Statistical Methods in Diagnostic Medicine

Xiao-Hua Zhou, fellow of the American Association for the Advancement of Science, fellow of the American Statistical Association, fellow of Institute of Mathematical Statistics, is PKU Distinguished Chair Professor and Chair of the Department of Biostatistics at Peking University, Beijing, China. His research focuses on statistical methods for diagnostic medicine, causal inference, and clinical trials, with extensive experience in regulatory statistics and biomedical research methodology. He has published more than 290 referred papers in those areas. Jiarui Sun is Senior Biostatistician in Shanghai Shengdi Pharmaceutical Co., Ltd. and received his Ph.D from the School of Mathematical Science at Peking University, Beijing, China. His research interests include statistical methods for diagnostic accuracy studies, biomarker evaluation, and computational approaches to medical statistics and diagnostic test validation. Gene A. Pennello, fellow of the American Statistical Association, is a statistical reviewer and research Mathematical Statistician at the U.S. Food and Drug Administration (FDA) in Silver Spring, Maryland. He specializes in statistical methods for medical device evaluation, diagnostic test assessment, and regulatory review processes for medical technologies. Nancy A. Obuchowski, fellow of the American Statistical Association, Professor of Medicine at the Cleveland Clinic Lerner College of Medicine at Case Western Reserve University, has extensive experience in the design, analysis, and development of new statistical methodology for the evaluation of diagnostic and screening tests and quantitative imaging biomarkers. 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.

• Preface xivAcknowledgments xviPart I Basic Concepts and Methods 11 Introduction 31.1 Diagnostic Test Accuracy Studies 31.2 Case Studies 51.3 Software 81.4 Topics Not Covered in This Book 82 Measures of Diagnostic Accuracy 92.1 Sensitivity and Specificity 92.2 Combined Measures of Sensitivity and Specificity 152.3 ROC Curve 172.4 Area Under the ROC Curve 202.5 Sensitivity at Fixed FPR 252.6 Partial Area Under the ROC Curve 252.7 Likelihood Ratios 262.8 ROC Analysis When the True Diagnosis Is Not Binary 302.9 C-statistics and Other Measures to Compare Prediction Models 322.10 Detection and Localization of Multiple Lesions 332.11 Positive and Negative Predictive Values, Bayes' Theorem, and Case Study 2 352.12 Optimal Decision Threshold on the ROC Curve 382.13 Interpreting the Results of Multiple Tests 403 Design of Diagnostic Accuracy Studies 453.1 Establish the Objective of the Study 453.2 Identify the Target Patient Population 493.3 Select a Sampling Plan for Patients 503.4 Select the Gold Standard 563.5 Choose a Measure of Accuracy 613.6 Identify Target Reader Population 633.7 Select Sampling Plan for Readers 643.8 Plan Data Collection 643.9 Plan Data Analyses 723.10 Determine Sample Size 774 Estimation and Hypothesis Testing in a Single Sample 794.1 Binary-scale Data 804.2 Ordinal-scale Data 894.3 Continuous-scale Data 1084.4 Testing the Hypothesis that the ROC Curve Area or Partial Area Is a Specific Value 1265 Comparing the Accuracy of Two Diagnostic Tests 1295.1 Binary-scale Data 1305.2 Ordinal- and Continuous-scale Data 1365.3 Tests of Equivalence 1486 Sample Size Calculations 1536.1 Studies Estimating the Accuracy of a Single Test 1536.2 Sample Size for Detecting a Difference in Accuracies of Two Tests 1616.3 Sample Size for Assessing Non-inferiority or Equivalency of Two Tests 1696.4 Sample Size for Determining a Suitable Cutoff Value 1726.5 Sample Size Determination for Multi-reader Studies 1736.6 Alternative to Sample Size Formulae 1807 Introduction to Meta-analysis for Diagnostic Accuracy Studies 1817.1 Objectives 1827.2 Retrieval of the Literature 1827.3 Inclusion/Exclusion Criteria 1867.4 Extracting Information from the Literature 1887.5 Statistical Analysis 1907.6 Public Presentation 202Part II Advanced Methods 2058 Regression Analysis for Independent ROC Data 2078.1 Four Clinical Studies 2088.2 Regression Models for Continuous-scale Tests 2108.3 Regression Models for Ordinal-scale Tests 2288.4 Covariate AROC Curves of Continuous-scale Tests 2339 Analysis of Multiple Reader and/or Multiple Test Studies 2359.1 Studies Comparing Multiple Tests with Covariates 2359.2 Studies with Multiple Readers and Multiple Tests 24510 Methods for Correcting Verification Bias 25710.1 Examples 25810.2 Impact of Verification Bias 26010.3 A Single Binary-scale Test 26110.4 Correlated Binary-scale Tests 26710.5 A Single Ordinal-scale Test 27610.6 Correlated Ordinal-scale Tests 28610.7 Continuous-scale Tests 29611 Methods for Correcting Imperfect Gold Standard Bias 31311.1 Examples 31411.2 Impact of Imperfect Gold Standard Bias 31511.3 One Single Binary Test in a Single Population 31711.4 One Single Binary Test in G Populations 32411.5 Multiple Binary Tests in One Single Population 32911.6 Multiple Binary Tests in G Populations 34111.7 Multiple Ordinal-scale Tests in One Single Population 34311.8 Multiple-scale Tests in One Single Population 34712 Location-specific ROC Methods for Diagnostic Imaging 35312.1 Examples 35312.2 LROC Approach 35512.3 FROC Approach 36012.4 ROI Approach 37712.5 Comparison Between Location-specific ROC Methods 38313 Technical Performance ("Accuracy") of Quantitative Imaging Biomarkers 38513.1 Quantitative Imaging Biomarkers 38513.2 Technical Performance Characteristics of a QIB 38713.3 Precision 38913.4 Bias and Linearity 39813.5 Other Metrics of QIB Performance 40513.6 Clinical Performance 40714 Medical Test Efficacy and Effectiveness 41314.1 General Notation 41414.2 Prognostic Effects 41614.3 Predictive Effects 41614.4 Test Strategies for Assigning Treatments 41714.5 Explanatory Versus Pragmatic Trials of Tests 41714.6 Explanatory Trial Designs 41814.7 Pragmatic Trial Designs 42014.8 Adaptive Treatment Strategy Trial Designs 42314.9 Treatment Selection Tests 42414.10 Follow-on Treatment Selection Tests 42514.11 Bibliographic Notes 42815 Statistical Analysis for Meta-analysis 43315.1 Binary-scale Data 43315.2 Ordinal- or Continuous-scale Data 43515.3 ROC Curve Area 44115.4 Publication Bias 44316 Risk Prediction 44916.1 Risk Calculators 45116.2 Calibration 45416.3 Discrimination 46416.4 Appendix 16-A: Survival Analysis 46916.5 Appendix 16-B: Survival Analysis for Competing Risks 47516.6 Appendix 16-C: Stochastic Processes for Survival Analysis 48016.7 Appendix 16-D: Bibliographic Notes 481Appendix-A: Case Studies and Chapter 8 Data 485Appendix-B: Jackknife and Bootstrap Methods of Estimating Variances and Confidence Intervals 513Bibliography 517Index 555