Statistical Methods in Diagnostic Medicine, Second Edition
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Praise for the First Edition

" . . . the book is a valuable addition to the literature in the field, serving as a much-needed guide for both clinicians and advanced students."—Zentralblatt MATH

A new edition of the cutting-edge guide to diagnostic tests in medical research

In recent years, a considerable amount of research has focused on evolving methods for designing and analyzing diagnostic accuracy studies. Statistical Methods in Diagnostic Medicine, Second Edition continues to provide a comprehensive approach to the topic, guiding readers through the necessary practices for understanding these studies and generalizing the results to patient populations.

Following a basic introduction to measuring test accuracy and study design, the authors successfully define various measures of diagnostic accuracy, describe strategies for designing diagnostic accuracy studies, and present key statistical methods for estimating and comparing test accuracy. Topics new to the Second Edition include:

  • Methods for tests designed to detect and locate lesions

  • Recommendations for covariate-adjustment

  • Methods for estimating and comparing predictive values and sample size calculations

  • Correcting techniques for verification and imperfect standard biases

  • Sample size calculation for multiple reader studies when pilot data are available

  • Updated meta-analysis methods, now incorporating random effects

Three case studies thoroughly showcase some of the questions and statistical issues that arise in diagnostic medicine, with all associated data provided in detailed appendices. A related web site features Fortran, SAS®, and R software packages so that readers can conduct their own analyses.

Statistical Methods in Diagnostic Medicine, Second Edition is an excellent supplement for biostatistics courses at the graduate level. It also serves as a valuable reference for clinicians and researchers working in the fields of medicine, epidemiology, and biostatistics.


Xiao-Hua Zhou, PhD, is Professor of Biostatistics at the University of Washington and Director and Research Career Scientist at the Biostatistics Unit of the Veterans Affairs Puget Sound Healthcare System. He is a Fellow of the American Statistical Association and the author of more than 100 published articles on statistical methods in diagnostic medicine and causal inferences.

Nancy A. Obuchowski, PhD, is Vice Chairperson of the Department of Quantitative Health Sciences at the Cleveland Clinic Foundation. A Fellow of the American Statistical Association, she has written more than 100 journal articles on the design and analysis of studies of screening and diagnostic tests.

Donna K. McClish, PhD, is Associate Professor and Graduate Program Director in Biostatistics at Virginia Commonwealth University. She has written more than 100 journal articles on statistical methods in epidemiology, diagnostic medicine, and health services research.


List of Figures xix

List of Tables xxiii

0.1 Preface xxix

0.2 Acknowledgements xxx

Part I. Basic Concepts and Methods

1. Introduction 3

1.1 Diagnostic Test Accuracy Studies 3

1.2 Case Studies 6

1.3 Software 10

1.4 Topics Not Covered in This Book 10

2. Measures of Diagnostic Accuracy 13

2.1 Sensitivity and Specificity 14

2.2 Combined Measures of Sensitivity and Specificity 21

2.3 Receiver Operating Characteristic (ROC) Curve 24

2.4 Area Under the ROC Curve 27

2.5 Sensitivity at Fixed EPR 34

2.6 Partial Area Under the ROC Curve 35

2.7 Likelihood Ratios 36

2.8 ROC Analysis When the True Diagnosis Is not Binary 41

2.9 C-Statistics and Other Measures to Compare Prediction Models 43

2.10 Detection and Localization of Multiple Lesions 44

2.11 Positive and Negative Predictive Values, Bayes Theorem, and Case Study 2 47

2.12 Optimal Decision Threshold on the ROC Curve 51

2.13 Interpreting the Results of Multiple Tests 54

3. Design of Diagnostic Accuracy Studies 57

3.1 Establish the Objective of the Study 58

3.2 Identify the Target Patient Population 63

3.3 Select a Sampling Plan for Patients 64

3.4 Select the Gold Standard 72

3.5 Choose A Measure of Accuracy 79

3.6 Identify Target Reader Population 82

3.7 Select Sampling Plan for Readers 83

3.8 Plan Data Collection 84

3.9 Plan Data Analyses 94

3.10 Determine Sample Size 101

4. Estimation and Hypothesis Testing in a Single Sample 103

4.1 Binary-Scale Data 104

4.2 Ordinal-Scale Data 117

4.3 Continuous-Scale Data 141

4.4 Testing the Hypothesis that the ROC Curve Area or Partial Area Is a Specific Value 163

5. Comparing the Accuracy of Two Diagnostic Tests 165

5.1 Binary-Scale Data 166

5.2 Ordinal- and Continuous-Scale Data 174

5.3 Tests of Equivalence 189

6. Sample Size Calculations 193

6.1 Studies Estimating the Accuracy of a Single Test 194

6.2 Sample Size for Detecting a Difference in Accuracies of Two Tests 203

6.3 Sample Size for Assessing Non-Inferiority of Equivalency of Two Tests 214

6.4 Sample Size for Determining a Suitable Cutoff Value 218

6.5 Sample Size Determination for Multi-Reader Studies 219

6.6 Alternative to Sample Size Formulae 228

7. Introduction to Meta-analysis for Diagnostic Accuracy Studies 231

7.1 Objectives 232

7.2 Retrieval of the Literature 233

7.3 Inclusion/Exclusion Criteria 237

7.4 Extracting Information from the Literature 241

7.5 Statistical Analysis 243

7.6 Public Presentation 258

Part II. Advanced Methods

8. Regression Analysis for Independent ROC Data 263

8.1 Four Clinical Studies 264

8.2 Regression Models for Continuous-Scale Tests 267

8.3 Regression Models for Ordinal-Scale Tests 287

8.4 Covariate Adjusted ROC Curves of Continuous-Scale tests 294

9. Analysis of Multiple Reader and/or Multiple Test Studies 297

9.1 Studies Comparing Multiple Tests with Covariates 298

9.2 Studies with Multiple Readers and Multiple Tests 310

9.3 Analysis of Multiple Tests Designed to Locate and Diagnose Lesions 325

10. Methods for Correcting Verification Bias 329

10.1 Examples 330

10.2 Impact of Verification Bias 333

10.3 A Single Binary-Scale Test 334

10.4 Correlated Binary-Scale Tests 341

10.5 A Single Ordinal-Scale Test 348

10.6 Correlated Ordinal-Scale Tests 360

10.7 Continuous-Scale Tests 372

11. Methods for Correcting Imperfect Gold Standard Bias 389

11.1 Examples 390

11.2 Impact of Imperfect Gold Standard Bias 393

11.3 One Single Binary test in a Single Population 395

11.4 One Single Binary test in G Populations 402

11.5 Multiple Binary Tests in One Single Population 408

11.6 Multiple Binary Tests in G Populations 423

11.7 Multiple Ordinal-Scale Tests in One Single Population 425

11.8 Multiple-Scale Tests in One Single Population 429

12. Statistical Analysis for Meta-analysis 435

12.1 Binary-Scale Data 436

12.2 Ordinal- or Continuous-Scale Data 438

12.3 ROC Curve Area 445

Appendix A. Case Studies and Chapter 8 Data 449

Appendix B. Jackknife and Bootstrap Methods of Estimating Variances and Confidence Intervals 477 


"The authors, overall, have done a good job of revising their first edition, addressing the critical reviews as well as expanding and updating their coverage . . . In summary, this is a good book, focusing on medical diagnosis as the name promises, presenting a wealth of methods in detail with good discussion." (Journal of Biopharmaceutical Statistics, 2011)

"Early chapters are accessible to readers with a basic knowledge of statistical and medical terminology, and the second section addresses data analysts with basic training in biostatistics. Later chapters assume deeper background in statistics, but the examples should be accessible to all. The 2002 edition has been updated throughout, and three new case studies have been added." (Booknews, 1 June 2011)