOVO Trial: Dose–Response Study
Fixed Subject Effects Model
Ignoring the Baseline Measurements
Adjusting for Carry-Over Effects
Random Subject Effects Model
Random Subject Effects
Recovery of Between-Subject Information
Small Sample Inference with Random Effects
Use of Baseline Measurements
Introduction and Examples
Notation and Basic Results
Period-Dependent Baseline Covariates
Baselines as Response Variables
Analyses for Higher-Order Two-Treatment Designs
Analysis for Balaam’s Design
General Linear Mixed Model
Analysis of Repeated Measurements within Periods
Example: Insulin Mixtures
Cross-Over Data as Repeated Measurements
Allowing More General Covariance Structures
Robust Analyses for Two-Treatment Designs
Case Study: An Analysis of a Trial with Many Periods
Example: McNulty’s Experiment
Fixed Effects Analysis
Random Subject Effects and Covariance Structure
Modeling the Period Effects
Analysis of Discrete Data
Modeling Dependent Categorical Data
Types of Model
Binary Data: Subject Effect Models
Dealing with the Subject Effects
Binary Data: Marginal Models
Example: Trial on Patients with Primary Dysmenorrhea
Types of Model for Categorical Outcomes
Subject Effects Models
Time to Event Data
Issues Associated with Scale
What Is Bioequivalence?
Testing for Average Bioequivalence
Case Study: Phase I Dose–Response Noninferiority Trial
Model for Dose Response
Testing for Noninferiority
Choosing Doses for the Fifth Period
Analysis of the Design Post-Interim
Case Study: Choosing a Dose–Response Model
Analysis of Variance
Case Study: Conditional Power
Variance Spending Approach
Interim Analysis of Sleep Trial
Case Study: Proof of Concept Trial with Sample Size Re-Estimation
Calculating the Sample Size
Case Study: Blinded Sample Size Re-Estimation in a Bioequivalence Study
Blinded Sample Size Re-Estimation (BSSR)
Case Study: Unblinded Sample Size Re-Estimation in a Bioequivalence Study That Has a Group Sequential Design
Sample Size Re-Estimation in a Group Sequential Design
Modification of Sample Size Re-Estimation in a Group Sequential Design
Case Study: Various Methods for an Unblinded Sample Size Re-Estimation in a Bioequivalence Study
Appendix A: Least Squares Estimation
Byron Jones is a senior biometrical fellow and executive director in the Statistical Methodology Group at Novartis Pharmaceuticals. Previously he was a senior statistical consultant/senior director at Pfizer and a senior director and UK head of the Research Statistics Unit at GlaxoSmithKline. In addition to 14 years of experience in the pharmaceutical industry, he has 25 years of experience in academia, ultimately holding the position of professor of medical statistics at De Montfort University. Currently he is an honorary professor at the London School of Hygiene and Tropical Medicine, visiting professor at University College London and at the University of Leicester, and a visiting professorial fellow at Queen Mary, University of London.
Michael G. Kenward is GlaxoSmithKline professor of biostatistics at the London School of Hygiene and Tropical Medicine. Previously he held positions at the Universities of Kent and Reading in the UK, and at research institutes in the UK, Iceland, and Finland. He has acted as a pharmaceutical industry consultant in biostatistics for more than 25 years. His research interests include the analysis of longitudinal data and cross-over trials, and modeling in biostatistics, with a particular interest in the problem of missing data. He has co-authored three textbooks and is well known for his 1994 Royal Statistical Society read paper on missing data.
"Jones and Kenward added several valuable case studies to the third edition of their book. The case studies illustrate elegantly the applications of recent innovations in statistical methodologies to cross-over trials. The new edition is an excellent reference for scientists who want to understand cross-over trials or are interested in learning how statistical advancements in the last decade could be used to expand the versatility of cross-over trials."
—Christy Chuang-Stein, Ph.D., Vice President, Head of Statistical Research and Consulting Center, Pfizer Inc.
"As in the previous two editions, this edition offers a comprehensive coverage on the design and analysis of cross-over trials. With several major noteworthy updates, it will assist statisticians to conveniently tackle practical issues that arise in a cross-over trial… The most substantial update is the addition of seven new chapters (Chapters 8–14) in the form of short case studies. These real-world examples cover a wide range of issues and solutions above and beyond what is commonly encountered in a cross-over trial and significantly broaden the book…the third edition of Design and Analysis of Cross-Over Trials remains an outstanding reference for statisticians who work on cross-over trials, whether occasionally or frequently."
—Haiying Chen, Wake Forest School of Medicine, in Journal of the American Statistical Association, Volume 111, 2016
"Jones and Kenward present students, academics, and researchers with the third edition of their text, dedicated to an understanding of a comparative trait known as the cross-over trial, through which patients involved in a study received different sequences of treatments. New for the third edition, the text includes seven new chapters devoted to case studies, coverage of the R package Crossover, updates related to the use of period baselines and the analysis of very small trials, and a variety of other features."
—Ringgold, Inc. Book News, February 2015
Praise for the Second Edition:
"In the second edition, updated from the original published in 1989, the authors have added discussions of new, more comprehensive (downloadable) datasets and some additional topics. ... Substantially updated with more than 130 new references, the book has been thoroughly modernized to reflect new developments in this area. Among the new material added to the book is a chapter on bioequivalence and a discussion of new methods for longitudinal and categorical data. This book continues to be a recommended choice as a valuable reference for clinical statisticians and those who study medical trials where treatments through cross-over design are a feasible approach. For those who already own the first edition, updating to the second will help keep you current on recent developments in this area."
—Journal of the American Statistics Association