Statistical Methods for Drug Safety

300 Pages·2015·4.212 MB·308\300

by  Robert D. Gibbons, Anup Amatya

Statistical
Methods for
Drug Safety
Robert D. Gibbons
University of Chicago
Illinois, USA
Anup K. Amatya
New Mexico State University
Las Cruces, USA
© 2016 by Taylor & Francis Group, LLC
Editor-in-Chief
Shein-Chung Chow, Ph.D., Professor, Department of Biostatistics and Bioinformatics,
Duke University School of Medicine, Durham, North Carolina
Series Editors
Byron Jones, Biometrical Fellow, Statistical Methodology, Integrated Information Sciences,
Novartis Pharma AG, Basel, Switzerland
Jen-pei Liu, Professor, Division of Biometry, Department of Agronomy,
National Taiwan University, Taipei, Taiwan
Karl E. Peace, Georgia Cancer Coalition, Distinguished Cancer Scholar, Senior Research Scientist
and Professor of Biostatistics, Jiann-Ping Hsu College of Public Health,
Georgia Southern University, Statesboro, Georgia
Bruce W. Turnbull, Professor, School of Operations Research and Industrial Engineering,
Cornell University, Ithaca, New York
Published Titles
Adaptive Design Methods in Bayesian Methods in Epidemiology
Clinical Trials, Second Edition Lyle D. Broemeling
Shein-Chung Chow and Mark Chang
Bayesian Methods in Health Economics
Adaptive Designs for Sequential Gianluca Baio
Treatment Allocation
Bayesian Missing Data Problems: EM,
Alessandro Baldi Antognini and
Data Augmentation and Noniterative
Alessandra Giovagnoli
Computation
Adaptive Design Theory and Ming T. Tan, Guo-Liang Tian,
Implementation Using SAS and R, and Kai Wang Ng
Second Edition
Bayesian Modeling in Bioinformatics
Mark Chang
Dipak K. Dey, Samiran Ghosh,
Advanced Bayesian Methods for Medical and Bani K. Mallick
Test Accuracy
Benefit-Risk Assessment in
Lyle D. Broemeling
Pharmaceutical Research and
Advances in Clinical Trial Biostatistics Development
Nancy L. Geller Andreas Sashegyi, James Felli, and
Rebecca Noel
Applied Meta-Analysis with R
Ding-Geng (Din) Chen and Karl E. Peace Biosimilars: Design and Analysis of
Follow-on Biologics
Basic Statistics and Pharmaceutical
Shein-Chung Chow
Statistical Applications, Second Edition
James E. De Muth Biostatistics: A Computing Approach
Stewart J. Anderson
Bayesian Adaptive Methods for
Clinical Trials Causal Analysis in Biomedicine and
Scott M. Berry, Bradley P. Carlin, Epidemiology: Based on Minimal
J. Jack Lee, and Peter Muller Sufficient Causation
Mikel Aickin
Bayesian Analysis Made Simple: An Excel
GUI for WinBUGS Clinical and Statistical Considerations
Phil Woodward in Personalized Medicine
Claudio Carini, Sandeep Menon,
Bayesian Methods for Measures of
and Mark Chang
Agreement
Lyle D. Broemeling
© 2016 by Taylor & Francis Group, LLC
Clinical Trial Data Analysis using R DNA Microarrays and Related Genomics
Ding-Geng (Din) Chen and Karl E. Peace Techniques: Design, Analysis, and
Interpretation of Experiments
Clinical Trial Methodology
David B. Allison, Grier P. Page,
Karl E. Peace and Ding-Geng (Din) Chen
T. Mark Beasley, and Jode W. Edwards
Computational Methods in Biomedical
Dose Finding by the Continual
Research
Reassessment Method
Ravindra Khattree and Dayanand N. Naik
Ying Kuen Cheung
Computational Pharmacokinetics
Elementary Bayesian Biostatistics
Anders Källén
Lemuel A. Moyé
Confidence Intervals for Proportions and
Empirical Likelihood Method in Survival
Related Measures of Effect Size
Analysis
Robert G. Newcombe
Mai Zhou
Controversial Statistical Issues in
Frailty Models in Survival Analysis
Clinical Trials
Andreas Wienke
Shein-Chung Chow
Generalized Linear Models: A Bayesian
Data and Safety Monitoring Committees
Perspective
in Clinical Trials
Dipak K. Dey, Sujit K. Ghosh,
Jay Herson
and Bani K. Mallick
Design and Analysis of Animal Studies in
Handbook of Regression and Modeling:
Pharmaceutical Development
Applications for the Clinical and
Shein-Chung Chow and Jen-pei Liu
Pharmaceutical Industries
Design and Analysis of Bioavailability and
Daryl S. Paulson
Bioequivalence Studies, Third Edition
Inference Principles for Biostatisticians
Shein-Chung Chow and Jen-pei Liu
Ian C. Marschner
Design and Analysis of Bridging Studies
Interval-Censored Time-to-Event Data:
Jen-pei Liu, Shein-Chung Chow,
Methods and Applications
and Chin-Fu Hsiao
Ding-Geng (Din) Chen, Jianguo Sun,
Design and Analysis of Clinical Trials for
and Karl E. Peace
Predictive Medicine
Introductory Adaptive Trial Designs:
Shigeyuki Matsui, Marc Buyse,
A Practical Guide with R
and Richard Simon
Mark Chang
Design and Analysis of Clinical Trials with
Time-to-Event Endpoints Joint Models for Longitudinal and Time-
to-Event Data: With Applications in R
Karl E. Peace
Dimitris Rizopoulos
Design and Analysis of Non-Inferiority
Measures of Interobserver Agreement
Trials
and Reliability, Second Edition
Mark D. Rothmann, Brian L. Wiens,
Mohamed M. Shoukri
and Ivan S. F. Chan
Medical Biostatistics, Third Edition
Difference Equations with Public Health
A. Indrayan
Applications
Lemuel A. Moyé and Asha Seth Kapadia Meta-Analysis in Medicine and Health
Policy
DNA Methylation Microarrays:
Dalene Stangl and Donald A. Berry
Experimental Design and Statistical
Analysis
Sun-Chong Wang and Arturas Petronis
© 2016 by Taylor & Francis Group, LLC
Mixed Effects Models for the Population Sample Size Calculations in Clinical
Approach: Models, Tasks, Methods and Research, Second Edition
Tools Shein-Chung Chow, Jun Shao
Marc Lavielle and Hansheng Wang
Modeling to Inform Infectious Disease Statistical Analysis of Human Growth
Control and Development
Niels G. Becker Yin Bun Cheung
Monte Carlo Simulation for the Statistical Design and Analysis of
Pharmaceutical Industry: Concepts, Stability Studies
Algorithms, and Case Studies Shein-Chung Chow
Mark Chang
Statistical Evaluation of Diagnostic
Multiple Testing Problems in Performance: Topics in ROC Analysis
Pharmaceutical Statistics Kelly H. Zou, Aiyi Liu, Andriy Bandos,
Alex Dmitrienko, Ajit C. Tamhane, Lucila Ohno-Machado, and Howard Rockette
and Frank Bretz
Statistical Methods for Clinical Trials
Noninferiority Testing in Clinical Trials: Mark X. Norleans
Issues and Challenges
Statistical Methods for Drug Safety
Tie-Hua Ng
Robert D. Gibbons and Anup K. Amatya
Optimal Design for Nonlinear Response
Statistical Methods in Drug Combination
Models
Studies
Valerii V. Fedorov and Sergei L. Leonov
Wei Zhao and Harry Yang
Patient-Reported Outcomes:
Statistics in Drug Research:
Measurement, Implementation and
Methodologies and Recent
Interpretation
Developments
Joseph C. Cappelleri, Kelly H. Zou,
Shein-Chung Chow and Jun Shao
Andrew G. Bushmakin, Jose Ma. J. Alvir,
Statistics in the Pharmaceutical Industry,
Demissie Alemayehu, and Tara Symonds
Third Edition
Quantitative Evaluation of Safety in Drug
Ralph Buncher and Jia-Yeong Tsay
Development: Design, Analysis and
Survival Analysis in Medicine and
Reporting
Genetics
Qi Jiang and H. Amy Xia
Jialiang Li and Shuangge Ma
Randomized Clinical Trials of
Theory of Drug Development
Nonpharmacological Treatments
Isabelle Boutron, Philippe Ravaud, and Eric B. Holmgren
David Moher Translational Medicine: Strategies and
Statistical Methods
Randomized Phase II Cancer Clinical
Dennis Cosmatos and Shein-Chung Chow
Trials
Sin-Ho Jung
Sample Size Calculations for Clustered
and Longitudinal Outcomes in Clinical
Research
Chul Ahn, Moonseong Heo, and
Song Zhang
© 2016 by Taylor & Francis Group, LLC
Statistical
Methods for
Drug Safety
Robert D. Gibbons
University of Chicago
Illinois, USA
Anup K. Amatya
New Mexico State University

Las Cruces, USA
© 2016 by Taylor & Francis Group, LLC
CRC Press
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Version Date: 20150604
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To Carol, Julie, Jason and Michael and the memory
of Donna and Sid
R.D.G.
To my family and friends
A.K.A.

© 2016 by Taylor & Francis Group, LLC
© 2016 by Taylor & Francis Group, LLC
Contents
Preface xv
Acknowledgments xix
1 Introduction 1
1.1 Randomized Clinical Trials . . . . . . . . . . . . . . . . . . . 2
1.2 Observational Studies . . . . . . . . . . . . . . . . . . . . . . 4
1.3 The Problem of Multiple Comparisons . . . . . . . . . . . . . 5
1.4 The Evolution of Available Data Streams . . . . . . . . . . . 6
1.5 The Hierarchy of Scientific Evidence . . . . . . . . . . . . . . 7
1.6 Statistical Significance . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Basic Statistical Concepts 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Relative Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Odds Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Statistical Power . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Maximum Likelihood Estimation . . . . . . . . . . . . . . . . 17
2.5.1 Example with a Closed Form Solution . . . . . . . . . 19
2.5.2 Example without a Closed Form Solution . . . . . . . 20
2.5.3 Bayesian Statistics . . . . . . . . . . . . . . . . . . . . 21
2.5.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Non-linear Regression Models . . . . . . . . . . . . . . . . . 23
2.7 Causal Inference . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7.1 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . 25
2.7.2 Average Treatment Effect . . . . . . . . . . . . . . . . 25
3 Multi-level Models 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Issues Inherent in Longitudinal Data . . . . . . . . . . . . . 29
3.2.1 Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 Missing Data . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.3 Irregularly Spaced Measurement Occasions . . . . . . 30
ix
© 2016 by Taylor & Francis Group, LLC
x Contents
3.3 Historical Background . . . . . . . . . . . . . . . . . . . . . . 31
3.4 StatisticalModelsfortheAnalysisofLongitudinaland/orClus-
tered Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.1 Mixed-effects RegressionModels . . . . . . . . . . . . 32
3.4.1.1 Random Intercept Model . . . . . . . . . . . 34
3.4.1.2 Random Intercept and Trend Model . . . . . 36
3.4.2 Matrix Formulation . . . . . . . . . . . . . . . . . . . 37
3.4.3 Generalized Estimating Equation Models . . . . . . . 39
3.4.4 Models for CategoricalOutcomes . . . . . . . . . . . . 40
4 Causal Inference 43
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Propensity Score Matching . . . . . . . . . . . . . . . . . . . 44
4.2.1 Illustration . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Marginal Structural Models . . . . . . . . . . . . . . . . . . . 50
4.3.1 Illustration . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 Instrumental Variables . . . . . . . . . . . . . . . . . . . . . 55
4.4.1 Illustration . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 Differential Effects . . . . . . . . . . . . . . . . . . . . . . . . 61
5 Analysis of Spontaneous Reports 69
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Proportional Reporting Ratio . . . . . . . . . . . . . . . . . 70
5.2.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.3 Bayesian Confidence PropagationNeural Network (BCPNN) 72
5.4 Empirical Bayes Screening . . . . . . . . . . . . . . . . . . . 77
5.5 Multi-item Gamma Poisson Shrinker . . . . . . . . . . . . . 80
5.6 Bayesian Lasso Logistic Regression . . . . . . . . . . . . . . 83
5.7 Random-effect PoissonRegression . . . . . . . . . . . . . . . 87
5.7.1 Rate Multiplier . . . . . . . . . . . . . . . . . . . . . . 88
5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6 Meta-analysis 93
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Fixed-effect Meta-analysis . . . . . . . . . . . . . . . . . . . 94
6.2.1 Correlation Coefficient . . . . . . . . . . . . . . . . . . 94
6.2.2 Mean Difference . . . . . . . . . . . . . . . . . . . . . 95
6.2.3 Relative Risk . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.3.1 Inverse Variance Method . . . . . . . . . . . 97
6.2.3.2 Mantel-Haenszel Method . . . . . . . . . . . 97
© 2016 by Taylor & Francis Group, LLC