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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley Series in Probability and Statistics
- Sprache: Englisch
Provides a one-stop resource for engineers learning biostatistics using MATLAB® and WinBUGS Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing bio-oriented engineering fields while implementing software packages that are familiar to engineers. The book is heavily oriented to computation and hands-on approaches so readers understand each step of the programming. Another dimension of this book is in parallel coverage of both Bayesian and frequentist approaches to statistical inference. It avoids taking sides on the classical vs. Bayesian paradigms, and many examples in this book are solved using both methods. The results are then compared and commented upon. Readers have the choice of MATLAB® for classical data analysis and WinBUGS/OpenBUGS for Bayesian data analysis. Every chapter starts with a box highlighting what is covered in that chapter and ends with exercises, a list of software scripts, datasets, and references. Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS also includes: * parallel coverage of classical and Bayesian approaches, where appropriate * substantial coverage of Bayesian approaches to statistical inference * material that has been classroom-tested in an introductory statistics course in bioengineering over several years * exercises at the end of each chapter and an accompanying website with full solutions and hints to some exercises, as well as additional materials and examples Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS can serve as a textbook for introductory-to-intermediate applied statistics courses, as well as a useful reference for engineers interested in biostatistical approaches.
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ENGINEERINGBIOSTATISTICS
An Introduction using MATLAB® and WinBUGS
BRANI VIDAKOVIC
This edition first published 2017© 2017 Brani Vidakovic
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Library of Congress Cataloging-in-Publication Data:
Names: Vidakovic, Brani, 1955- author. Title: Engineering biostatistics: an introduction using MATLAB and WinBUGS / Brani Vidakovic. Description: Hoboken, New Jersey : John Wiley & Sons, 2017. | Includes bibliographical references and index. Identifiers: LCCN 2016042853| ISBN 9781119168966 (cloth) | ISBN 9781119168980 (epub) Subjects: LCSH: MATLAB. | WinBUGS. | Biometry--Statistical methods. | Engineering--Statistical methods.
Classification: LCC QH323.5 .V53 2017 | DDC 570.1/5195--dc23 LC record available at https://lccn.loc.gov/2016042853
Cover images: (Background) © John Lund/Gettyimages; (Figures) Courtesy of author Cover design by Wiley
CONTENTS
Preface
Acknowledgments
Chapter 1: Introduction
Chapter References
Chapter 2: The Sample and Its Properties
2.1 Introduction
2.2 A MATLAB Session on Univariate Descriptive Statistics
2.3 Location Measures
2.4 Variability Measures
2.5 Ranks
2.6 Displaying Data
2.7 Multidimensional Samples: Fisher's Iris Data and Body Fat Data
2.8 Multivariate Samples and Their Summaries*
2.9 Principal Components of Data
2.10 Visualizing Multivariate Data
2.11 Observations as Time Series
2.12 About Data Types
2.13 Big Data Paradigm
2.14 Exercises
Chapter References
Chapter 3: Probability, Conditional Probability, and Bayes’ Rule
3.1 Introduction
3.2 Events and Probability
3.3 Odds
3.4 Venn Diagrams*
3.5 Counting Principles*
3.6 Conditional Probability and Independence of Events
3.7 Total Probability
3.8 Reassessing Probabilities: Bayes’ Rule
3.9 Bayesian Networks*
3.10 Exercises
Chapter References
Chapter 4: Sensitivity, Specificity, and Relatives
4.1 Introduction
4.2 Notation
4.3 Combining Two or More Tests
4.4 ROC Curves
4.5 Exercises
Chapter References
Chapter 5: Random Variables
5.1 Introduction
5.2 Discrete Random Variables
5.3 Some Standard Discrete Distributions
5.4 Continuous Random Variables
5.5 Some Standard Continuous Distributions
5.6 Random Numbers and Probability Tables
5.7 Transformations of Random Variables*
5.8 Mixtures*
5.9 Markov Chains*
5.10 Exercises
Chapter References
Chapter 6: Normal Distribution
6.1 Introduction
6.2 Normal Distribution
6.3 Examples with a Normal Distribution
6.4 Combining Normal Random Variables
6.5 Central Limit Theorem
6.6 Distributions Related to Normal
6.7 Delta Method and Variance-Stabilizing Transformations
*
6.8 Exercises
Chapter References
Chapter 7: Point and Interval Estimators
7.1 Introduction
7.2 Moment-Matching and Maximum Likelihood Estimators
7.3 Unbiasedness and Consistency of Estimators
7.4 Estimation of a Mean, Variance, and Proportion
7.5 Confidence Intervals
7.6 Prediction and Tolerance Intervals
*
7.7 Confidence Intervals for Quantiles
*
7.8 Confidence Intervals for the Poisson Rate
*
7.9 Exercises
Chapter References
Chapter 8: Bayesian Approach to Inference
8.1 Introduction
8.2 Ingredients for Bayesian Inference
8.3 Conjugate Priors
8.4 Point Estimation
8.5 Prior Elicitation
8.6 Bayesian Computation and Use of WinBUGS
8.7 Bayesian Interval Estimation: Credible Sets
8.8 Learning by Bayes' Theorem
8.9 Bayesian Prediction
8.10 Consensus Means*
8.11 Exercises
Chapter References
Chapter 9: Testing Statistical Hypotheses
9.1 Introduction
9.2 Classical Testing Problem
9.3 Bayesian Approach to Testing
9.4 Criticism and Calibration of
p
-Values
*
9.5 Testing the Normal Mean
9.6 Testing the Multivariate Normal Mean
*
9.7 Testing the Normal Variances
9.8 Testing the Proportion
9.9 Multiplicity in Testing, Bonferroni Correction, and False Discovery Rate
9.10 Exercises
Chapter References
Chapter 10: Two Samples
10.1 Introduction
10.2 Means and Variances in Two Independent Normal Populations
10.3 Testing the Equality of Normal Means When Samples Are Paired
10.4 Two Multivariate Normal Means*
10.5 Two Normal Variances
10.6 Comparing Two Proportions
10.7 Risk Differences, Risk Ratios, and Odds Ratios
10.8 Two Poisson Rates*
10.9 Equivalence Tests*
10.10 Exercises
Chapter References
Chapter 11: ANOVA and Elements of Experimental Design
11.1 Introduction
11.2 One-Way ANOVA
11.3 Welch's ANOVA*
11.4 Two-Way ANOVA and Factorial Designs
11.5 Blocking
11.6 Repeated Measures Design
11.7 Nested Designs*
11.8 Power Analysis in ANOVA
11.9 Functional ANOVA*
11.10 Analysis of Means (ANOM)*
11.11 The Capability of a Measurement System (Gauge R&R ANOVA)*
11.12 Testing Equality of Several Proportions
11.13 Testing the Equality of Several Poisson Means*
11.14 Exercises
Chapter References
Chapter 12: Models for Tables
12.1 Introduction
12.2 Contingency Tables: Testing for Independence
12.3 Three-Way Tables
12.4 Contingency Tables with Fixed Marginals: Fisher's Exact Test
12.5 Stratified Tables: Mantel–Haenszel Test
12.6 Paired Tables: McNemar's Test
12.7 Risk Differences, Risk Ratios, and Odds Ratios for Paired Tables
12.8 Exercises
Chapter References
Chapter 13: Correlation
13.1 Introduction
13.2 The Pearson Coefficient of Correlation
13.3 Spearman's Coefficient of Correlation
13.4 Kendall's Tau
13.5
Cum hoc ergo propter hoc
13.6 Exercises
Chapter References
Chapter 14: Regression
14.1 Introduction
14.2 Simple Linear Regression
14.3 Inference in Simple Linear Regression
14.4 Calibration
14.5 Testing the Equality of Two Slopes*
14.6 Multiple Regression
14.7 Diagnostics in Multiple Regression
14.8 Sample Size in Regression
14.9 Linear Regression That Is Nonlinear in Predictors
14.10 Errors-in-Variables Linear Regression*
14.11 Analysis of Covariance
14.12 Exercises
Chapter References
Chapter 15: Regression for Binary and Count Data
15.1 Introduction
15.2 Logistic Regression
15.3 Poisson Regression
15.4 Log-linear Models
15.5 Exercises
Chapter References
Chapter 16: Inference for Censored Data and Survival Analysis
16.1 Introduction
16.2 Definitions
16.3 Inference with Censored Observations
16.4 The Cox Proportional Hazards Model
16.5 Bayesian Approach
16.6 Survival Analysis in WinBUGS
16.7 Exercises
Chapter References
Chapter 17: Goodness-of-Fit Tests
17.1 Introduction
17.2 Probability Plots
17.3 Pearson's Chi-Square Test
17.4 Kolmogorov–Smirnov Tests
17.5 Cramér-von Mises and Watson's Tests*
17.6 Rosenblatt's Test*
17.7 Moran's Test*
17.8 Departures from Normality
17.9 Ellimination of Unknown Parameters by Transformations
17.10 Exercises
Chapter References
Chapter 18: Distribution-Free Methods
18.1 Introduction
18.2 Sign Test
18.3 Wilcoxon Signed-Rank Test
18.4 Wilcoxon Sum-Rank and Mann–Whitney Tests
18.5 Kruskal–Wallis Test
18.6 Friedman's Test
18.7 Resampling Methods
18.8 Exercises
Chapter References
Chapter 19: Bayesian Inference Using Gibbs Sampling - BUGS Project
19.1 Introduction
19.2 Step-by-Step Session
19.3 Built-in Functions and Common Distributions in WinBUGS
19.4 MATBUGS: A MATLAB Interface to WinBUGS
19.5 Exercises
Chapter References
Index
EULA
List of Tables
Chapter 2
Table 2.1
Table 2.2
Chapter 3
Table 3.1
Table 3.2
Chapter 6
Table 6.1
Chapter 8
Table 8.1
Chapter 9
Table 9.1
Chapter 12
Table 12.1
Table 12.2
Table 12.3
Table 12.4
Table 12.5
Chapter 14
Table 14.1
Table 14.2
Chapter 15
Table 15.1
Table 15.2
Table 15.3
Table 15.4
Table 15.5
Table 15.6
Table 15.7
Chapter 19
Table 19.1
Table 19.2
Guide
Cover
Table of Contents
Preface
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Preface
Let's say you commit to 2 hours per day and you're able to write 3 pages per hour. To write an average length book of 300 pages will take 50 days. (300 pages per book/6 pages per day = 50 days).
A posting on Life Learning Today: How to Write a Book in 60 Days or Less.
By not following the recommendations from the above quote the writing of this book took much longer. The book is a result of many semesters of teaching various statistical courses to engineering students at Duke University and the Georgia Institute of Technology. Through its scope and depth of coverage, the book addresses the needs of the vibrant and rapidly growing engineering fields while implementing software that engineers are familiar with.
This book is substantially revised version of the text originally published by Springer in 2011 (ISBN 978-1-4614-0394-4). In addition to providing many new examples and exercises, a number of new sections is added. The original edition served as a primary textbook for the course Introduction to Bioengineering Statistics, at The Wallace H. Coulter Department of Biomedical Engineering at Georgia Tech for 6 consecutive semesters. I noticed that it was used not only as a textbook but students found it useful as a repository of techniques for data analysis in other courses, class projects, senior design projects, and day-to-day laboratory data analysis. So by its scope this book is both: a textbook for introductory-to-intermediate applied biostatistics courses and a reference book with a coverage of a number of rather specialized techniques.
This book is heavily oriented to computation and hands-on approaches. The approach enforced avoids the use of mainstream statistical packages in which the procedures are often black-boxed. Rather, the students are expected to code the procedures on their own. The results may not be as flashy as they would be if the specialized packages were used, but the student will go through the process and understand each step of the program.
The computational support for this text is the MATLAB© programming environment since this software is predominant in the engineering communities.
Another dimension of this book is in the substantial coverage of Bayesian approaches to statistical inference. I avoided taking sides on the traditional (classical, frequentist) vs. Bayesian approach; it was my goal to expose students to both approaches. It is undeniable that classical statistics is overwhelmingly used in conducting and reporting inference among practitioners, and that Bayesian statistics is gaining in popularity, acceptance, and usage (FDA, Guidance for the Use of Bayesian Statistics in Medical Device Clinical Trials, 5 February 2010). Many examples in this book are solved using both the traditional and Bayesian methods, and the results are compared and commented upon.
This diversification is made possible by advances in Bayesian computation and the availability of the free software WinBUGS/OpenBUGS that provides painless computational support for Bayesian solutions. WinBUGS and MATLAB communicate well due to the interface software MATBUGS, written by Kevin P. Murphy and coauthors. The book also relies on stat toolbox within MATLAB.
The World Wide Web (WWW) facilitates the book. All custom-made MATLAB and WinBUGS programs (compatible with MATLAB R2017a and WinBUGS 1.4.3 or OpenBUGS 3.2.3) as well as data sets used in this book are available on the Web:
http://statbook.gatech.edu/
With the size of this book in mind the solutions and hints to some exercises can be found on the book's Web site. The computer scripts and examples are an integral part of the book, and all MATLAB codes and outputs are shown in blue typewriter font while all WinBUGS programs are given in red-brown typewriter font. The comments in MATLAB and WinBUGS codes are presented in green typewriter font.
The three icons , , and are used to point to data sets, MATLAB codes, and WinBUGS codes, respectively.
The difficulty of the material covered necessarily varies. More difficult sections that may be omitted in the basic coverage are denoted by a star, *. However, it is my experience that advanced undergraduate bioengineering students affiliated with school research labs need and use the “starred” material, such as functional ANOVA, variance stabilizing transforms, and nested experimental designs, to name just a few. Tricky or difficult places are marked with Donald Knut's “bend” .
Each chapter starts with a box titled WHAT IS COVERED IN THIS CHAPTER and ends with chapter exercises, a box called MATLAB AND WINBUGS FILES AND DATA SETS USED IN THIS CHAPTER, and chapter references.
The examples are numbered and the end of each example is marked with .
I am aware that this work could be improved with respect to both exposition and coverage. Thus, I would welcome any criticism and pointers from readers as to how this book could be improved.
Acknowledgments
I am indebted to many students and colleagues who commented on various drafts of the book. In particular I am grateful to colleagues from the Department of Biomedical Engineering at the Georgia Institute of Technology and Emory University and their undergraduate and graduate advisees/researchers who contributed many examples and data sets from their research labs.
Colleagues Tom Bylander of the University of Texas at San Antonio, John H. McDonald of the University of Delaware, and Roger W. Johnson of the South Dakota School of Mines & Technology kindly gave permission to use their data and examples. Special thanks go to Dr. Gary M. Raymond from University of Washington who provided useful feedback on several occasions. Several MATLAB codes used in this book come from the MATLAB Central File Exchange forum. In particular, I am grateful to Antonio Truillo-Ortiz and his team (Universidad Autonoma de Baja California) and to Giuseppe Cardillo (MeriGen Research) for their excellent contributions.
The book benefited from the input of many diligent students when it was used either as a supplemental reading or later as a draft textbook for a semester-long course at Georgia Tech: BMED2400 Introduction to Bioengineering Statistics. A complete list of students who provided useful feedback would be quite long, but the most diligent ones were Erin Hamilton, Kiersten Petersen, David Dreyfus, Jessica Kanter, Radu Reit, Amoreth Gozo, Nader Aboujamous, and Allison Chan. Special thanks go to Brett Jordan, who, as multiple-time Teaching Assistant for Bioengineering Statistics course, pointed out numerous places for text improvement.
Wiley's team kindly helped along the way. I am grateful to Jon Gurstelle, Allison McGinniss, Kathleen Pagliaro, and Melissa Yanuzzi for their encouragement and support. Finally, it hardly needs stating that the book would have been considerably less fun to write without the unconditional support of my family.
BRANI VIDAKOVIC
School of Industrial and Systems Engineering and
School of Biomedical Engineering
Georgia Institute of Technology
