Statistical Methods in Diagnostic Medicine, 2nd Edition

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