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E-raamat: ROC Curves for Continuous Data

(Imperial College, London, UK), (University of Exeter, Exeter, UK)
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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 curvesThe 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 topicsThe 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.

Arvustused

... 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 Hands 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 ... 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 Hands 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

About the Authors xi
Preface xiii
Chapter 1: Introduction 1
1.1 Background
1
1.2 Classification
2
1.3 Classifier performance assessment
6
1.4 The ROC curve
11
1.5 Further reading
14
Chapter 2: Population ROC curves 17
2.1 Introduction
17
2.2 The ROC curve
18
2.3 Slope of the ROC curve and optimality results
24
2.4 Summary indices of the ROC curve
25
2.5 The binormal model
31
2.6 Further reading
35
Chapter 3: Estimation 37
3.1 Introduction
37
3.2 Preliminaries: classification rule and error rates
39
3.3 Estimation of ROC curves
41
3.4 Sampling properties and confidence intervals
57
3.5 Estimating summary indices
63
3.6 Further reading
74
Chapter 4: Further inference on single curves 75
4.1 Introduction
75
4.2 Tests of separation of P and N population scores
76
4.3 Sample size calculations
78
4.4 Errors in measurements
82
4.5 Further reading
86
Chapter 5: ROC curves and covariates 87
5.1 Introduction
87
5.2 Covariate adjustment of the ROC curve
89
5.3 Covariate adjustment of summary statistics
97
5.4 Incremental value
102
5.5 Matching in case-control studies
104
5.6 Further reading
105
Chapter 6: Comparing ROC curves 107
6.1 Introduction
107
6.2 Comparing summary statistics of two ROC curves
109
6.3 Comparing AUCs for two ROC curves
113
6.4 Comparing entire curves
115
6.5 Identifying where ROC curves differ
121
6.6 Further reading
122
Chapter 7: Bayesian methods 123
7.1 Introduction
123
7.2 General ROC analysis
125
7.3 Meta-analysis
128
7.4 Uncertain or unknown group labels
132
7.5 Further reading
139
Chapter 8: Beyond the basics 141
8.1 Introduction
141
8.2 Alternatives to ROC curves
141
8.3 Convex hull ROC curves
145
8.4 ROC curves for more than two classes
147
8.5 Other issues
154
8.6 Further reading
155
Chapter 9: Design and interpretation issues 157
9.1 Introduction
157
9.2 Missing values
158
9.3 Bias in ROC studies
165
9.4 Choice of optimum threshold
172
9.5 Medical imaging
176
9.6 Further reading
179
Chapter 10: Substantive applications 181
10.1 Introduction
181
10.2 Machine learning
182
10.3 Atmospheric sciences
184
10.4 Geosciences
190
10.5 Biosciences
192
10.6 Finance
195
10.7 Experimental psychology
198
10.8 Sociology
199
Appendix: ROC software 201
References 203
Index 227
Wojtek J. Krzanowski is Emeritus Professor of Statistics at the University of Exeter and Senior Research Investigator at Imperial College. Dr. Krzanowskis 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.