ROC Curves for Continuous Data

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Features

  • Describes the major methodological developments and provides many illustrative examples
  • Includes appropriate mathematical theory without making the treatment too dense
  • Surveys the uses made of the methodology across a range of areas, from atmospheric science and geoscience to experimental psychology and sociology
  • Lists a number of websites from which software implementing the various techniques can be downloaded

Summary

Since ROC curves have become ubiquitous in many application areas, the various advances have been scattered across disparate articles and texts. ROC Curves for Continuous Data is the first book solely devoted to the subject, bringing together all the relevant material to provide a clear understanding of how to analyze ROC curves.

The fundamental theory of ROC curves
The book first discusses the relationship between the ROC curve and numerous performance measures and then extends the theory into practice by describing how ROC curves are estimated. Further building on the theory, the authors present statistical tests for ROC curves and their summary statistics. They consider the impact of covariates on ROC curves, examine the important special problem of comparing two ROC curves, and cover Bayesian methods for ROC analysis.

Special topics
The text then moves on to extensions of the basic analysis to cope with more complex situations, such as the combination of multiple ROC curves and problems induced by the presence of more than two classes. Focusing on design and interpretation issues, it covers missing data, verification bias, sample size determination, the design of ROC studies, and the choice of optimum threshold from the ROC curve. The final chapter explores applications that not only illustrate some of the techniques but also demonstrate the very wide applicability of these techniques across different disciplines.

With nearly 5,000 articles published to date relating to ROC analysis, the explosive interest in ROC curves and their analysis will continue in the foreseeable future. Embracing this growth of interest, this timely book will undoubtedly guide present and future users of ROC analysis.

Table of Contents

Introduction

Background

Classification

Classifier performance assessment

The ROC curve

Population ROC Curves

Introduction

The ROC curve

Slope of the ROC curve and optimality results

Summary indices of the ROC curve

The binormal model

Estimation

Introduction

Preliminaries: classification rule and error rates

Estimation of ROC curves

Sampling properties and confidence intervals

Estimating summary indices

Further Inference on Single Curves

Introduction

Tests of separation of P and N population scores

Sample size calculations

Errors in measurements

ROC Curves and Covariates

Introduction

Covariate adjustment of the ROC curve

Covariate adjustment of summary statistics

Incremental value

Matching in case-control studies

Comparing ROC Curves

Introduction

Comparing summary statistics of two ROC curves

Comparing AUCs for two ROC curves

Comparing entire curves

Identifying where ROC curves differ

Bayesian Methods

Introduction

General ROC analysis

Meta-analysis

Uncertain or unknown group labels

Beyond the Basics

Introduction

Alternatives to ROC curves

Convex hull ROC curves

ROC curves for more than two classes

Other issues

Design and Interpretation Issues

Introduction

Missing values

Bias in ROC studies

Choice of optimum threshold

Medical imaging

Substantive Applications

Introduction

Machine learning

Atmospheric sciences

Geosciences

Biosciences

Finance

Experimental psychology

Sociology

Appendix: ROC Software

References

Further reading suggestions appear at the end of each chapter.

Author Bio(s)

Wojtek J. Krzanowski is Emeritus Professor of Statistics at the University of Exeter and Senior Research Investigator at Imperial College. Dr. Krzanowski’s research interests include multivariate analysis, statistical modeling, classification, and computational methods. He has published 6 books, over 30 book contributions, and 100 articles in scientific journals.

David J. Hand is head of the statistics section and head of the mathematics in banking and finance program at Imperial College. Currently president of the Royal Statistical Society, Dr. Hand has been a recipient of the Guy Medal of the Royal Statistical Society, the Royal Society Wolfson Research Merit Award, and the IEEE ICDM Research Contributions Award. He has published extensively on a wide range of statistical topics.

Editorial Reviews

... a most timely and welcome book by two well known experts in this area. … I would give this book 8 points out of 10.
— Walter Krämer in Statistics Papers, 2011

Drs. Krzanowski and Hand provide a thorough overview of ROC curve analysis, similar to books already available, but with a more comprehensive approach, including many recent advancements from the literature. … Broad in scope, it covers not only application to medical testing but extends to other fields where ROC analysis can be very useful: geosciences, finance, psychology, and sociology. … this book is an excellent enhancement to the biostatistics literature. It will be a helpful reference not only for those in medicine but for researchers in all sectors, including government, industry, and academia. It provides a very broad review of ROC curve analysis comprising recent developments and includes a very extensive reference list.
Journal of the American Statistical Association, Vol. 105, No. 492, December 2010

Wojtek Krzanowski and David Hand succeeded in writing the first comprehensive monograph on ROC curves for continuous data. Each chapter closes with references for further reading which keeps the book the size of a handy handbook containing an overview of the most important information on the topic while offering further references [for] the interested reader. The book is well structured and easy to read. … highly recommended as [a] comprehensive handbook to researchers …
ISCB News, No. 50, December 2010

The book is well written for any researcher with any background. It is an excellent up-to-date reference book for beginning researchers and practitioners interested in using ROC curve. … It is strongly recommended to have this book handy for anyone interested in ROC curve.
—Lianfen Qian, Technometrics, November 2010

… there was a need in the literature for a book devoted solely to ROC curves … This book aims to answer this need; it succeeds, by offering the reader a concise and informative treatment of ROC curves. Krzanowski and Hand’s long research experience in multivariate analysis and classification is reflected in the book. They explain various aspects of ROC analysis very simply, using only the necessary mathematics. … the authors expand the theory to more advanced concepts of statistical inference, using informal language accompanied by a large number of examples from various scientific areas. Hence, the reading is easy, interesting, and bound to stimulate curiosity for further exploration of the literature. … very useful, highly readable, and can serve as a guide to ROC curves for any scientist who has the basic statistics background. I therefore recommend it to all researchers and practitioners who work with multivariate data, especially those who are concerned with classification problems.
Computing Reviews, November 2009