Sample Size Determination and Power E-Book

Thomas P. Ryan

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 779

Veröffentlichungsjahr: 2013

Beschreibung

A comprehensive approach to sample size determination and power with applications for a variety of fields Sample Size Determination and Power features a modern introduction to the applicability of sample size determination and provides a variety of discussions on broad topics including epidemiology, microarrays, survival analysis and reliability, design of experiments, regression, and confidence intervals. The book distinctively merges applications from numerous fields such as statistics, biostatistics, the health sciences, and engineering in order to provide a complete introduction to the general statistical use of sample size determination. Advanced topics including multivariate analysis, clinical trials, and quality improvement are addressed, and in addition, the book provides considerable guidance on available software for sample size determination. Written by a well-known author who has extensively class-tested the material, Sample Size Determination and Power: * Highlights the applicability of sample size determination and provides extensive literature coverage * Presents a modern, general approach to relevant software to guide sample size determination including CATD (computer-aided trial design) * Addresses the use of sample size determination in grant proposals and provides up-to-date references for grant investigators An appealing reference book for scientific researchers in a variety of fields, such as statistics, biostatistics, the health sciences, mathematics, ecology, and geology, who use sampling and estimation methods in their work, Sample Size Determination and Power is also an ideal supplementary text for upper-level undergraduate and graduate-level courses in statistical sampling.

Leseprobe

Contents

Cover

Series

Title Page

Copyright

Preface

Chapter 1: Brief Review of Hypothesis Testing Concepts/Issues and Confidence Intervals

1.1 BASIC CONCEPTS OF HYPOTHESIS TESTING

1.2 REVIEW OF CONFIDENCE INTERVALS AND THEIR RELATIONSHIP TO HYPOTHESIS TESTS

1.3 SPORTS APPLICATIONS

1.4 OBSERVED POWER, RETROSPECTIVE POWER, CONDITIONAL POWER, AND PREDICTIVE POWER

1.5 TESTING FOR EQUALITY, EQUIVALENCE, NONINFERIORITY, OR SUPERIORITY

REFERENCES

EXERCISES

Chapter 2: Methods of Determining Sample Sizes

2.1 INTERNAL PILOT STUDY VERSUS EXTERNAL PILOT STUDY

2.2 EXAMPLES: FREQUENTIST AND BAYESIAN

2.3 FINITE POPULATIONS

2.4 SAMPLE SIZES FOR CONFIDENCE INTERVALS

2.5 CONFIDENCE INTERVALS ON SAMPLE SIZE AND POWER

2.6 SPECIFICATION OF POWER

2.7 COST OF SAMPLING

2.8 ETHICAL CONSIDERATIONS

2.9 STANDARDIZATION AND SPECIFICATION OF EFFECT SIZES

2.10 EQUIVALENCE TESTS

2.11 SOFTWARE AND APPLETS

2.12 SUMMARY

REFERENCES

EXERCISES

Chapter 3: Means and Variances

3.1 ONE MEAN, NORMALITY, AND KNOWN STANDARD DEVIATION

3.2 ONE MEAN, STANDARD DEVIATION UNKNOWN, NORMALITY ASSUMED

3.3 CONFIDENCE INTERVALS ON POWER AND/OR SAMPLE SIZE

3.4 ONE MEAN, STANDARD DEVIATION UNKNOWN, NONNORMALITY ASSUMED

3.5 ONE MEAN, EXPONENTIAL DISTRIBUTION

3.6 TWO MEANS, KNOWN STANDARD DEVIATIONS—INDEPENDENT SAMPLES

3.7 TWO MEANS, UNKNOWN BUT EQUAL STANDARD DEVIATIONS—INDEPENDENT SAMPLES

3.8 TWO MEANS, UNEQUAL VARIANCES AND SAMPLE SIZES—INDEPENDENT SAMPLES

3.9 TWO MEANS, UNKNOWN AND UNEQUAL STANDARD DEVIATIONS—INDEPENDENT SAMPLES

3.10 TWO MEANS, KNOWN AND UNKNOWN STANDARD DEVIATIONS—DEPENDENT SAMPLES

3.11 BAYESIAN METHODS FOR COMPARING MEANS

3.12 ONE VARIANCE OR STANDARD DEVIATION

3.13 TWO VARIANCES

3.14 MORE THAN TWO VARIANCES

3.15 CONFIDENCE INTERVALS

3.16 RELATIVE PRECISION

3.17 COMPUTING AIDS

3.18 SOFTWARE

3.19 SUMMARY

APPENDIX

REFERENCES

EXERCISES

Chapter 4: Proportions and Rates

4.1 ONE PROPORTION

4.2 TWO PROPORTIONS

4.3 MULTIPLE PROPORTIONS

4.4 MULTINOMIAL PROBABILITIES AND DISTRIBUTIONS

4.5 ONE RATE

4.6 TWO RATES

4.7 BAYESIAN SAMPLE SIZE DETERMINATION METHODS FOR RATES

4.8 SOFTWARE

4.9 SUMMARY

APPENDIX

REFERENCES

EXERCISES

Chapter 5: Regression Methods and Correlation

5.1 LINEAR REGRESSION

5.2 LOGISTIC REGRESSION

5.3 COX REGRESSION

5.4 POISSON REGRESSION

5.5 NONLINEAR REGRESSION

5.6 OTHER TYPES OF REGRESSION MODELS

5.7 CORRELATION

5.8 SOFTWARE

5.9 SUMMARY

REFERENCES

EXERCISES

Chapter 6: Experimental Designs

6.1 ONE FACTOR—TWO FIXED LEVELS

6.2 ONE FACTOR—MORE THAN TWO FIXED LEVELS

6.3 TWO FACTORS

6.4 2K DESIGNS

6.5 2K−P DESIGNS

6.6 DETECTING CONDITIONAL EFFECTS

6.7 GENERAL FACTORIAL DESIGNS

6.8 REPEATED MEASURES DESIGNS

6.9 RESPONSE SURFACE DESIGNS

6.10 MICROARRAY EXPERIMENTS

6.11 OTHER DESIGNS

6.12 DESIGNS FOR NONNORMAL RESPONSES

6.13 DESIGNS WITH RANDOM FACTORS

6.14 ZERO PATIENT DESIGN

6.15 COMPUTER EXPERIMENTS

6.16 NONINFERIORITY AND EQUIVALENCE DESIGNS

6.17 PHARMACOKINETIC EXPERIMENTS

6.18 BAYESIAN EXPERIMENTAL DESIGN

6.19 SOFTWARE

6.20 SUMMARY

APPENDIX

DERIVATION OF EQ. (6.1)

REFERENCES

EXERCISES

Chapter 7: Clinical Trials

7.1 CLINICAL TRIALS

7.2 BIOEQUIVALENCE STUDIES

7.3 ETHICAL CONSIDERATIONS

7.4 THE USE OF POWER IN CLINICAL STUDIES

7.5 PRECLINICAL EXPERIMENTATION

7.6 PHARMACODYNAMIC, PHARMACOKINETIC, AND PHARMACOGENETIC EXPERIMENTS

7.7 METHOD OF COMPETING PROBABILITY

7.8 BAYESIAN METHODS

7.9 COST AND OTHER SAMPLE SIZE DETERMINATION METHODS FOR CLINICAL TRIALS

7.10 META-ANALYSES OF CLINICAL TRIALS

7.11 MISCELLANEOUS

7.12 SURVEY RESULTS OF PUBLISHED ARTICLES

7.13 SOFTWARE

7.14 SUMMARY

REFERENCES

EXERCISES

Chapter 8: Quality Improvement

8.1 CONTROL CHARTS

8.2 MEDICAL APPLICATIONS

8.3 PROCESS CAPABILITY INDICES

8.4 TOLERANCE INTERVALS

8.5 MEASUREMENT SYSTEM APPRAISAL

8.6 ACCEPTANCE SAMPLING

8.7 RELIABILITY AND LIFE TESTING

8.8 SOFTWARE

8.9 SUMMARY

REFERENCES

EXERCISES

Chapter 9: Survival Analysis and Reliability

9.1 SURVIVAL ANALYSIS

9.2 RELIABILITY ANALYSIS

9.3 SUMMARY

REFERENCES

EXERCISES

Chapter 10: Nonparametric Methods

10.1 WILCOXON ONE-SAMPLE TEST

10.2 WILCOXON TWO--SAMPLE TEST (MANN--WHITNEY TEST)

10.3 KRUSKAL--WALLIS ONE-WAY ANOVA

10.4 SIGN TEST

10.5 McNEMAR'S TEST

10.6 CONTINGENCY TABLES

10.7 QUASI-LIKELIHOOD METHOD

10.8 RANK CORRELATION COEFFICIENTS

10.9 SOFTWARE

10.10 SUMMARY

REFERENCES

EXERCISES

Chapter 11: Miscellaneous Topics

11.1 CASE–CONTROL STUDIES

11.2 EPIDEMIOLOGY

11.3 LONGITUDINAL STUDIES

11.4 MICROARRAY STUDIES

11.5 RECEIVER OPERATING CHARACTERISTIC ROC CURVES

11.6 META-ANALYSES

11.7 SEQUENTIAL SAMPLE SIZES

11.8 SAMPLE SURVEYS

11.9 CLUSTER SAMPLING

11.10 FACTOR ANALYSIS

11.11 MULTIVARIATE ANALYSIS OF VARIANCE AND OTHER MULTIVARIATE METHODS

11.12 STRUCTURAL EQUATION MODELING

11.13 MULTILEVEL MODELING

11.14 PREDICTION INTERVALS

11.15 MEASURES OF AGREEMENT

11.16 SPATIAL STATISTICS

11.17 AGRICULTURAL APPLICATIONS

11.18 ESTIMATING THE NUMBER OF UNSEEN SPECIES

11.19 TEST RELIABILITY

11.20 AGREEMENT STUDIES

11.21 GENOME-WIDE ASSOCIATION STUDIES

11.22 NATIONAL SECURITY

11.23 MISCELLANEOUS

11.24 SUMMARY

REFERENCES

Answers to Selected Exercises

Index

WILEY SERIES IN PROBABILITY AND STATISTICS

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Cover design: John Wiley & Sons, Inc. Cover image: © Thomas P. Ryan

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Library of Congress Cataloging-in-Publication Data:

Ryan, Thomas P., 1945–   Sample size determination and power / Thomas P. Ryan.     p. ; cm.   Includes bibliographical references and index.   ISBN 978-1-118-43760-5 (cloth)   I. Title.   [DNLM: 1. Sample Size.  2. Clinical Trials as Topic.  3. Mathematical Computing.  4. Regression Analysis.  5. Sampling Studies. WA 950]   615.5072′4–dc23

2013000329

Preface

Determining a good sample size to use in a scientific study is of utmost importance, especially in clinical studies with some participants receiving a placebo or nothing at all and others taking a drug whose efficacy has not been established. It is imperative that a large enough sample be used so that an effect that is large enough to be of practical significance has a high probability of being detected from the study. That is, the study should have sufficient power. It is also important that sample sizes not be larger than necessary so that the cost of a study not be any larger than necessary and to minimize risk to human subjects in drug studies.

Compared to other subjects in the field of statistics, there is a relative paucity of books on sample size determination and power, especially general purpose books. The classic book on the subject has for decades been Jacob Cohen's Statistical Power Analysis for the Behavioral Sciences, the second edition of which was published in 1988. That book is oriented, as the title indicates, toward the behavioral sciences, with the statistical methodology being quite useful in the behavioral sciences. The second edition has 567 numbered pages, 208 of which are tables, reflecting the “noncomputer” age in which the two editions of the book were written. In contrast, the relatively recent book by Patrick Dattalo, Determining Sample Size: Balancing Power, Precision, and Practicality (2008), which is part of the series in Pocket Guides to Social Work Research Methods, is 167 pages with more than 20% consisting of tables and screen displays reflecting the now heavy reliance on software for sample size determination. An even smaller book is Sample Size Methodology (1990) by Desu and Raghavarao at 135 pages, while How Many Subjects: Statistical Power Analysis in Research (1987) by Kraemer and Thiemann is just 120 pages and was stated in a review as being an extension of a 1985 journal article by Kraemer. Sample-Size Determination (1964) by Mace is larger at 226 pages and Sample Size Choice: Charts for Experimenters, 2nd ed. (1991) by Odeh and Fox is 216 pages. Thus, some rather small books have been published on the subject, with almost all of these books having been published over 20 years ago.

At the other extreme in terms of size, focus, and mathematical sophistication, there are books on sample determination for clinical studies, such as Sample Size Calculations in Clinical Research, 2nd ed. (2008) by Chow, Shao, and Wang, that are mathematically sophisticated, with the title of this book perhaps suggesting that. A similar recent book is Sample Sizes for Clinical Trials (2010) by Julious, whereas Sample Size Calculations: Practical Methods for Engineers and Scientists (2010) by Mathews is oriented toward engineering and industrial applications.

There are additional statistical methods that are useful in fields other than behavioral sciences, social sciences, and clinical trials, however, and during the past two decades new needs for sample size determination have arisen in fields that are part of the advancement of science, such as microarray experiments.

Although many formulas are given in Cohen's book, they are not derived in either the chapters or chapter appendices, so the inquisitive reader is left wondering how the formulas came about.

Software is also not covered in Cohen's book, nor is software discussed in the books by Mathews, Julious or Chow, Shao, and Wang. Software and Java applets for sample size determination are now fairly prevalent and, of course, are more useful than tables since theoretically there are an infinite number of values that could be entered for one or more parameter values. There was a need for a book that has a broader scope than Cohen's book and that gives some of the underlying math for interested readers, as well as having a strong software focus, along the lines of Dattalo's book, but is not too mathematical for a general readership. No such book met these requirements at the time of writing, which is why this book was written.

This book can be used as a reference book as well as a textbook in special topics courses. Software discussion and illustration is integrated with the subject matter, and there is also a summary section on software at the end of most chapters. Mixing software discussion with subject matter may seem unorthodox, but I believe this is the best way to cover the material since almost every experimenter faced with software determination will probably feel the need to use software and should know what is available in terms of various software and applets. So the book is to a significant extent a software guide, with considerable discussion about the capabilities of each software package. There is also a very large number of references, considerably more than in any other book on the subject.

THOMAS P. RYAN

Smyrna, GeorgiaOctober 2012

CHAPTER 2

Methods of Determining Sample Sizes

Sample size and power determinations are an important and necessary component of research grant proposals, including proposals involving clinical trials submitted to the National Institutes of Health (NIH). Biostatisticians often assist in the statistical part of grant proposals and are often a member of the research team. The guidelines for researchers provided by the Quantitative Methods Core of the Department of Quantitative Health Sciences in the University of Massachusetts Medical School may be of interest ().