Quantitative Drug Safety and Benefit-Risk Evaluation: Practical and Cross-Disciplinary Approaches

Abstract

This book, which wants to be called OODA, is in an emerging genre, the statistical autobiography. Marron and Dryden have expanded the frontiers of data analysis in many directions over their careers, and they document the challenges encountered along the way. Their data illustrate growth in the statistical landscape in both size and complexity. Functional data analysis, and its cousin shape analysis, took data analysis beyond the familiar matrix format by replacing frequently unordered columns by continuous and usually differentiable curves. The functional transition in one sense was easy because it remained within the Hilbert space framework. But the space of operations on curves is larger than linear algebra, since it includes differentiation to fit data with differential equations, integration to compute arc length and the nonlinear transformation of domains so as to align curve features. The authors add to the mix the graph structures trees and networks, as well as curved manifolds. This binding of new data objects to new transformation groups coincided roughly with the advent of object oriented programming systems, and hence the title. The first three chapters provide short overviews of several example analyses followed by tutorial material on variants of principle component analysis. Chapters 4 , 5, and 6 provide examples of data exploration and confirmation, respectively, as well as tips on visualizing results. Chapter 7 turns from PCA to distance based analyses and multidimensional scaling, and chapter 8 to shape and manifold representations. Chapter 9 illustrates data alignment using domain warping by the Fisher-Rao method. Chapter 10 looks at tree graphs and networks as data. Chapters 11 and 12 consider novel classification and clustering techniques. Chapters 13 and 14 offer methods for inference and asymptotic, respectively, in high-dimensional contexts. Chapter 15 describes the statistical graphics tool SiZer and chapter 16 outlines robust estimation techniques. The book concludes with additional material on PCA and a final chapter on general reflections on object oriented data. By my count the book examines 19 substantial and varied datasets, most of which are available on gitHub along with analyses using Matlab. They also add to these a number of toy sets used as illustrations. Their use of color and other statistical graphics tools is outstanding, and makes displays exciting even if not always essential. My personal favorite is the display of 3D rectum-prostate-bladder structures, require a solid background in finite element analysis to produce. The target audience is graduate students in statistics and machine learning, and the book provides a gold mine of fascinating potential class projects. However, as a teaching tool it does have some limitations. The many literature citations that seem to accompany any assertion, and make for cluttered reading. Restricting these to an annotated resource section at the end of each chapter would have been helpful. Citations are often used where some lines of text would be more instructive. Topics are often announced without warning or subsequent definition. Students will be spending a lot of time in libraries, or more likely, Wikipedia. Will the title survive? Perhaps not, since most graduate students are too young to have witnessed the transition from C to C++ or S to R. But, being an admirer of applications, I found this volume to both irresistible and inspirational. My alternative title might have been “Prospecting in the Statistical Outback,” and Marron and Dryden will inspire to uncover many more gems.