Confidence Intervals for Proportions and Related Measures of Effect Size

463 Pages·2012·7.172 MB·English

by  Robert G. Newcombe

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Statistics
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Confidence Intervals for Proportions and Related Measures of d e
Confidence Intervals
Effect Size illustrates the use of effect size measures and corresponding n
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confidence intervals as more informative alternatives to the most basic
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and widely used significance tests. The book provides you with a deep
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in situations far removed from the familiar Gaussian case. u t Related Measures
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Drawing on his extensive work as a statistician and professor at Cardiff e r
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University School of Medicine, the author brings together methods for a of Effect Size
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calculating confidence intervals for proportions and several other important l
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measures, including differences, ratios, and nonparametric effect size
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measures generalizing Mann–Whitney and Wilcoxon tests. He also explains o
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three important approaches to obtaining intervals for related measures. f r
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Many examples illustrate the application of the methods in the health and c P
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social sciences. Requiring little computational skills, the book offers user- t
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friendly Excel spreadsheets for download, enabling you to easily apply the S p
methods to your own empirical data. iz o
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Features t
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• Discusses the rationale for point and interval estimates as the
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mainstays of statistical inference
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• Develops and evaluates confidence intervals for a wide range of
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measures related to proportions
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• Presents an in-depth treatment of criteria for optimality and evaluation d
issues
• Contains a wealth of application examples related to real-world
research studies
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Robert G. Newcombe
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K10649
K10649_Cover.indd 1 7/23/12 9:42 AM

Confidence Intervals
for Proportions and
Related Measures
of Effect Size
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 Jen-pei Liu
Biometrical Fellow Professor
Statistical Methodology Division of Biometry
Department of Agronomy
Integrated Information Sciences
National Taiwan University
Novartis Pharma AG
Taipei, Taiwan
Basel, Switzerland

Karl E. Peace Bruce W. Turnbull
Georgia Cancer Coalition Professor
Distinguished Cancer Scholar School of Operations Research
Senior Research Scientist and and Industrial Engineering
Professor of Biostatistics Cornell University
Jiann-Ping Hsu College of Public Health Ithaca, New York
Georgia Southern University
Statesboro, Georgia
Adaptive Design Methods in Clinical Trial Methodology
Clinical Trials, Second Edition Karl E. Peace and Ding-Geng (Din) Chen
Shein-Chung Chow and Mark Chang
Computational Methods in Biomedical
Adaptive Design Theory and Research
Implementation Using SAS and R Ravindra Khattree and Dayanand N. Naik
Mark Chang
Computational Pharmacokinetics
Advanced Bayesian Methods for Medical Anders Källén
Test Accuracy
Confidence Intervals for Proportions and
Lyle D. Broemeling
Related Measures of Effect Size
Advances in Clinical Trial Biostatistics Robert G. Newcombe
Nancy L. Geller
Controversial Statistical Issues in
Basic Statistics and Pharmaceutical Clinical Trials
Statistical Applications, Second Edition Shein-Chung Chow
James E. De Muth
Data and Safety Monitoring Committees
Bayesian Adaptive Methods for in Clinical Trials
Clinical Trials Jay Herson
Scott M. Berry, Bradley P. Carlin,
Design and Analysis of Animal Studies in
J. Jack Lee, and Peter Muller
Pharmaceutical Development
Bayesian Analysis Made Simple: An Excel Shein-Chung Chow and Jen-pei Liu
GUI for WinBUGS
Design and Analysis of Bioavailability and
Phil Woodward
Bioequivalence Studies, Third Edition
Bayesian Methods for Measures of Shein-Chung Chow and Jen-pei Liu
Agreement
Design and Analysis of Bridging Studies
Lyle D. Broemeling
Chin-Fu Hsiao, Jen-pei Liu,
Bayesian Missing Data Problems: EM, and Shein-Chung Chow
Data Augmentation and Noniterative
Design and Analysis of Clinical Trials with
Computation
Time-to-Event Endpoints
Ming T. Tan, Guo-Liang Tian,
Karl E. Peace
and Kai Wang Ng
Design and Analysis of Non-Inferiority
Bayesian Modeling in Bioinformatics
Trials
Dipak K. Dey, Samiran Ghosh,
Mark D. Rothmann, Brian L. Wiens,
and Bani K. Mallick
and Ivan S. F. Chan
Biostatistics: A Computing Approach
Difference Equations with Public Health
Stewart J. Anderson
Applications
Causal Analysis in Biomedicine and Lemuel A. Moyé and Asha Seth Kapadia
Epidemiology: Based on Minimal
DNA Methylation Microarrays:
Sufficient Causation
Experimental Design and Statistical
Mikel Aickin
Analysis
Clinical Trial Data Analysis using R Sun-Chong Wang and Arturas Petronis
Ding-Geng (Din) Chen and Karl E. Peace
DNA Microarrays and Related Genomics Multiple Testing Problems in
Techniques: Design, Analysis, and Pharmaceutical Statistics
Interpretation of Experiments Alex Dmitrienko, Ajit C. Tamhane,
David B. Allison, Grier P. Page, and Frank Bretz
T. Mark Beasley, and Jode W. Edwards
Randomized Clinical Trials of
Dose Finding by the Continual Nonpharmacological Treatments
Reassessment Method Isabelle Boutron, Philippe Ravaud, and
Ying Kuen Cheung David Moher
Elementary Bayesian Biostatistics Sample Size Calculations in Clinical
Lemuel A. Moyé Research, Second Edition
Shein-Chung Chow, Jun Shao
Frailty Models in Survival Analysis
and Hansheng Wang
Andreas Wienke
Statistical Design and Analysis of
Generalized Linear Models: A Bayesian
Stability Studies
Perspective
Shein-Chung Chow
Dipak K. Dey, Sujit K. Ghosh,
and Bani K. Mallick Statistical Evaluation of Diagnostic
Performance: Topics in ROC Analysis
Handbook of Regression and Modeling:
Kelly H. Zou, Aiyi Liu, Andriy Bandos,
Applications for the Clinical and
Lucila Ohno-Machado, and Howard Rockette
Pharmaceutical Industries
Daryl S. Paulson Statistical Methods for Clinical Trials
Mark X. Norleans
Measures of Interobserver Agreement
and Reliability, Second Edition Statistics in Drug Research:
Mohamed M. Shoukri Methodologies and Recent
Developments
Medical Biostatistics, Third Edition
Shein-Chung Chow and Jun Shao
A. Indrayan
Statistics in the Pharmaceutical Industry,
Meta-Analysis in Medicine and Health
Third Edition
Policy
Ralph Buncher and Jia-Yeong Tsay
Dalene Stangl and Donald A. Berry
Translational Medicine: Strategies and
Monte Carlo Simulation for the
Statistical Methods
Pharmaceutical Industry: Concepts,
Dennis Cosmatos and Shein-Chung Chow
Algorithms, and Case Studies
Mark Chang
Confidence Intervals
for Proportions and
Related Measures
of Effect Size
Robert G. Newcombe
CRC Press
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Contents
Preface......................................................................................................................xv
Acknowledgments...............................................................................................xxi
Author..................................................................................................................xxiii
Acronyms.............................................................................................................xxv
1. Hypothesis Tests and Confidence Intervals...............................................1
1.1. Sample.and.Population.........................................................................1
1.2. Hypothesis.Testing.and.Confidence.Intervals:.The.
Fundamentals.........................................................................................3
1.2.1. A.Confidence.Interval.for.a.Single.Group.............................3
1.2.2. Comparing.Two.Groups.Using.Hypothesis.Tests................7
1.2.3. Comparing.Two.Groups.Using.Confidence.Intervals.........8
1.3. Why.Confidence.Intervals.Are.Generally.More.Informative.
Than.p-Values.......................................................................................10
1.4. Measures.of.Effect.Size.......................................................................13
1.4.1. An.Example.to.Illustrate.the.Need.for.Effect.Size.
Measures.and.Their.Associated.Confidence.Intervals......14
1.4.2. How.Effect.Size.Measures.Add.Value.................................16
1.5. When.Are.Point.and.Interval.Estimates.Less.Helpful?..................17
1.5.1. An.Example.Where.a.p-Value.Really.Is.More.
Informative..............................................................................17
1.5.2. An.Example.Where.neither.p-Values.nor.Effect.
Size Measures.Are.Particularly.Informative......................18
1.6. Frequentist,.Bayesian.and.Likelihood.Intervals..............................19
1.7. Just.What.Is.Meant.by.the.Population?.............................................20
1.7.1. An.Outbreak.Investigation....................................................21
1.7.2. Sampling.from.a.Finite.Population......................................21
1.8. The.Unit.of.Data...................................................................................22
1.9. Sample.Size.Planning..........................................................................23
1.9.1. Sample.Size.Assessment.Based.on.a.Confidence.
Interval.for.a.Single.Group....................................................24
1.9.2. Sample.Size.Assessment.Based.on.Power.for.a.
Comparison.of.Two.Groups..................................................25
1.9.3. Sample.Size.Assessment.Based.on.Projected.
Confidence.Interval.Width.for.a.Comparison.of.
Two Groups..............................................................................26
1.9.4. Prior.and.Posterior.Power......................................................27
vii
viii Contents
2. Means and Their Differences.....................................................................29
2.1. Confidence.Interval.for.a.Mean.........................................................29
2.2. Confidence.Interval.for.the.Difference.between.Means.of.
Independent.Samples..........................................................................33
2.3. Confidence.Interval.for.the.Difference.between.Two.Means.
Based.on.Individually.Paired.Samples.............................................37
2.4. Scale.Transformation...........................................................................39
2.4.1. How.Log.Transformation.Works..........................................39
2.4.2. When.Is.Log.Transformation.Indicated?.............................43
2.4.3. Log.Transformation.for.Interrelated.Variables...................45
2.4.4. Other.Scale.Transformations.................................................51
2.5. Non-Parametric.Methods...................................................................52
2.6. The.Effect.of.Dichotomising.Continuous.Variables........................53
3. Confidence Intervals for a Simple Binomial Proportion.......................55
3.1. Introduction..........................................................................................55
3.2. The.Wald.Interval................................................................................56
3.3. Boundary.Anomalies..........................................................................58
3.4. Alternative.Intervals............................................................................60
3.4.1. The.Continuity-Corrected.Wald.Interval............................60
3.4.2. The.Delta.Logit.Interval.........................................................61
3.4.3. The.Wilson.Score.Interval.....................................................62
3.4.4. The.Clopper–Pearson.Exact.Interval...................................63
3.4.5. The.Mid-p.Interval..................................................................65
3.4.6. Bayesian.or.Beta.Intervals.....................................................66
3.4.7. Modified.Wald.Intervals........................................................67
3.4.8. Other.Intervals........................................................................68
3.5. Algebraic.Definitions.for.Several.Confidence.Intervals.for.
the.Binomial.Proportion.....................................................................69
3.6. Implementation.of.Wilson.Score.Interval.in.MS.Excel...................72
3.7. Sample.Size.for.Estimating.a.Proportion.........................................73
4. Criteria for Optimality.................................................................................77
4.1. How.Can.We.Say.Which.Methods.Are.Good.Ones?......................77
4.1.1. Structural.Criteria.for.Optimality........................................77
4.1.2. Performance.Criteria.for.Optimality...................................78
4.2. Coverage................................................................................................79
4.2.1. Just.What.Is.the.Nominal.Coverage,.1.–.α,.Meant.to.
Represent?................................................................................80
4.2.2. Why.the.First.Dip.in.Coverage.May.Be.Disregarded........82
4.2.3. Empirical.Results.Regarding.Coverage...............................86
4.3. Expected.Width....................................................................................87
4.4. Interval.Location..................................................................................90
4.4.1. General.Principles...................................................................91
4.4.2. Interval.Location.in.Simulation.Studies.of.Coverage........93