1st Edition
Handbook of Multiple Comparisons
Written by experts that include originators of some key ideas, chapters in the Handbook of Multiple Testing cover multiple comparison problems big and small, with guidance toward error rate control and insights on how principles developed earlier can be applied to current and emerging problems. Some highlights of the coverages are as follows.
Error rate control is useful for controlling the incorrect decision rate. Chapter 1 introduces Tukey's original multiple comparison error rates and point to how they have been applied and adapted to modern multiple comparison problems as discussed in the later chapters.
Principles endure. While the closed testing principle is more familiar, Chapter 4 shows the partitioning principle can derive confidence sets for multiple tests, which may become important as the profession goes beyond making decisions based on p-values.
Multiple comparisons of treatment efficacy often involve multiple doses and endpoints. Chapter 12 on multiple endpoints explains how different choices of endpoint types lead to different multiplicity adjustment strategies, while Chapter 11 on the MCP-Mod approach is particularly useful for dose-finding. To assess efficacy in clinical trials with multiple doses and multiple endpoints, the reader can see the traditional approach in Chapter 2, the Graphical approach in Chapter 5, and the multivariate approach in Chapter 3.
Personalized/precision medicine based on targeted therapies, already a reality, naturally leads to analysis of efficacy in subgroups. Chapter 13 draws attention to subtle logical issues in inferences on subgroups and their mixtures, with a principled solution that resolves these issues. This chapter has implication toward meeting the ICHE9R1 Estimands requirement.
Besides the mere multiple testing methodology itself, the handbook also covers related topics like the statistical task of model selection in Chapter 7 or the estimation of the proportion of true null hypotheses (or, in other words, the signal prevalence) in Chapter 8. It also contains decision-theoretic considerations regarding the admissibility of multiple tests in Chapter 6. The issue of selected inference is addressed in Chapter 9.
Comparison of responses can involve millions of voxels in medical imaging or SNPs in genome-wide association studies (GWAS). Chapter 14 and Chapter 15 provide state of the art methods for large scale simultaneous inference in these settings.
Chapter 1. An Overview of Multiple Comparisons
Xinping Cui, Thorsten Dickhaus, Ying Ding, and Jason C. Hsu
Chapter 2. Multiple Test Procedures Based on p-Values
Ajit C. Tamhane and Jiangtao Gou
Chapter 3. Multivariate multiple test procedures
Thorsten Dickhaus, Andre Neumann, and Taras Bodnar
Chapter 4. Partitioning for Confidence Sets, Confident Directions, and Decision Paths
Helmut Finner, Szu-Yu Tang, Xinping Cui, and Jason C. Hsu
Chapter 5. Graphical approaches for multiple comparison procedures
Dong Xi and Frank Bretz
Chapter 6. Decision Theoretic Considerations of Multiple Comparisons
Arthur Cohen and Harold Sackrowitz
Chapter 7. Identifying important predictors in large data bases - multiple testing and model selection
Malgorzata Bogdan and Florian Frommlet
Chapter 8. Prevalence Estimation
Jonathan D. Rosenblatt
Chapter 9. On agnostic post hoc approaches to false positive control
Giles Blanchard, Pierre Neuvial, and Etienne Roquain
Chapter 10. Group sequential and adaptive designs
Ekkehard Glimm and Lisa V. Hampson
Chapter 11. Multiple testing for dose finding
Frank Bretz, Dong Xi, and Björn Bornkamp
Chapter 12. Multiple Endpoints
Bushi Wang
Chapter 13. Subgroups Analysis for Personalized and Precision Medicine Development
Yi Liu, Hong Tian and Jason C. Hsu
Chapter 14. Exploratory inference: localizing relevant effects with confidence
Aldo Solari and Jelle J. Goeman
Chapter 15. Testing SNPs in Targeted Drug Development
Ying Ding, Yue Wei, Xinjun Wang, and Jason C. Hsu
Biography
Xinping Cui is professor and chair of the Department of Statistics at the University of California, Riverside, USA. Her interdisciplinary research focuses on multiple testing, statistical genomics, precision medicine and system biology.
Thorsten Dickhaus is full professor of Mathematical Statistics at the University of Bremen, Germany. He is a (co-) author of approx. 50 journal articles and four books. For more than 15 years, his research focuses on simultaneous statistical inference and multiple testing.
Ying Ding is Associate Professor in the Department of Biostatistics at the University of Pittsburgh. Her research focuses on survival analysis, large-scale genomics and proteomics analysis, multiple testing, and precision medicine.
Jason C. Hsu is an Emeritus Professor in Statistics at the Ohio State University. His research interests are in multiple comparison, logic-respecting estimands, and targeted therapies for personalized/precision medicine.
"The main strength of the book is that it provides extensive mathematical arguments along with formulas to help readers understand the fundamentals behind the methods for the appropriate analysis of multiple comparisons. A strong foundation in mathematical statistics is necessary to understand and use this book effectively. Topics are covered in sufficient depth for mastery of the material if the book is read carefully. ... Graduate students would also likely find this book useful to help in picking a dissertation topic if they are interested in problems related to multiple comparisons. Statisticians working in theory and methods development would find this book helpful as a reference. Applied statisticians may find the second half of the book helpful, as specific examples are provided for how these methods are to be used. Overall, this book is highly recommended for advanced graduate students and researchers wanting a deeper understanding of multiple comparison problems."
-Amit K. Chowdhry in Journal of the Royal Statistical Society Series A, March 2022
