Medical Biostatistics

Medical Biostatistics

Fourth Edition

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 Clinical

Trials, Second Edition

Shein-Chung Chow and Mark Chang

Adaptive Designs for Sequential

Treatment Allocation

Alessandro Baldi Antognini

and Alessandra Giovagnoli

Adaptive Design Theory and

Implementation Using SAS and R,

Second Edition

Mark Chang

Advanced Bayesian Methods for

Medical Test Accuracy

Lyle D. Broemeling

Analyzing Longitudinal Clinical Trial Data:

A Practical Guide

Craig Mallinckrodt and Ilya Lipkovich

Applied Biclustering Methods for Big

and High-Dimensional Data Using R

Adetayo Kasim, Ziv Shkedy,

Sebastian Kaiser, Sepp Hochreiter,

and Willem Talloen

Applied Meta-Analysis with R

Ding-Geng (Din) Chen and Karl E. Peace

Applied Surrogate Endpoint Evaluation

Methods with SAS and R

Ariel Alonso, Theophile Bigirumurame,

Tomasz Burzykowski, Marc Buyse,

Geert Molenberghs, Leacky Muchene,

Nolen Joy Perualila, Ziv Shkedy,

and Wim Van der Elst

Basic Statistics and Pharmaceutical

Statistical Applications, Second Edition

James E. De Muth

Bayesian Adaptive Methods for

Clinical Trials

Scott M. Berry, Bradley P. Carlin,

J. Jack Lee, and Peter Muller

Bayesian Analysis Made Simple:

An Excel GUI for WinBUGS

Phil Woodward

Bayesian Designs for Phase I–II

Clinical Trials

Ying Yuan, Hoang Q. Nguyen,

and Peter F. Thall

Bayesian Methods for Measures

of Agreement

Lyle D. Broemeling

Bayesian Methods for Repeated Measures

Lyle D. Broemeling

Bayesian Methods in Epidemiology

Lyle D. Broemeling

Bayesian Methods in Health Economics

Gianluca Baio

Bayesian Missing Data Problems: EM,

Data Augmentation and Noniterative

Computation

Ming T. Tan, Guo-Liang Tian,

and Kai Wang Ng

Bayesian Modeling in Bioinformatics

Dipak K. Dey, Samiran Ghosh,

and Bani K. Mallick

Benefit-Risk Assessment in

Pharmaceutical Research and

Development

Andreas Sashegyi, James Felli,

and Rebecca Noel

Benefit-Risk Assessment Methods in

Medical Product Development: Bridging

Qualitative and Quantitative Assessments

Qi Jiang and Weili He

Bioequivalence and Statistics in Clinical

Pharmacology, Second Edition

Scott Patterson and Byron Jones

Biosimilar Clinical Development:

Scientific Considerations and New

Methodologies

Kerry B. Barker, Sandeep M. Menon,

Ralph B. D’Agostino, Sr., Siyan Xu, and Bo Jin

Biosimilars: Design and Analysis of

Follow-on Biologics

Shein-Chung Chow

Biostatistics: A Computing Approach

Stewart J. Anderson

Cancer Clinical Trials: Current and

Controversial Issues in Design and

Analysis

Stephen L. George, Xiaofei Wang,

and Herbert Pang

Causal Analysis in Biomedicine and

Epidemiology: Based on Minimal

Sufficient Causation

Mikel Aickin

Clinical and Statistical Considerations in

Personalized Medicine

Claudio Carini, Sandeep Menon, and Mark Chang

Clinical Trial Data Analysis Using R

Ding-Geng (Din) Chen and Karl E. Peace

Clinical Trial Data Analysis Using R and SAS,

Second Edition

Ding-Geng (Din) Chen, Karl E. Peace,

and Pinggao Zhang

Clinical Trial Methodology

Karl E. Peace and Ding-Geng (Din) Chen

Clinical Trial Optimization Using R

Alex Dmitrienko and Erik Pulkstenis

Cluster Randomised Trials:

Second Edition

Richard J. Hayes and Lawrence H. Moulton

Computational Methods in Biomedical

Research

Ravindra Khattree and Dayanand N. Naik

Computational Pharmacokinetics

Anders Källén

Confidence Intervals for Proportions

and Related Measures of Effect Size

Robert G. Newcombe

Controversial Statistical Issues in

Clinical Trials

Shein-Chung Chow

Data Analysis with Competing Risks

and Intermediate States

Ronald B. Geskus

Data and Safety Monitoring Committees

in Clinical Trials, Second Edition

Jay Herson

Design and Analysis of Animal Studies

in Pharmaceutical Development

Shein-Chung Chow and Jen-pei Liu

Design and Analysis of Bioavailability

and Bioequivalence Studies, Third Edition

Shein-Chung Chow and Jen-pei Liu

Design and Analysis of Bridging Studies

Jen-pei Liu, Shein-Chung Chow,

and Chin-Fu Hsiao

Design & Analysis of Clinical Trials for

Economic Evaluation & Reimbursement:

An Applied Approach Using SAS & STATA

Iftekhar Khan

Design and Analysis of Clinical Trials

for Predictive Medicine

Shigeyuki Matsui, Marc Buyse,

and Richard Simon

Design and Analysis of Clinical Trials with

Time-to-Event Endpoints

Karl E. Peace

Design and Analysis of Non-Inferiority Trials

Mark D. Rothmann, Brian L. Wiens,

and Ivan S. F. Chan

Published Titles

Difference Equations with Public Health

Applications

Lemuel A. Moyé and Asha Seth Kapadia

DNA Methylation Microarrays:

Experimental Design and Statistical

Analysis

Sun-Chong Wang and Arturas Petronis

DNA Microarrays and Related Genomics

Techniques: Design, Analysis, and

Interpretation of Experiments

David B. Allison, Grier P. Page,

T. Mark Beasley, and Jode W. Edwards

Dose Finding by the Continual

Reassessment Method

Ying Kuen Cheung

Dynamical Biostatistical Models

Daniel Commenges and

Hélène Jacqmin-Gadda

Elementary Bayesian Biostatistics

Lemuel A. Moyé

Emerging Non-Clinical Biostatistics in

Biopharmaceutical Development and

Manufacturing

Harry Yang

Empirical Likelihood Method in

Survival Analysis

Mai Zhou

Essentials of a Successful Biostatistical

Collaboration

Arul Earnest

Exposure–Response Modeling: Methods

and Practical Implementation

Jixian Wang

Frailty Models in Survival Analysis

Andreas Wienke

Fundamental Concepts for New Clinical

Trialists

Scott Evans and Naitee Ting

Generalized Linear Models: A Bayesian

Perspective

Dipak K. Dey, Sujit K. Ghosh, and

Bani K. Mallick

Handbook of Regression and Modeling:

Applications for the Clinical and

Pharmaceutical Industries

Daryl S. Paulson

Inference Principles for Biostatisticians

Ian C. Marschner

Interval-Censored Time-to-Event Data:

Methods and Applications

Ding-Geng (Din) Chen, Jianguo Sun,

and Karl E. Peace

Introductory Adaptive Trial Designs:

A Practical Guide with R

Mark Chang

Joint Models for Longitudinal and Time￾to-Event Data: With Applications in R

Dimitris Rizopoulos

Measures of Interobserver Agreement

and Reliability, Second Edition

Mohamed M. Shoukri

Medical Biostatistics, Fourth Edition

A. Indrayan

Meta-Analysis in Medicine and

Health Policy

Dalene Stangl and Donald A. Berry

Methods in Comparative Effectiveness

Research

Constantine Gatsonis and Sally C. Morton

Mixed Effects Models for the Population

Approach: Models, Tasks, Methods

and Tools

Marc Lavielle

Modeling to Inform Infectious Disease

Control

Niels G. Becker

Modern Adaptive Randomized Clinical

Trials: Statistical and Practical Aspects

Oleksandr Sverdlov

Monte Carlo Simulation for the

Pharmaceutical Industry: Concepts,

Algorithms, and Case Studies

Mark Chang

Multiregional Clinical Trials for

Simultaneous Global New Drug

Development

Joshua Chen and Hui Quan

Multiple Testing Problems in

Pharmaceutical Statistics

Alex Dmitrienko, Ajit C. Tamhane,

and Frank Bretz

Published Titles

Published Titles

Noninferiority Testing in Clinical Trials:

Issues and Challenges

Tie-Hua Ng

Optimal Design for Nonlinear Response

Models

Valerii V. Fedorov and Sergei L. Leonov

Patient-Reported Outcomes:

Measurement, Implementation and

Interpretation

Joseph C. Cappelleri, Kelly H. Zou,

Andrew G. Bushmakin, Jose Ma. J. Alvir,

Demissie Alemayehu, and Tara Symonds

Quantitative Evaluation of Safety in Drug

Development: Design, Analysis and

Reporting

Qi Jiang and H. Amy Xia

Quantitative Methods for

HIV/AIDS Research

Cliburn Chan, Michael G. Hudgens, and

Shein-Chung Chow

Quantitative Methods for Traditional

Chinese Medicine Development

Shein-Chung Chow

Randomized Clinical Trials of

Nonpharmacological Treatments

Isabelle Boutron, Philippe Ravaud,

and David Moher

Randomized Phase II Cancer

Clinical Trials

Sin-Ho Jung

Repeated Measures Design with

Generalized Linear Mixed Models for

Randomized Controlled Trials

Toshiro Tango

Sample Size Calculations for Clustered

and Longitudinal Outcomes in Clinical

Research

Chul Ahn, Moonseong Heo,

and Song Zhang

Sample Size Calculations in Clinical

Research, Third Edition

Shein-Chung Chow, Jun Shao, Hansheng

Wang, and Yuliya Lokhnygina

Statistical Analysis of Human Growth

and Development

Yin Bun Cheung

Statistical Design and Analysis of Clinical

Trials: Principles and Methods

Weichung Joe Shih and Joseph Aisner

Statistical Design and Analysis of

Stability Studies

Shein-Chung Chow

Statistical Evaluation of Diagnostic

Performance: Topics in ROC Analysis

Kelly H. Zou, Aiyi Liu, Andriy Bandos,

Lucila Ohno-Machado, and Howard Rockette

Statistical Methods for Clinical Trials

Mark X. Norleans

Statistical Methods for Drug Safety

Robert D. Gibbons and Anup K. Amatya

Statistical Methods for Healthcare

Performance Monitoring

Alex Bottle and Paul Aylin

Statistical Methods for Immunogenicity

Assessment

Harry Yang, Jianchun Zhang, Binbing Yu,

and Wei Zhao

Statistical Methods in Drug Combination

Studies

Wei Zhao and Harry Yang

Statistical Testing Strategies in the

Health Sciences

Albert Vexler, Alan D. Hutson,

and Xiwei Chen

Statistics in Drug Research:

Methodologies and Recent

Developments

Shein-Chung Chow and Jun Shao

Statistics in the Pharmaceutical Industry,

Third Edition

Ralph Buncher and Jia-Yeong Tsay

Survival Analysis in Medicine and

Genetics

Jialiang Li and Shuangge Ma

Theory of Drug Development

Eric B. Holmgren

Translational Medicine: Strategies and

Statistical Methods

Dennis Cosmatos and Shein-Chung Chow

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Medical Biostatistics

Fourth Edition

Abhaya Indrayan

Rajeev Kumar Malhotra

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ix

Contents

Summary Tables..................................................................................................................................................................................xxix

Preface..................................................................................................................................................................................................xxxv

Frequently Used Notations............................................................................................................................................................ xxxvii

1. Medical Uncertainties......................................................................................................................................................................1

1.1 Uncertainties in Health and Disease....................................................................................................................................2

1.1.1 Uncertainties due to Intrinsic Variation .................................................................................................................2

1.1.1.1 Biologic Variability.....................................................................................................................................2

1.1.1.2 Genetic Variability .....................................................................................................................................3

1.1.1.3 Variation in Behavior and Other Host Factors.......................................................................................3

1.1.1.4 Environmental Variability ........................................................................................................................3

1.1.1.5 Sampling Fluctuations...............................................................................................................................3

1.1.2 Natural Variation in Assessment.............................................................................................................................4

1.1.2.1 Observer Variability...................................................................................................................................4

1.1.2.2 Variability in Treatment Strategies ..........................................................................................................4

1.1.2.3 Instrument and Laboratory Variability ..................................................................................................4

1.1.2.4 Imperfect Tools ...........................................................................................................................................4

1.1.2.5 Incomplete Information on the Patient ...................................................................................................5

1.1.2.6 Poor Compliance with the Regimen........................................................................................................5

1.1.3 Knowledge Limitations.............................................................................................................................................5

1.1.3.1 Epistemic Uncertainties.............................................................................................................................5

1.1.3.2 Chance Variability......................................................................................................................................6

1.1.3.3 Diagnostic, Therapeutic, and Prognostic Uncertainties .......................................................................6

1.1.3.4 Predictive and Other Uncertainties.........................................................................................................6

1.2 Uncertainties in Medical Research.......................................................................................................................................7

1.2.1 Empiricism in Medical Research.............................................................................................................................7

1.2.1.1 Laboratory Experiments............................................................................................................................7

1.2.1.2 Clinical Trials..............................................................................................................................................7

1.2.1.3 Surgical Procedures ...................................................................................................................................7

1.2.1.4 Epidemiological Research.........................................................................................................................8

1.2.2 Elements of Minimizing the Impact of Uncertainties on Research ...................................................................8

1.2.2.1 Proper Design .............................................................................................................................................8

1.2.2.2 Improved Medical Methods .....................................................................................................................8

1.2.2.3 Analysis and Synthesis..............................................................................................................................9

1.3 Uncertainties in Health Planning and Evaluation.............................................................................................................9

1.3.1 Health Situation Analysis.........................................................................................................................................9

1.3.1.1 Identification of the Specifics of the Problem.......................................................................................10

1.3.1.2 Magnitude of the Problem ......................................................................................................................10

1.3.1.3 Health Infrastructure...............................................................................................................................10

1.3.1.4 Feasibility of Remedial Steps..................................................................................................................11

1.3.2 Evaluation of Health Programs .............................................................................................................................11

1.4 Management of Uncertainties: About This Book .............................................................................................................11

1.4.1 Contents of the Book ...............................................................................................................................................12

1.4.1.1 Chapters.....................................................................................................................................................12

1.4.1.2 Limitations and Strengths ......................................................................................................................13

1.4.1.3 New in the Fourth Edition......................................................................................................................14

1.4.1.4 Unique Contribution of This Book ........................................................................................................14

x Contents

1.4.2 Salient Features of the Text.....................................................................................................................................15

1.4.2.1 System of Notations .................................................................................................................................15

1.4.2.2 Guide Chart of the Biostatistical Methods ...........................................................................................16

References .........................................................................................................................................................................................16

Exercises ............................................................................................................................................................................................16

2. Basics of Medical Studies .............................................................................................................................................................17

2.1 Study Protocol .......................................................................................................................................................................17

2.1.1 Problem, Objectives, and Hypotheses ..................................................................................................................17

2.1.1.1 Problem......................................................................................................................................................17

2.1.1.2 Broad and Specific Objectives ................................................................................................................18

2.1.1.3 Hypotheses................................................................................................................................................18

2.1.2 Protocol Content.......................................................................................................................................................19

2.2 Types of Medical Studies .....................................................................................................................................................21

2.2.1 Elements of a Study Design....................................................................................................................................22

2.2.2 Basic Types of Study Design ..................................................................................................................................22

2.2.2.1 Descriptive Studies ..................................................................................................................................23

2.2.2.2 Analytical Studies and Their Basic Types ............................................................................................24

2.2.3 Choosing a Design...................................................................................................................................................24

2.2.3.1 Recommended Design for Particular Setups.......................................................................................24

2.2.3.2 Choice of Design by Level of Evidence .................................................................................................25

2.3 Data Collection ......................................................................................................................................................................27

2.3.1 Nature of Data..........................................................................................................................................................27

2.3.1.1 Factual, Knowledge-Based, and Opinion-Based Data........................................................................27

2.3.1.2 Method of Obtaining the Data ...............................................................................................................27

2.3.2 Tools of Data Collection..........................................................................................................................................28

2.3.2.1 Existing Records.......................................................................................................................................28

2.3.2.2 Questionnaires and Schedules...............................................................................................................28

2.3.2.3 Likert Scale................................................................................................................................................29

2.3.2.4 Guttman Scale...........................................................................................................................................30

2.3.3 Pretesting and Pilot Study......................................................................................................................................30

2.4 Nonsampling Errors and Other Biases..............................................................................................................................31

2.4.1 Nonresponse.............................................................................................................................................................31

2.4.2 Variety of Biases to Guard Against.......................................................................................................................31

2.4.2.1 List of Biases..............................................................................................................................................31

2.4.2.2 Steps for Minimizing Bias.......................................................................................................................35

References .........................................................................................................................................................................................35

Exercises ............................................................................................................................................................................................36

3. Sampling Methods .........................................................................................................................................................................37

3.1 Sampling Concepts ...............................................................................................................................................................37

3.1.1 Advantages and Limitations of Sampling............................................................................................................37

3.1.1.1 Sampling Fluctuations.............................................................................................................................37

3.1.1.2 Advantages of Sampling .........................................................................................................................38

3.1.1.3 Limitations of Sampling..........................................................................................................................38

3.1.2 Some Special Terms Used in Sampling ................................................................................................................38

3.1.2.1 Unit of Inquiry and Sampling Unit .......................................................................................................38

3.1.2.2 Sampling Frame........................................................................................................................................39

3.1.2.3 Parameters and Statistics ........................................................................................................................39

3.1.2.4 Sample Size ...............................................................................................................................................39

3.1.2.5 Nonrandom and Random Sampling.....................................................................................................39

3.1.2.6 Sampling Weight......................................................................................................................................39

Contents xi

3.2 Common Methods of Random Sampling..........................................................................................................................40

3.2.1 Simple Random Sampling......................................................................................................................................40

3.2.2 Stratified Random Sampling..................................................................................................................................41

3.2.3 Multistage Random Sampling ...............................................................................................................................43

3.2.4 Cluster Random Sampling .....................................................................................................................................43

3.2.5 Systematic Random Sampling ...............................................................................................................................45

3.2.6 Choice of the Method of Random Sampling........................................................................................................46

3.3 Some Other Methods of Sampling .....................................................................................................................................46

3.3.1 Other Random Methods of Sampling...................................................................................................................46

3.3.1.1 Probability Proportional to Size Sampling...........................................................................................47

3.3.1.2 Area Sampling..........................................................................................................................................47

3.3.1.3 Inverse Sampling......................................................................................................................................47

3.3.1.4 Consecutive Subjects Attending a Clinic..............................................................................................48

3.3.1.5 Sequential Sampling................................................................................................................................48

3.3.2 Nonrandom Methods of Sampling .......................................................................................................................48

3.3.2.1 Convenience Sample................................................................................................................................48

3.3.2.2 Other Types of Purposive Samples........................................................................................................49

References .........................................................................................................................................................................................49

Exercises ............................................................................................................................................................................................49

4. Designs for Observational Studies.............................................................................................................................................51

4.1 Some Basic Concepts ............................................................................................................................................................51

4.1.1 Antecedent and Outcome .......................................................................................................................................51

4.1.2 Confounders .............................................................................................................................................................52

4.1.3 Effect Size..................................................................................................................................................................53

4.1.4 Ecological Studies ....................................................................................................................................................53

4.2 Prospective Studies...............................................................................................................................................................53

4.2.1 Variations of Prospective Studies ..........................................................................................................................54

4.2.1.1 Cohort Study.............................................................................................................................................54

4.2.1.2 Longitudinal Study..................................................................................................................................54

4.2.1.3 Repeated Measures Study.......................................................................................................................55

4.2.2 Selection of Subjects for a Prospective Study ......................................................................................................55

4.2.2.1 Comparison Group in a Prospective Study..........................................................................................55

4.2.3 Potential Biases in Prospective Studies ................................................................................................................56

4.2.3.1 Selection Bias ............................................................................................................................................56

4.2.3.2 Bias due to Loss in Follow-Up................................................................................................................56

4.2.3.3 Assessment Bias and Errors....................................................................................................................56

4.2.3.4 Bias due to Change in the Status............................................................................................................57

4.2.3.5 Confounding Bias.....................................................................................................................................57

4.2.3.6 Post Hoc Bias.............................................................................................................................................57

4.2.4 Merits and Demerits of Prospective Studies........................................................................................................57

4.2.4.1 Merits of Prospective Studies .................................................................................................................57

4.2.4.2 Demerits of Prospective Studies ............................................................................................................57

4.3 Retrospective Studies ...........................................................................................................................................................58

4.3.1 Case–Control Design...............................................................................................................................................58

4.3.1.1 Nested Case–Control Design .................................................................................................................59

4.3.2 Selection of Cases and Controls.............................................................................................................................59

4.3.2.1 Selection of Cases .....................................................................................................................................60

4.3.2.2 Selection of Controls ................................................................................................................................60

4.3.2.3 Sampling Methods in Retrospective Studies .......................................................................................60

4.3.2.4 Confounders and Matching....................................................................................................................60

4.3.3 Merits and Demerits of Case–Control Studies ....................................................................................................61

4.3.3.1 Merits of Case–Control Studies .............................................................................................................61

4.3.3.2 Demerits of Case–Control Studies.........................................................................................................61

xii Contents

4.4 Cross-Sectional Studies........................................................................................................................................................62

4.4.1 Selection of Subjects for a Cross-Sectional Study ...............................................................................................62

4.4.2 Merits and Demerits of Cross-Sectional Studies.................................................................................................62

4.4.2.1 Demerits of Cross-Sectional Studies .....................................................................................................62

4.4.2.2 Merits of Cross-Sectional Studies ..........................................................................................................63

4.5 Comparative Performance of Prospective, Retrospective, and Cross-Sectional Studies ...........................................63

4.5.1 Comparative Features and Performance Comparison...................................................................................... 64

4.5.2 Reporting Results of Observational Studies: STROBE.......................................................................................65

References .........................................................................................................................................................................................66

Exercises ............................................................................................................................................................................................66

5. Medical Experiments .....................................................................................................................................................................67

5.1 Basic Features of Medical Experiments .............................................................................................................................67

5.1.1 Statistical Principles of Experimentation .............................................................................................................68

5.1.1.1 Control Group...........................................................................................................................................68

5.1.1.2 Randomization .........................................................................................................................................68

5.1.1.3 Replication.................................................................................................................................................69

5.1.2 Advantages and Limitations of Experiments ......................................................................................................69

5.1.2.1 Advantages................................................................................................................................................69

5.1.2.2 Limitations ................................................................................................................................................70

5.2 Design of Experiments .........................................................................................................................................................70

5.2.1 Classical Designs: One-Way, Two-Way, and Factorial........................................................................................71

5.2.1.1 One-Way Design.......................................................................................................................................71

5.2.1.2 Two-Way Design.......................................................................................................................................71

5.2.1.3 Interaction..................................................................................................................................................72

5.2.1.4 K-Way and Factorial Experiments..........................................................................................................73

5.2.2 Some Common Unconventional Designs.............................................................................................................74

5.2.2.1 Repeated Measures Design.....................................................................................................................74

5.2.2.2 Crossover Design .....................................................................................................................................75

5.2.2.3 Other Complex Designs ..........................................................................................................................76

5.3 Choice of Sampling of Units for Laboratory Experiments..............................................................................................76

5.3.1 Choice of Experimental Unit..................................................................................................................................77

5.3.2 Sampling Methods in Laboratory Experiments..................................................................................................77

5.3.3 Choosing a Design of Experiment ........................................................................................................................77

5.3.4 Pharmacokinetic Studies ........................................................................................................................................78

References .........................................................................................................................................................................................78

Exercises ............................................................................................................................................................................................79

6. Clinical Trials..................................................................................................................................................................................81

6.1 Therapeutic Trials .................................................................................................................................................................81

6.1.1 Phases of a Clinical Trial.........................................................................................................................................81

6.1.1.1 Phase I Trial...............................................................................................................................................81

6.1.1.2 Phase II Trial .............................................................................................................................................82

6.1.1.3 Phase III Trial............................................................................................................................................82

6.1.1.4 Phase IV: Postmarketing Surveillance ..................................................................................................83

6.1.2 Randomized Controlled Trials: Selection of Subjects.........................................................................................83

6.1.2.1 Selection of Participants for RCT ...........................................................................................................83

6.1.2.2 Control Group in a Clinical Trial...........................................................................................................84

6.1.3 Randomization and Matching...............................................................................................................................85

6.1.3.1 Randomization .........................................................................................................................................86

6.1.3.2 Matching....................................................................................................................................................86

6.1.4 Methods of Random Allocation.............................................................................................................................87

6.1.4.1 Allocation Out of a Large Number of Available Subjects ..................................................................87

6.1.4.2 Random Allocation of Consecutive Patients Coming to a Clinic .....................................................87

6.1.4.3 Block, Cluster, and Stratified Randomization......................................................................................88

Contents xiii

6.1.5 Blinding and Masking ............................................................................................................................................89

6.1.5.1 Blinding .....................................................................................................................................................89

6.1.5.2 Concealment of Allocation......................................................................................................................89

6.1.5.3 Masking .....................................................................................................................................................90

6.2 Issues in Clinical Trials ........................................................................................................................................................90

6.2.1 Outcome Assessment ..............................................................................................................................................90

6.2.1.1 Specification of End Points or Outcome................................................................................................90

6.2.1.2 Causal Inference.......................................................................................................................................91

6.2.1.3 Side Effects ................................................................................................................................................91

6.2.1.4 Effectiveness versus Efficacy..................................................................................................................92

6.2.1.5 Pragmatic Trials........................................................................................................................................92

6.2.2 Various Equivalences in Clinical Trials................................................................................................................92

6.2.2.1 Superiority, Equivalence, and Noninferiority Trials...........................................................................92

6.2.2.2 Therapeutic Equivalence and Bioequivalence .....................................................................................93

6.2.3 Designs for Clinical Trials ......................................................................................................................................94

6.2.3.1 n-of-1, Up-and-Down, and Sequential Designs ...................................................................................94

6.2.3.2 Choosing a Design for a Clinical Trial..................................................................................................95

6.2.4 Designs with Interim Appraisals ..........................................................................................................................95

6.2.4.1 Designs with Provision to Stop Early....................................................................................................96

6.2.4.2 Adaptive Designs .....................................................................................................................................96

6.2.5 Biostatistical Ethics for Clinical Trials ..................................................................................................................97

6.2.5.1 Equipoise ...................................................................................................................................................97

6.2.5.2 Ethical Cautions........................................................................................................................................98

6.2.5.3 Statistical Considerations in a Multicentric Trial ................................................................................98

6.2.5.4 Multiple Treatments with Different Outcomes in the Same Trial.....................................................98

6.2.5.5 Size of the Trial .........................................................................................................................................99

6.2.5.6 Compliance................................................................................................................................................99

6.2.6 Reporting the Results of a Clinical Trial ..............................................................................................................99

6.2.6.1 CONSORT Statement...............................................................................................................................99

6.2.6.2 Registration of Trials and Open Access ..............................................................................................100

6.3 Trials Other than for Therapeutics ...................................................................................................................................101

6.3.1 Clinical Trials for Diagnostic and Prophylactic Modalities ............................................................................101

6.3.1.1 Diagnostic Trials.....................................................................................................................................101

6.3.1.2 Prophylactic Trials in Clinics................................................................................................................102

6.3.2 Field Trials for Screening, Prophylaxis, and Vaccines......................................................................................102

6.3.2.1 Screening Trials ......................................................................................................................................102

6.3.2.2 Prophylactic Trials in the Field.............................................................................................................102

6.3.2.3 Vaccine Trials ..........................................................................................................................................103

6.3.3 Issues in Field Trials ..............................................................................................................................................103

6.3.3.1 Randomization and Blinding in Field Trials......................................................................................103

6.3.3.2 Designs for Field Trials..........................................................................................................................104

References .......................................................................................................................................................................................104

Exercises ..........................................................................................................................................................................................105

7. Numerical Methods for Representing Variation...................................................................................................................107

7.1 Types of Measurement .......................................................................................................................................................107

7.1.1 Nominal, Metric, and Ordinal Scales .................................................................................................................107

7.1.1.1 Nominal Scale.........................................................................................................................................107

7.1.1.2 Metric Scale .............................................................................................................................................108

7.1.1.3 Ordinal Scale...........................................................................................................................................108

7.1.1.4 Grouping of a Metric Scale (Categorizing Continuous Measurements) ........................................109

7.1.2 Other Classifications of the Types of Measurement.........................................................................................110

7.1.2.1 Discrete and Continuous Variables .....................................................................................................110

7.1.2.2 Qualitative and Quantitative Data ......................................................................................................111

7.1.2.3 Stochastic and Deterministic Variables ..............................................................................................111

xiv Contents

7.2 Tabular Presentation...........................................................................................................................................................111

7.2.1 Contingency Tables and Frequency Distribution .............................................................................................112

7.2.1.1 Empty Cells.............................................................................................................................................113

7.2.1.2 Problems in Preparing a Contingency Table on Metric Data ..........................................................113

7.2.1.3 Features of a Table..................................................................................................................................113

7.2.2 Other Types of Statistical Tables.......................................................................................................................... 114

7.2.2.1 Multiple Responses Tables.................................................................................................................... 114

7.2.2.2 Statistical Tables......................................................................................................................................115

7.2.2.3 What Is a Good Statistical Table? .........................................................................................................115

7.3 Rates and Ratios ..................................................................................................................................................................115

7.3.1 Proportion, Rate, and Ratio ..................................................................................................................................115

7.3.1.1 Proportion ...............................................................................................................................................116

7.3.1.2 Rate...........................................................................................................................................................116

7.3.1.3 Ratio .........................................................................................................................................................116

7.4 Central and Other Locations .............................................................................................................................................117

7.4.1 Central Values: Mean, Median, and Mode.........................................................................................................117

7.4.1.1 Understanding Mean, Median, and Mode .........................................................................................118

7.4.1.2 Calculation in the Case of Grouped Data...........................................................................................118

7.4.1.3 Which Central Value to Use? ................................................................................................................120

7.4.1.4 Geometric Mean.....................................................................................................................................121

7.4.1.5 Harmonic Mean......................................................................................................................................121

7.4.2 Other Locations: Quantiles ..................................................................................................................................122

7.4.2.1 Quantiles in Ungrouped Data..............................................................................................................123

7.4.2.2 Quantiles in Grouped Data...................................................................................................................123

7.4.2.3 Interpretation of Quantiles ...................................................................................................................124

7.5 Measuring Variability ........................................................................................................................................................125

7.5.1 Variance and Standard Deviation .......................................................................................................................126

7.5.1.1 Variance and Standard Deviation in Ungrouped Data ....................................................................126

7.5.1.2 Variance and Standard Deviation in Grouped Data.........................................................................128

7.5.1.3 Variance of Sum or Difference of Two Measurements .....................................................................128

7.5.1.4 Measuring Variation in Skewed and Nominal Data: Interquartile Range and Variation Ratio........128

7.5.2 Coefficient of Variation .........................................................................................................................................129

References .......................................................................................................................................................................................131

Exercises ..........................................................................................................................................................................................131

8. Presentation of Variation by Figures: Data Visualization...................................................................................................133

8.1 Graphs for Frequency Distribution ..................................................................................................................................133

8.1.1 Histogram and Its Variants ..................................................................................................................................134

8.1.1.1 Histogram................................................................................................................................................134

8.1.1.2 Stem-and-Leaf Plot.................................................................................................................................134

8.1.1.3 Line Histogram and Dot Plot ...............................................................................................................136

8.1.2 Polygon and Its Variants .......................................................................................................................................136

8.1.2.1 Frequency Polygon.................................................................................................................................136

8.1.2.2 Area Diagram .........................................................................................................................................136

8.1.3 Frequency Curve....................................................................................................................................................136

8.2 Pie, Bar, and Line Diagrams ..............................................................................................................................................136

8.2.1 Pie Diagram ............................................................................................................................................................137

8.2.1.1 Useful Features of a Pie Diagram ........................................................................................................138

8.2.1.2 Donut Diagram.......................................................................................................................................138

8.2.2 Bar Diagram............................................................................................................................................................138

8.2.3 Scatter and Line Diagrams ...................................................................................................................................140

8.2.3.1 Scatter Diagram......................................................................................................................................140

8.2.3.2 Bubble Chart ...........................................................................................................................................140

8.2.3.3 Line Diagram..........................................................................................................................................142

8.2.3.4 Complex Line Diagram .........................................................................................................................142