Table Of Content

R C Statistics e o l n a fi t e d Confidence Intervals for Proportions and Related Measures of d e Confidence Intervals Effect Size illustrates the use of effect size measures and corresponding n M c confidence intervals as more informative alternatives to the most basic e e for Proportions and and widely used significance tests. The book provides you with a deep a I understanding of what happens when these statistical methods are applied s n in situations far removed from the familiar Gaussian case. u t Related Measures r e Drawing on his extensive work as a statistician and professor at Cardiff e r s v University School of Medicine, the author brings together methods for a of Effect Size o calculating confidence intervals for proportions and several other important l f s measures, including differences, ratios, and nonparametric effect size E f measures generalizing Mann–Whitney and Wilcoxon tests. He also explains o f three important approaches to obtaining intervals for related measures. f r e Many examples illustrate the application of the methods in the health and c P r social sciences. Requiring little computational skills, the book offers user- t o friendly Excel spreadsheets for download, enabling you to easily apply the S p methods to your own empirical data. iz o e r Features t i o • Discusses the rationale for point and interval estimates as the n mainstays of statistical inference s • Develops and evaluates confidence intervals for a wide range of a measures related to proportions n • 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 N e w c o m b Robert G. Newcombe e 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 Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20120629 International Standard Book Number-13: 978-1-4398-1279-2 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com 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