Methods and Applications of Statistics in Clinical Trials, Volume 2 E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Methods and Applications of Statistics
- Sprache: Englisch
Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods includes updates of established literature from the Wiley Encyclopedia of Clinical Trials as well as original material based on the latest developments in clinical trials. Prepared by a leading expert, the second volume includes numerous contributions from current prominent experts in the field of medical research. In addition, the volume features: * Multiple new articles exploring emerging topics, such as evaluation methods with threshold, empirical likelihood methods, nonparametric ROC analysis, over- and under-dispersed models, and multi-armed bandit problems * Up-to-date research on the Cox proportional hazard model, frailty models, trial reports, intrarater reliability, conditional power, and the kappa index * Key qualitative issues including cost-effectiveness analysis, publication bias, and regulatory issues, which are crucial to the planning and data management of clinical trials
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Seitenzahl: 2045
Veröffentlichungsjahr: 2014
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Contents
Cover
Half Title page
Title page
Copyright page
Contributors
Preface
Chapter 1: Analysis of Over- and Underdispersed Data
1.1 Introduction
1.2 Overdispersed Binomial and Count Models
1.3 Other Approaches to Account for Overdispersion
1.4 Underdispersion
1.5 Software Notes
References
Chapter 2: Analysis of Variance (ANOVA)
2.1 Introduction
2.2 Factors, Levels, Effects, and Cells
2.3 Cell Means Model
2.4 One-Way Classification
2.5 Parameter Estimation
2.6 The R(.) Notation—Partitioning Sum of Squares
2.7 ANOVA—Hypothesis of Equal Means
2.8 Multiple Comparisons
2.9 Two-Way Crossed Classification
2.10 Balanced and Unbalanced Data
2.11 Interaction Between Rows and Columns
2.12 Analysis of Variance Table
References
Chapter 3: Assessment of Health-Related Quality of Life
3.1 Introduction
3.2 Choice of HRQOL Instruments
3.3 Establishment of Clear Objectives in HRQOL Assessments
3.4 Methods for HRQOL Assessment
3.5 HRQOL as the Primary End Point
3.6 Interpretation of HRQOL Results
3.7 Examples
3.8 Conclusion
References
Further Reading
Chapter 4: Bandit Processes and Response-Adaptive Clinical Trials: The Art of Exploration Versus Exploitation
4.1 Introduction
4.2 Exploration Versus Exploitation with Complete Observations
4.3 Exploration Versus Exploitation with Censored Observations
4.4 Conclusion
References
Chapter 5: Bayesian Dose-Finding Designs in Healthy Volunteers
5.1 Introduction
5.2 A Bayesian Decision-Theoretic Design
5.3 An Example of Dose Escalation in Healthy Volunteer Studies
5.4 Discussion
References
Chapter 6: Bootstrap
6.1 Introduction
6.2 Plug-In Principle
6.3 Monte Carlo Sampling— The “Second Bootstrap Principle”
6.4 Bias and Standard Error
6.5 Examples
6.6 Model Stability
6.7 Accuracy of Bootstrap Distributions
6.8 Bootstrap Confidence Intervals
6.9 Hypothesis Testing
6.10 Planning Clinical Trials
6.11 How Many Bootstrap Samples Are Needed
6.12 Additional References
References
Chapter 7: Conditional Power in Clinical Trial Monitoring
7.1 Introduction
7.2 Conditional Power
7.3 Weight-Averaged Conditional Power or Bayesian Predictive Power
7.4 Conditional Power of a Different Kind: Discordance Probability
7.5 Analysis of a Randomized Trial
7.6 Conditional Power: Pros and Cons
References
Chapter 8: Cost-Effectiveness Analysis
8.1 Introduction
8.2 Definitions and Design Issues
8.3 Cost and Effectiveness Data
8.4 The Analysis of Costs and Outcomes
8.5 Robustness and Generalizability in Cost-Effectiveness Analysis
References
Further Reading
Chapter 9: Cox-Type Proportional Hazards Models
9.1 Introduction
9.2 Cox Model for Univariate Failure Time Data Analysis
9.3 Marginal Models for Multivariate Failure Time Data Analysis
9.4 Practical Issues in Using the Cox Model
9.5 Examples
9.6 Extensions
9.7 Softwares and Codes
References
Further Reading
Chapter 10: Empirical Likelihood Methods in Clinical Experiments
10.1 Introduction
10.2 Classical EL: Several Ingredients for Theoretical Evaluations
10.3 The Relationship Between Empirical Likelihood and Bootstrap Methodologies
10.4 Bayes Methods Based on Empirical Likelihoods
10.5 Mixtures of Likelihoods
10.6 An Example: ROC Curve Analyses Based on Empirical Likelihoods
10.7 Applications of Empirical Likelihood Methodology in Clinical Trials or Other Data Analyses
10.8 Concluding Remarks
Appendix
References
Chapter 11: Frailty Models
11.1 Introduction
11.2 Univariate Frailty Models
11.3 Multivariate Frailty Models
11.4 Software
References
Chapter 12: Futility Analysis
12.1 Introduction
12.2 Common Statistical Approaches to Futility Monitoring
12.3 Examples
12.4 Discussion
References
Further Reading
Chapter 13: Imaging Science in Medicine I: Overview
13.1 Introduction
13.2 Advances in Medical Imaging
13.3 Evolutionary Developments in Imaging
13.4 Conclusion
References
Chapter 14: Imaging Science in Medicine, II: Basics of X-Ray Imaging
14.1 Introduction to Medical Imaging: Different Ways of Creating Visible Contrast Among Tissues
14.2 What the Body Does to the X-Ray Beam: Subject Contrast From Differential Attenuation of the X-Ray Beam by Various Tissues
14.3 What the X-Ray Beam Does to the Body: Known Medical Benefits Versus Possible Radiogenic Risks
14.4 Capturing the Visual Image: Analog (20th Century) X-Ray Image Receptors
Chapter 15: Imaging Science in Medicine, III: Digital (21st Century) X-Ray Imaging
15.1 The Computer in Medical Imaging
15.2 The Digital Planar X-Ray Modalities: Computed Radiography and Digital Radiography and Fluoroscopy
15.3 Digital Fluoroscopy and Digital Subtraction Angiography
15.4 Digital Tomosynthesis: Planar Imaging in Three Dimensions
15.5 Computed Tomography: Superior Contrast in Three-Dimensional X-Ray Attenuation Maps
Chapter 16: Intention-to-Treat Analysis
16.1 Introduction
16.2 Missing Information
16.3 The Intention-to-Treat Design
16.4 Efficiency of the Intent-to-Treat Analysis
16.5 Compliance-Adjusted Analyses
16.6 Conclusion
References
Further Reading
Chapter 17: Interim Analyses
17.1 Introduction
17.2 Opportunities and Dangers of Interim Analyses
17.3 The Development of Techniques for Conducting Interim Analyses
17.4 Methodology for Interim Analyses
17.5 An Example: Statistics for Lamivudine
17.6 Interim Analyses in Practice
17.7 Conclusions
References
Chapter 18: Interrater Reliability
18.1 Definition
18.2 The Importance of Reliability in Clinical Trials
18.3 How Large a Reliability Coefficient Is Large Enough?
18.4 Design and Analysis of Reliability Studies
18.5 Estimate of the Reliability Coefficient—Parametric
18.6 Estimation of the Reliability Coefficient— Nonparametric
18.7 Estimation of the Reliability Coefficient—Binary
18.8 Estimation of the Reliability Coefficient—Categorical
18.9 Strategies to Increase Reliability (Spearman–Brown Projection)
18.10 Other Types of Reliabilities
References
Chapter 19: Intrarater Reliability
19.1 Introduction
19.2 Intrarater Reliability for Continuous Scores
19.3 Nominal Scale Score Data
19.4 Ordinal and Interval Score Data
19.5 Concluding Remarks
References
Further Reading
Chapter 20: Kaplan—Meier Plot
20.1 Introduction
20.2 Estimation of Survival Function
20.3 Additional Topics
References
Chapter 21: Logistic Regression
21.1 Introduction
21.2 Fitting the Logistic Regression Model
21.3 The Multiple Logistic Regression Model
21.4 Fitting the Multiple Logistic Regression Model
21.5 Example
21.6 Testing for the Significance of the Model
21.7 Interpretation of the Coefficients of the Logistic Regression Model
21.8 Dichotomous Independent Variable
21.9 Polytomous Independent Variable
21.10 Continuous Independent Variable
21.11 Multivariate Case
References
Chapter 22: Metadata
22.1 Introduction
22.2 History/Background
22.3 Data Set Metadata
22.4 Analysis Results Metadata
22.5 Regulatory Submission Metadata
References
Chapter 23: Microarray
23.1 Introduction
23.2 What is a Microarray?
23.3 Other Array Technologies
23.4 Define Objectives of the Study
23.5 Experimental Design for Microarray
23.6 Data Extraction
23.7 Microarray Informatics
23.8 Statistical Analysis
23.9 Annotation
23.10 Pathway, GO, and Class-Level Analysis Tools
23.11 Validation of Microarray Experiments
23.12 Conclusions
References
Chapter 24: Multi-Armed Bandits, Gittins Index, and Its Calculation
24.1 Introduction
24.2 Mathematical Formulation of Multi-Armed Bandits
24.3 Off-Line Algorithms for Computing Gittins Index
24.4 On-Line Algorithms for Computing Gittins Index
24.5 Computing Gittins Index for the Bernoulli Sampling Process
24.6 Conclusion
References
Chapter 25: Multiple Comparisons
25.1 Introduction
25.2 Strong and Weak Control of the FWE
25.3 Criteria for Deciding Whether Adjustment is Necessary
25.4 Implicit Multiplicity: Two-Tailed Testing
25.5 Specific Multiple Comparison Procedures
References
Chapter 26: Multiple Evaluators
26.1 Introduction
26.2 Agreement for Continuous Data
26.3 Agreement for Categorical Data
26.4 Summary and Discussion
References
Chapter 27: Noncompartmental Analysis
27.1 Introduction
27.2 Terminology
27.3 Objectives and Features of Noncompartmental Analysis
27.4 Comparison of Noncompartmental and Compartmental Models
27.5 Assumptions of NCA and Its Reported Descriptive Statistics
27.6 Calculation Formulas for NCA
27.7 Guidelines for Performance of NCA Based on Numerical Integration
27.8 Conclusions and Perspectives
References
Further Reading
Chapter 28: Nonparametric ROC Analysis for Diagnostic Trials
28.1 Introduction
28.2 Different Aspects of Study Design
28.3 Nonparametric Models and Hypotheses
28.4 Point Estimator
28.5 Asymptotic Distribution and Variance Estimator
28.6 Derivation of the Confidence Interval
28.7 Statistical Tests
28.8 Adaptations for Cluster Data
28.9 Results of a Diagnostic Study
28.10 Summary and Final Remarks
References
Chapter 29: Optimal Biological Dose for Molecularly Targeted Therapies
29.1 Introduction
29.2 Phase I Dose-Finding Designs for Cytotoxic Agents
29.3 Phase I Dose-Finding Designs for Molecularly Targeted Agents
29.4 Discussion
References
Further Reading
Chapter 30: Over- and Underdispersion Models
30.1 Introduction
30.2 Count Dispersion Models
30.3 Count Explanatory Models
30.4 Summary and Final Remarks
References
Chapter 31: Permutation Tests in Clinical Trials
31.1 Randomization Inference—Introduction
31.2 Permutation Tests—How They Work
31.3 Normal Approximation to Permutation Tests
31.4 Analyze as You Randomize
31.5 Interpretation of Permutation Analysis Results
31.6 Summary
References
Chapter 32: Pharmacoepidemiology, Overview
32.1 Introduction
32.2 The Case-Crossover Design
32.3 Confounding Bias
32.4 Risk Functions Over Time
32.5 Probabilistic Approach for Causality Assessment
32.6 Methods Based on Prescription Data
References
Chapter 33: Population Pharmacokinetic and Pharmacodynamic Methods
33.1 Introduction
33.2 Terminology
33.3 Fixed Effects Models
33.4 Random Effects Models
33.5 Model Building and Parameter Estimation
33.6 Software
33.7 Model Evaluation
33.8 Stochastic Simulation
33.9 Experimental Design
33.10 Applications
References
Further Reading
Chapter 34: Proportions: Inferences and Comparisons
34.1 Introduction
34.2 One-Sample Case
34.3 Two Independent Samples
34.4 Note on Software
References
Chapter 35: Publication Bias
35.1 Publication Bias and the Validity of Research Reviews
35.2 Research on Publication Bias
35.3 Data Suppression Mechanisms Related to Publication Bias
35.4 Prevention of Publication Bias
35.5 Assessment of Publication Bias
35.6 Impact of Publication Bias
References
Further Reading
Chapter 36: Quality of Life
36.1 Background
36.2 Measuring Health-Related Quality of Life
36.3 Development and Validation of HRQoL Measures
36.4 Use in Research Studies
36.5 Interpretation/Clinical Significance
36.6 Conclusions
References
Chapter 37: Relative Risk Modeling
37.1 Introduction
37.2 Why Model Relative Risks?
37.3 Data Structures and Likelihoods
37.4 Approaches to Model Specification
37.5 Mechanistic Models
References
Chapter 38: Sample Size Considerations for Morbidity/Mortality Trials
38.1 Introduction
38.2 General Framework for Sample Size Calculation
38.3 Choice of Test Statistics
38.4 Adjustment of Treatment Effect
38.5 Informative Noncompliance
References
Chapter 39: Sample Size for Comparing Means
39.1 Introduction
39.2 One-Sample Design
39.3 Two-Sample Parallel Design
39.4 Two-Sample Crossover Design
39.5 Multiple-Sample One-Way ANOVA
39.6 Multiple-Sample Williams Design
39.7 Discussion
References
Chapter 40: Sample Size for Comparing Proportions
40.1 Introduction
40.2 One-Sample Design
40.3 Two-Sample Parallel Design
40.4 Two-Sample Crossover Design
40.5 Relative Risk—Parallel Design
40.6 Relative Risk—Crossover Design
40.7 Discussion
References
Chapter 41: Sample Size for Comparing Time-to-Event Data
41.1 Introduction
41.2 Exponential Model
41.3 Cox’s Proportional Hazards Model
41.4 Log-Rank Test
41.5 Discussion
References
Chapter 42: Sample Size for Comparing Variabilities
42.1 Introduction
42.2 Comparing Intrasubject Variabilities
42.3 Comparing Intersubject Variabilities
42.4 Comparing Total Variabilities
42.5 Discussion
References
Chapter 43: Screening, Models of
43.1 Introduction
43.2 What is Screening?
43.3 Why Use Modeling?
43.4 Characteristics of Screening Models
43.5 A Simple Disease and Screening Model
43.6 Analytic Models for Cancer
43.7 Simulation Models for Cancer
43.8 Model Fitting and Validation
43.9 Models for Other Diseases
43.10 Current State and Future Directions
References
Chapter 44: Screening Trials
44.1 Introduction
44.2 Design Issues
44.3 Sample Size
44.5 Analysis
44.6 Trial Monitoring
References
Chapter 45: Secondary Efficacy End Points
45.1 Introduction
45.2 Literature Review
45.3 Review of Methodology for Multiplicity Adjustment and Gatekeeping Strategies for Secondary End Points
45.4 Summary
References
Further Reading
Chapter 46: Sensitivity, Specificity, and Receiver Operator Characteristic (ROC) Methods
46.1 Evaluating a Single Binary Test Against a Binary Criterion
46.2 Evaluation of a Single Binary Test: ROC Methods
46.3 Evaluation of a Test Response Measured on an Ordinal Scale: ROC Methods
46.4 Evaluation of Multiple Different Tests
46.5 The Optimal Sequence of Tests
46.6 Sampling and Measurement Issues
46.7 Summary
References
Chapter 47: Software for Genetics/Genomics
47.1 Introduction
47.2 Data Management
47.3 Genetic Analysis
47.4 Genomic Analysis
47.5 Other
References
Further Reading
Chapter 48: Stability Study Designs
48.1 Introduction
48.2 Stability Study Designs
48.3 Criteria for Design Comparison
48.4 Stability Protocol
48.5 Basic Design Considerations
48.6 Conclusions
References
Chapter 49: Subgroup Analysis
49.1 Introduction
49.2 The Dilemma of Subgroup Analysis
49.3 Planned Versus Unplanned Subgroup Analysis
49.4 Frequentist Methods
49.5 Testing Treatment by Subgroup Interactions
49.6 Subgroup Analyses in Positive Clinical Trials
49.7 Confidence Intervals for Treatment Effects within Subgroups
49.8 Bayesian Methods
References
Chapter 50: Survival Analysis, Overview
50.1 Introduction
50.2 History
50.3 Survival Analysis Concepts
50.4 Nonparametric Estimation and Testing
50.5 Parametric Inference
50.6 Comparison with Expected Survival
50.7 The Cox Regression Model
50.8 Other Regression Models for Survival Data
50.9 Multistate Models
50.10 Other Kinds of Incomplete Observation
50.11 Multivariate Survival Analysis
50.12 Concluding Remarks
References
Chapter 51: The FDA and Regulatory Issues
51.1 Caveat
51.2 Introduction
51.3 Chronology of Drug Regulation in the United States
51.4 FDA Basic Structure
51.5 IND Application Process
51.6 Drug Development and Approval Time Frame
51.7 NDA Process
51.8 U.S. Pharmacopeia and FDA
51.9 CDER Freedom of Information Electronic Reading Room
51.10 Conclusion
Chapter 52: The Kappa Index
52.1 Introduction
52.2 The Kappa Index
52.3 Inference for Kappa via Generalized Estimating Equations
52.4 The Dependence of Kappa on Marginal Rates
52.5 General Remarks
References
Chapter 53: Treatment Interruption
53.1 Introduction
53.2 Therapeutic TI Studies in HIV/AIDS
53.3 Management of Chronic Disease
53.4 Analytic Treatment Interruption in Therapeutic Vaccine Trials
53.5 Randomized Discontinuation Designs
53.6 Final Comments
References
Chapter 54: Trial Reports: Improving Reporting, Minimizing Bias, and Producing Better Evidence-Based Practice
54.1 Introduction
54.2 Reporting Issues in Clinical Trials
54.3 Moral Obligation to Improve the Reporting of Trials
54.4 Consequences of Poor Reporting of Trials
54.5 Distinguishing Between Methodological and Reporting Issues
54.6 One Solution to Poor Reporting: CONSORT 2010 and CONSORT Extensions
54.7 Impact of CONSORT
54.8 Guidance for Reporting Randomized Trial Protocols: SPIRIT
54.9 Trial Registration
54.10 Final Thoughts
References
Chapter 55: U.S. Department of Veterans Affairs Cooperative Studies Program
55.1 Introduction
55.2 History of the Cooperative Studies Program (CSP)
55.3 Organization and Functioning of the CSP
55.4 Roles of the Biostatistician and Pharmacist in the CSP
55.5 Ongoing and Completed Cooperative Studies (1972–2000)
55.6 Current Challenges and Opportunities
55.7 Concluding Remarks
References
Chapter 56: Women’s Health Initiative: Statistical Aspects and Selected Early Results
56.1 Introduction
56.2 WHI Clinical Trial and Observational Study
56.3 Study Organization
56.4 Principal Clinical Trial Comparisons, Power Calculations, and Safety and Data Monitoring
56.5 Biomarkers and Intermediate Outcomes
56.6 Data Management and Computing Infrastructure
56.7 Quality Assurance Program Overview
56.8 Early Results from the WHI Clinical Trial
56.9 Summary and Discussion
References
Chapter 57: World Health Organization (WHO): Global Health Situation
57.1 Introduction
57.2 Program Activities to the End of the Twentieth Century
57.3 Vision for the Use and Generation of Data in the First Quarter of the Twenty-First Century
Reference
Further Reading
Index
Methods and Applications of Statistics in Clinical Trials
WILEY SERIES IN METHODS AND APPLICATIONS OF STATISTICS
Advisory Editor
N. Balakrishnan
McMaster University, Canada
The Wiley Series in Methods and Applications of Statistics is a unique grouping of research that features classic contributions from Wiley’s Encyclopedia of Statistical Sciences, Second Edition (ESS, 2e) alongside newly written articles that explore various problems of interest and their intrinsic connection to statistics. The goal of this collection is to encompass an encyclopedic scope of coverage within individual books that unify the most important and interesting applications of statistics within a specific field of study. Each book in the series successfully upholds the goals of ESS, 2e by combining established literature and newly-developed contributions written by leading academics, researchers, and practitioners in a comprehensive and accessible format. The result is a succinct reference that unveils modern, cutting-edge approaches to acquiring, analyzing, and presenting data across diverse subject areas.
WILEY SERIES IN METHODS AND APPLICATIONS OF STATISTICS
Balakrishnan • Methods and Applications of Statistics in the Life and Health Sciences
Balakrishnan • Methods and Applications of Statistics in Business, Finance, and Management Science
Balakrishnan • Methods and Applications of Statistics in Engineering, Quality Control, and the Physical Sciences
Balakrishnan • Methods and Applications of Statistics in the Social and Behavioral Sciences
Balakrishnan • Methods and Applications of Statistics in the Atmospheric and Earth Sciences
Balakrishnan • Methods and Applications of Statistics in Clinical Trials, Volume 1: Concepts, Principles, Trials, and Designs
Balakrishnan • Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods
Copyright © 2014 by John Wiley & Sons, Inc. All rights reserved.
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Library of Congress Cataloging-in-Publication Data:
Methods and applications of statistics in clinical trials vol 2/ [edited by] N. Balakrishnan. p.; cm. — (Methods and applications of statistics) Includes bibliographical references and index. ISBN 978-1-118-30476-1 (cloth) I. Balakrishnan, N., 1956– editor of compilation. II. Series: Wiley series in methods and applications of statistics. [DNLM: 1. Clinical Trials as Topic. 2. Statistics as Topic. QV 771.4] R853.C55 610.72’4—dc23
2013034342
Contributors
Per Kragh Andersen, University of Copenhagen, Copenhagen, Denmark, [email protected]
Garnet L. Anderson, Fred Hutchinson Cancer Research Center, Seattle, WA, [email protected]
Chul Ahn, University of Texas Southwestern Medical Center, Dallas, TX, [email protected]
Edgar Brunner, Professor Emeritus of Biostatistics, University Medical Center, Göttingen, Germany, [email protected]
Jürgen B. Bulitta, State University of New York at Buffalo, Buffalo, NY, [email protected]
Jianwen Cai, University of North Carolina, Chapel Hill, NC, [email protected]
Patrizio Capasso, University of Kentucky, Lexington, KY, [email protected]
Robert C. Capen, Merck Research Laboratories West Point, PA
Jhelum Chakravorty, McGill University, Montreal, QC, Canada, [email protected]
Chi Wan Chen, Pfizer Inc., New York, NY
David H. Christiansen, Christiansen Consulting, Boise, ID
Shein-Chung Chow, Duke University Durham, NC, [email protected]
Joseph F. Collins
Jason T. Connor, Berry Consultants, Orlando, FL, [email protected]
Richard J. Cook, University of Waterloo, Waterloo, ON, Canada, [email protected]
Xiangqin Cui, University of Alabama at Birmingham, Birmingham, AL. [email protected]
C. B. Dean, Western University, Western Science Centre, London, ON, Canada, [email protected]
Yu Deng, University of North Carolina, Chapel Hill, NC, [email protected]
Diane L. Fairclough, University of Colorado Health Sciences, Center Denver, CO, [email protected]
John R. Feussner, Medical University of South Carolina, Charleston, SC
Boris Freidlin, National Cancer Institute, Bethesda, MD, [email protected]
Patricia A. Granz, UCLA Jonsson Comprehensive Cancer Center, Los Angeles, CA, [email protected]
Courtney Gray-McGuire, Case Western Reserve University, Cleveland, OH, [email protected]
Birgit Grund, University of Minnesota, Minneapolis, MN, [email protected]
Kilem L. Gwet, Advanced Analytics, LLC, Gaithersburg, MD, [email protected]
H. R. Hapsara, World Health Organization, Geneva, Switzerland, [email protected]
William R. Hendee, Medical College of Wisconsin, Milwaukee, WI, [email protected]
William G. Henderson
Tim Hesterberg, Insightful Corporation, Seattle, WA
Nicholas H. G. Holford, University of Auckland, Auckland, New Zealand, [email protected]
Norbert Holländer, University Hospital of Freiburg, Freiburg, Germany, [email protected]
David W. Hosmer, University of Massachusetts, Amherst, MA, [email protected]
Alan D. Hutson, University at Buffalo, Buffalo, NY, [email protected]
Peter B. Imrey, Cleveland Clinic, Cleveland, OH, [email protected]
Elizabeth Juarez-Colunga, University of Colorado Denver, Aurora, CO, [email protected]
Seung-Ho Kang, Ewha Woman’s University, Seoul, South Korea
Jörg Kaufmann, AG Schering SBU Diagnostics & Radiopharmaceuticals, Berlin, Germany
Niels Keiding, University of Copenhagen, Copenhagen, Denmark, [email protected]
Célestin C. Kokonendji, University of Franche-Comté, Besançon, France, [email protected]
Helena Chmura Kraemer, Stanford University, Palo Alto, CA, [email protected]
John M. Lachin, George Washington University, Washington, DC, [email protected]
Philip W. Lavori, Stanford University School of Medicine, Standford, CA, [email protected]
Morven Leese, Institute of Psychiatry—Health Services and Population Research Department, London, UK
Stanley Lemeshow, Ohio State University, Columbus, OH, [email protected]
Jason J. Z. Liao, Merck Research Laboratories West Point, PA, [email protected]
Tsae-Yun Daphne Lin, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Rockville, MD, [email protected]
Qing Lu, Michigan State University, East Lansing, MI, [email protected]
Aditya Mahajan, McGill University, Montreal, QC, Canada, [email protected]
Michael A. McIsaac, University of Waterloo, Waterloo, ON, Canada, [email protected]
David Moher, Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada and Department of Epidemiology and Community Medicine, University of Ottawa, Ottawa, ON, Canada, [email protected]
Grier P. Page, RTI International, Research Triangle Park, NC, [email protected]
Peter Peduzzi, Yale School of Public Health, New Haven, CT, [email protected]
Ross L. Prentice, Fred Hutchinson Cancer Research Center, Seattle, WA, [email protected]
Philip C. Prorok, National Institutes of Health, Bethesda, MD, [email protected]
Michael A. Proschan, National Institute of Allergy and Infectious Diseases, Bethesda, MD, [email protected]
Frank Rockhold, GlaxoSmithKline R&D, King of Prussia, PA, [email protected]
Hannah R. Rothstein, City University of New York, NY, [email protected]
W. Janusz Rzeszotarski, U.S. Food and Drug Administration, Rockville, MD
Mike R. Sather, Department of Veterans Affairs, Albuquerque, NM, [email protected]
Tony Segreti, Research Triangle Institute, Research Triangle, NC
Larissa Shamseer, Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada and Department of Epidemiology and Community Medicine, University of Ottawa, Ottawa, ON, Canada, [email protected]
Joanna H. Shih, National Cancer Institute, Bethesda, MD
Richard M. Simon, National Cancer Institute, Bethesda, MD, [email protected]
Yeunjoo Song, Case Western Reserve University, Cleveland, OH
Chris Stevenson, Monash University, Victoria, Australia, [email protected]
Samy Suissa, McGill University, Montreal, QC, Canada, [email protected]
Ming T. Tan, Georgetown University, Washington, DC, [email protected]
Duncan C. Thomas University of Southern California, Los Angeles, CA, [email protected]
Susan Todd, University of Reading Reading, Berkshire, UK, [email protected]
Lucy Turner, Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada, [email protected]
Albert Vexler, University at Buffalo, Buffalo, NY, [email protected]
Hansheng Wang, Peking University Beijing, P. R. China, [email protected]
Xikui Wang, University of Manitoba, Winnipeg, MN, Canada, [email protected]
C. S. Wayne Weng, Chung Yuan Christian University, Chungli, Taiwan
Andreas Wienke, University Halle-Wittenberg, Halle, Germany, [email protected]
Anthony B. Wolbarst, University of Kentucky, Lexington, KY, [email protected]
Andrew R. Wyant, University of Kentucky, Lexington, KY, [email protected]
Yang Xie, University of Texas Southwestern Medical Center, Dallas, TX
Jihnhee Yu, University at Buffalo, Buffalo, NY, [email protected]
Antonia Zapf, University Medical Center, Göttingen, Germany, [email protected]
Donglin Zeng, University of North Carolina, Chapel Hill, NC, [email protected]
Yinghui Zhou, The University of Reading, Reading, Berkshire, UK
David M. Zucker, Hebrew University of Jerusalem Jerusalem, Israel, [email protected]
Preface
Planning, developing, and implementing clinical trials, have become an important and integral part of life. More and more efforts and care go into conducting various clinical trials as they have been responsible in making key advances in medicine and treatments to different illnesses. Today, clinical trials have become mandatory in the development and evaluation of modern drugs and in identifying the association of risk factors to diseases. Due to the complexity of various issues surrounding clinical trials, regulatory agencies oversee their approval and also ensure impartial review. The main purpose of this two-volume handbook is to provide a detailed exposition of historical developments and also to highlight modern advances on methods and analysis for clinical trials.
It is important to mention that the four-volume Wiley Encyclopedia of Clinical Trials served as a basis for this handbook. While many pertinent entries from this Encyclopedia have been included here, a number of them have been updated to reflect recent developments on their topics. Some new articles detailing modern advances in statistical methods in clinical trials and their applications have also been included.
A volume of this size and nature cannot be successfully completed without the cooperation and support of the contributing authors, and my sincere thanks and gratitude go to all of them. Thanks are also due to Mr. Steve Quigley and Ms. Sari Friedman (of John Wiley & Sons, Inc.) for their keen interest in this project from day one, as well as for their support and constant encouragement (and, of course, occasional nudges, too) throughout the course of this project. Careful and diligent work of Mrs. Debbie Iscoe in the typesetting of this volume and of Angioline Loredo at the production state, is gratefully acknowledged. Partial financial support of the Natural Sciences and Engineering Research Council of Canada also assisted in the preparation of this handbook, and this support is much appreciated.
This is the seventh in a series of handbooks on methods and applications of statistics. While the first handbook has focused on life and health sciences, the second handbook has focused on business, finance, and management sciences, the third has focused on engineering, quality control, and physical sciences, the fourth has focused on behavioral and social sciences, the fifth has focused on atmospheric and earth sciences, and the sixth handbook has concentrated on methods and applications of statistics to clinical trials. This is the second of two volumes describing in detail statistical developments concerning clinical trials, focusing specifically on planning, analysis, and inferential methods.
It is my sincere hope that this handbook and the others in the series will become basic reference resources for those involved in these fields of research!
PROF. N. BALAKRISHNAN McMASTER UNIVERSITY
Hamilton, Canada February 2014
Chapter 1
Analysis of Over- and Underdispersed Data
Elizabeth Juarez-Colunga and C. B. Dean
1.1 Introduction
In the analysis of discrete data, for example, count data analyzed under a Poisson model, or binary data analyzed under a binomial model quite often the empirical variance exceeds the theoretical variance under the presumed model. This phenomenon is called overdispersion. If overdispersion is ignored, standard errors of parameter estimates will be underestimated, and therefore p-values for tests and hypotheses will be too small, leading to incorrectly declaring a predictor as significant when in fact it may not be.
The Poisson and binomial distributions are simple models but have strict assumptions. In particular, they assume a special mean-variance relationship since each of these distributions is determined by a single parameter. On the other hand, the normal distribution is determined by two parameters, the mean μ and variance σ2, which characterize the location and the spread of the data around the mean. In both the Poisson and binomial distributions, the variance is fixed once the mean or the probability of success has been defined.
Hilbe [25] provides a very comprehensive discussion of what he calls apparent overdispersion, which refers to scenarios in which the data exhibit variation beyond what can be explained by the model and this lack of fit is due to several “fixable” reasons. These reasons may be omitting important predictors in the model, the presence of outliers, omitting important interactions as predictors, the need of a transformation for a predictor, and misspecifying the link function for relating the mean response to the predictors. Hilbe [25] also discusses how to recognize overdispersion, and how to adjust for it when it is present beyond apparent cases, and provides an excellent overall review of the topic.
It is important to note that if apparent overdispersion has been ruled out, in log-linear or logistic analyses, the point estimates of the covariate effects will be quite similar regardless of whether overdispersion is accounted for or not. Hence, treatment and other effects will not be aberrant or give a hint of the presence of overdispersion. As well, this suggests that adjusting for overdispersion can be handled through adjustments of variance estimates [35].
Evidence of apparent or real overdispersion exists when the Pearson or deviance residuals are too large [6]; the corresponding Pearson and deviance goodness-of-fit statistics indicate a poor fit. Several tests have been developed for overdispersion in the context of Poisson or binomial analyses [11, 12, 54], as well as in the context of zero-heavy data [30, 51, 53, 52],
1.2 Overdispersed Binomial and Count Models
1.2.1 Overdispersed Binomial Model
In the binomial context, overdispersion typically arises because the independence assumption is violated. This is commonly caused by clustering of responses; for instance, clinics or hospitals may induce a clustering effect due to differences in patient care strategies across institutions.
(1)
1.2.2 Overdispersed Poisson Model
A simple way to incorporate overdispersion is through the use of an individual-specific random effect vi. Given vi, and the covariate vector xi corresponding to the ith individual, the counting process Ni(t) may be modeled as a Poisson process with intensity function
(2)
(3)
where
(4)
and
(5)
(6)
is the likelihood for a mixed Poisson model based on the total counts observed for individual i. The likelihood L(θ) becomes the negative binomial if vi is gamma distributed (i.e., G(vi;.) is a gamma distribution). If there is a single panel, Lp(θ) [see Equation (3)] will reduce to the simple mixed Poisson kernel, L(θ), where the response is the total count of events in the entire follow-up time.
Overdispersed recurrent event counts are often encountered in trials where the main interest is to test whether certain treatments are effective in reducing the recurrences of events, as illustrated in the example Section 1.2.3. In this case, the βs are parametrized such that the treatment effects are measured relative to treatment 1, so that β1 reflects the overall mean and α describes the shape of the intensity function ρ(t, α); common forms of ρ(t, α) are exponential (exp(αt)) and Weibull (αtα−1).
1.2.3 Example
Consider a clinical trial, conducted by the Veterans Administration Co-operative Urological Research Group, that studied the effects of placebo pills, pyridoxine pills, and periodic instillation of thiotepa into the bladder on the frequency of recurrence of bladder cancer [8]. The data appear in Andrews and Herzberg [2]. All 116 patients had bladder cancer when they entered the study; the tumors were removed, and the patients were randomly assigned to one of the three treatments. Here we consider estimation of the treatment effect under both a design with continuous follow-up, as in the study, and an artificial design, for illustrative purposes, with 2 equally spaced scheduled follow-up visits over 64 months; for the panel design, we record information on event recurrences at the scheduled follow-up times and at termination times.
Table 1: Parameter estimates (Est) and their standard errors (SE), resulting from the Poisson and negative binomial (NB) likelihood fit to the bladder cancer data. The regression parameters β1, β2, β3 correspond to the three treatment groups, parametrized with respect to the placebo, and α parametrizes the baseline intensity function.
1.3 Other Approaches to Account for Overdispersion
1.3.1 Generalized Linear Mixed Model
A general class of models that encompasses the incorporation of several random effects, not necessarily independent, is generalized linear mixed models. This may include an individual-specific random effect, as discussed above and also more complex structures that can accommodate dependencies in outcome variables as well as in random effects. A generalized linear mixed model specifies that
(7)
where μ and xi are the mean of the response and the vector of covariates, corresponding to the ith individual, respectively; zi is a vector of covariates determining the random effects structure, and the vector of random effects γ is distributed with a mean of zero and finite variance matrix; g is the link function. Conditional on γ, the responses are assumed to have a distribution in the exponential family, for example, Poisson or binomial.
Maximum likelihood estimation involves q-dimensional integration, where q is the dimension of γ; often random effects are assumed to be Gaussian. Tuerlinckx et al. [47] provide a review of methods used for estimation of generalized linear mixed models, discussing methods used to approximate the integral when integrating over the random effects distribution and methods that approximate the integrand of the marginal likelihood. Within the first set of methods, quadrature, Monte Carlo-based numerical methods, and expectation-maximization algorithms are reviewed; within the second, which approximate the integrand, Laplace’s and quasi-likelihood methods are considered.
With overdispersion present, the use of the Poisson or binomial maximum likelihood equations for estimating the regression parameters in the mean is still valid. The usual likelihood equations obtained assuming a generalized linear model are unbiased, estimating equations regardless of any misspecification of the variance structure. Hence, an alternate approach to the use of generalized linear mixed models is to use the corresponding generalized linear model and adjust variance estimates. In this case, often as a final step, the variance is estimated by the sandwich estimator formula, which is an empirical estimator; this approach has become very popular in the last few decades [31, 46].
Nonparametric approaches for handling random effects have also been developed. Lindsay [32] provides a classic comprehensive source on the topic. More recently, Böhning and Seidel [3] provide a review of advances in estimation in mixture models, including nonparametric estimation, the EM algorithm, likelihood ratio tests for testing the number of components in the mixture, special mixtures such as zero-inflated Poisson models, multivariate mixtures, and testing and adjusting for heterogeneity. Groeneboom et al. [20] propose an algorithm, called the support reduction algorithm, to estimate M-estimators in mixture models through iterative unconstrained optimization. Wang [50] proposes three algorithms based on the constrained Newton method [49] to estimate semiparametric mixture models. In these, the mixture distribution G is left unspecified and a finite-dimensional parameter β is common to all mixture components. The three methods are based on (1) alternating estimation of parameters G and β, (2) profiling the likelihood, and (3) modifying the support set; they all use the constrained Newton method and an additional optimization algorithm for unconstrained problems.
There have been some efforts in combining models that account both for overdispersion and clustering effects, the latter perhaps arising from longitudinal measurements. Booth et al. [4] propose a negative binomial model to account for overdispersion, which incorporates random effects, in the linear predictor of the mean, to account for such clustering effects; numerical methods or the EM algorithm is proposed for estimation. Along the same lines, Molenberghs et al. [36] discuss a similar model with gamma and normal random effects to account for overdispersion and clustering effects and Molenberghs et al. [37] generalize the model to a family of generalized linear models for repeated measures with normal and conjugate random effects. Iddi and Molenberghs [27] discuss a marginalized model to account for overdispersion and longitudinal correlation.
Serial correlation may also be accommodated, in addition to overdispersion, through Gaussian time series [23]. Jowaheer and Sutradhar [28] use generalized estimating equations to account for autocorrelation structures as well as overdispersion in longitudinal counts. Parameters are estimated via a two-stage iterative procedure. Henderson and Shimakura [24] and Fiocco et al. [18] discuss a model that, conditional on a frailty, follows a Poisson distribution for counts of events and uses a gamma serially correlated process to model dependency between observations arising from the same individual. In this generalization of the individual frailty model, the random effects are first-order autocor-related. Henderson and Shimakura [24] estimate the parameters of the model using a composite likelihood method based on pairs of time points, while Fiocco et al. [18] discuss an alternative approach using a two-stage procedure. In the two-stage procedure all parameters except the frailty correlation are estimated at the first stage while, in the second stage, the correlation of the frailties is estimated, based on pairs of observations.
1.3.2 Zero-Inflated Models
Sometimes apparent overdispersion is induced by the presence of another mode in the data, often at 0. In these cases, the remedy is to fit a model that handles the extra zeros that cannot be accounted for through the Poisson distribution [7, 40]. However, it may also occur that there is overdispersion beyond zero-inflation, in which case models accounting for both extra zeros and overdispersion have been developed, for example, the zero-inflated negative binomial [19]. There has been great interest in the last decade in accounting as well for correlation structures such as longitudinal, cluster, or spatial components. Ainsworth [1] provides a review of zero-inflated models, pointing out several references, mainly in the field of environmental statistics, that address such challenges in zero-heavy models. Hall [22] considers the challenges of simultaneously modeling within—and between—subject heterogeneity, while Dobbie and Welsh [14] consider serial correlation; both of these are framed in the context of zero-heavy count data models. Along the same lines, Wan and Chan [48] discuss a modeling approach based on a geometric process that accounts for overdispersion in zero-heavy models and, additionally, can handle serial correlation.
1.4 Underdispersion
1.5 Software Notes
Software for incorporating overdispersion includes SAS [42], using, for instance, procedures LOGISTIC, GENMOD, GLIMMIX, and NLMIXED, and R [39] using, for example, packages glm, lmer, and lme4. Parametric mixture models can also be conducted in the MCMC framework using WinBUGS [34], OpenBUGS [33], JAGS [38], or the package mcmc in R.
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Chapter 2
Analysis of Variance (ANOVA)
Jörg Kaufman
2.1 Introduction
The development of analysis of variance (ANOVA) methodology has in turn had an influence on the types of experimental research being carried out in many fields. ANOVA is one of the most commonly used statistical techniques, with applications across the full spectrum of experiments in agriculture, biology, chemistry, toxicology, pharmaceutical research, clinical development, psychology, social science, and engineering. The procedure involves the separation of total observed variation in the data into individual components attributable to various factors as well as those caused by random or chance fluctuation. It allows performing hypothesis tests of significance to determine which factors influence the outcome of the experiment. However, although hypothesis testing is certainly a very useful feature of the ANOVA, it is by no means the only aspect. The methodology was originally developed by Sir Ronald A. Fisher [1], the pioneer and innovator of the use and applications of statistical methods in experimental design, who coined the name “Analysis of Variance—ANOVA.”
For most biological phenomena, inherent variability exists within the response processes of treated subjects as well as among the conditions under which treatment is received, which results in sampling variability, meaning that results for a subject included in a study will differ to some extent from those of other subjects in the affected population. Thus, the sources of variability must be investigated and must be suitably taken into account when data from comparative studies are evaluated correctly. Clinical studies are in particular a fruitful field for the application of this methodology.
The basis for generalizability of a successful clinical trial is strengthened when the coverage of a study is as broad as possible with respect to geographical area, patient demographics, and pretreatment characteristics as well as other factors that are potentially associated with the response variables. At the same time, heterogeneity among patients becomes more extensive and conflicts with the precision of statistical estimates, which is usually enhanced by homogeneity of subjects. The methodology of the ANOVA is a means to structure the data and their validation by accounting for the sources of variability such that homogeneity is regained in subsets of subjects and heterogeneity is attributed to the relevant factors. The ANOVA method is based on the use of sums of squares of the deviation of the observations from respective means (→ Linear Model).
The tradition of arraying sums of squares and resulting F-statistics in an ANOVA table is so firmly entrenched in the analysis of balanced data that extension of the analysis to unbalanced data is necessary. For unbalanced data, many different sums of squares can be defined and then be used in the numerators of F-statistics. providing tests for a wide variety of hypotheses. In order to provide a practically relevant and useful approach, the ANOVA through the cell means model is introduced below.
The concept of the cell means model was introduced by Searle [2,3]. Hocking and Speed [4], and Hocking [5] to resolve some of the confusion associated with ANOVA models with unbalanced data. The simplicity of such a model is readily apparent: No confusion exists on which functions are estimable, what their estimators are, and what hypotheses can be tested. The cell means model is conceptually easier, it is useful for understanding the ANOVA models, and it is, from the sampling point of view, the appropriate model to use.
In many applications, the statistical analysis is characterized by the fact that a number of detailed questions need to be answered. Even if an overall test is significant, further analyses are, in general, necessary to assess specific differences in the treatments. The cell means model provides within the ANOVA framework the appropriate model for a correct statistical inference and provides such honest statements on statistical significance in a clinical investigation.
2.2 Factors, Levels, Effects, and Cells
One of the principal uses of statistical models is to explain variation in measurements. This variation may be caused by the variety of factors of influence, and it manifests itself as variation from one experimental unit to another. In well-controlled clinical studies, the sponsor deliberately changes the levels of experimental factors (e.g., treatment) to induce variation in the measured quantities to lead to a better understanding of the relationship between those experimental factors and the response. Those factors are called independent and the measured quantities are called dependent variables. For example, consider a clinical trial in which three different diagnostic imaging modalities are used on both men and women in different centers. Table 1 shows schematically how the resulting data could be arrayed in a tabular fashion.
Table 1: Factors, Levels, and Cells (i j k)
2.3 Cell Means Model
In linear model form, it is written
(1)
where the errors eir are identically independent normal N(0, σ2) distributed (i.i.d. variables). Note that, a model consists of more than just a model equation: It is an equation such as Equation 1 plus statements that describe the terms of the equation. In the example above, μi is defined as the population mean of the ith population and is equal to the expectation of yir
