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Applied Mathematics for the Analysis of Biomedical Data E-Book

Peter J. Costa

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Herausgeber: John Wiley & Sons
Kategorie: Wissenschaft und neue Technologien
Sprache: Englisch

Beschreibung

Features a practical approach to the analysis of biomedical data via mathematical methods and provides a MATLAB® toolbox for the collection, visualization, and evaluation of experimental and real-life data Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® presents a practical approach to the task that biological scientists face when analyzing data. The primary focus is on the application of mathematical models and scientific computing methods to provide insight into the behavior of biological systems. The author draws upon his experience in academia, industry, and government-sponsored research as well as his expertise in MATLAB to produce a suite of computer programs with applications in epidemiology, machine learning, and biostatistics. These models are derived from real-world data and concerns. Among the topics included are the spread of infectious disease (HIV/AIDS) through a population, statistical pattern recognition methods to determine the presence of disease in a diagnostic sample, and the fundamentals of hypothesis testing. In addition, the author uses his professional experiences to present unique case studies whose analyses provide detailed insights into biological systems and the problems inherent in their examination. The book contains a well-developed and tested set of MATLAB functions that act as a general toolbox for practitioners of quantitative biology and biostatistics. This combination of MATLAB functions and practical tips amplifies the book's technical merit and value to industry professionals. Through numerous examples and sample code blocks, the book provides readers with illustrations of MATLAB programming. Moreover, the associated toolbox permits readers to engage in the process of data analysis without needing to delve deeply into the mathematical theory. This gives an accessible view of the material for readers with varied backgrounds. As a result, the book provides a streamlined framework for the development of mathematical models, algorithms, and the corresponding computer code. In addition, the book features: * Real-world computational procedures that can be readily applied to similar problems without the need for keen mathematical acumen * Clear delineation of topics to accelerate access to data analysis * Access to a book companion website containing the MATLAB toolbox created for this book, as well as a Solutions Manual with solutions to selected exercises Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® is an excellent textbook for students in mathematics, biostatistics, the life and social sciences, and quantitative, computational, and mathematical biology. This book is also an ideal reference for industrial scientists, biostatisticians, product development scientists, and practitioners who use mathematical models of biological systems in biomedical research, medical device development, and pharmaceutical submissions.

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Leseprobe

APPLIED MATHEMATICS FOR THE ANALYSIS OF BIOMEDICAL DATA

Models, Methods, and MATLAB®

PETER J. COSTA

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Names: Costa, Peter J., author.

Title: Applied mathematics for the analysis of biomedical data : models, methods, and

MATLAB / Peter J. Costa.

Description: Hoboken, New Jersey : John Wiley & Sons, 2016. | Includes bibliographical references

and index.

Identifiers: LCCN 2016017319 | ISBN 9781119269496 (cloth) | ISBN 9781119269519

(epub)

Subjects: LCSH: Biomathematics. | Bioinformatics--Mathematical models.

Classification: LCC QH323.5 .C683 2016 | DDC 570.1/51–dc23

LC record available at https://lccn.loc.gov/2016017319

In Dedication

Per la mia bella Anne.

L'amore della mia vita,

una luce per la nostra famiglia,

un faro per il mondo.

To William J. Satzer

A great mathematical scientist.

A better friend.

In Memoriam

I was the beneficiary of many superlative educators. Among them the late Professors George Craft, Allen Ziebur (SUNY @ Binghamton), and Edward J. Scott (University of Illinois) are owed more than I can possibly repay. It is impossible for me to adequately thank my dissertation advisor, the late Professor Melvyn S. Berger (University of Massachusetts), for his profound influence on my mathematical and personal development. But thanks are all I can presently offer. My great and avuncular late colleague, Frank P. Morrison, was an enormously positive presence in my life.

Finally, to my long deceased grandparents, I offer my most profound gratitude. You braved an ocean to come to a country where you understood neither the language nor the culture. And yet you persevered, raised families, and lived to see your grandson earn a doctorate in applied mathematics. I hope that this book honors your sacrifices, hardships, and accomplishments. Molto grazie Nonna e Nonno. Io non ho dimenticato.

Preface

Acknowledgements

About the companion website

Introduction

0.1 How to Use This Book

0.2 Data and Solutions

0.3 An Example: PSA Data

Exercises

References

1: Data

1.1 Data Visualization

Exercises

1.2 Data Transformations

Exercises

1.3 Data Filtering

Exercises

1.4 Data Clustering

Exercises

1.5 Data Quality and Data Cleaning

References

Notes

2: Some Examples

2.1 Glucose–Insulin Interaction

Exercises

2.2 Transition from

HIV

AIDS

Exercises

2.3 Real-Time Polymerase Chain Reaction

References

Further Reading

Note

3: SEIR Models

3.1 PRACTICAL APPLICATIONS OF

SEIR

MODELS

Exercises

Exercise

References

Further Reading

Notes

4: Statistical Pattern Recognition and Classification

4.1 Measurements and Data Classes

Exercise

4.2 Data Preparation, Normalization, and Weighting Matrix

4.3 Principal Components

Exercise

4.4 Discriminant Analysis

Exercises

4.5 Regularized Discriminant Analysis and Classification

Exercise

4.6 Minimum Bayes Score, Maximum Likelihood, and Minimum Bayes Risk

Exercises

4.7 The Confusion Matrix, Receiver–Operator Characteristic Curves, and Assessment Metrics

Exercises

4.8 An Example

Exercise

4.9 Nonlinear Methods

Exercises

References

Further Reading

5: Biostatistics and Hypothesis Testing

5.1 Hypothesis Testing Framework

Exercises

5.2 Test of Means

Exercise

5.3 Tests of Proportions

Exercise

5.4 Tests of Variances

Exercise

5.5 Other Hypothesis Tests

Exercises

References

Further Reading

6: Clustered Data and Analysis of Variance

6.1 Clustered Matched-Pair Data and Non-Inferiority

Exercises

6.2 Clustered Data, Assessment Metrics, and Diagnostic Likelihood Ratios

Exercise

6.3 Relative Diagnostic Likelihood Ratios

Exercises

6.4 Analysis of Variance for Clustered Data

Exercises

6.5 Examples for Anova

Exercise

6.6 Bootstrapping and Confidence Intervals

Exercise

References

Further Reading

Appendix: Mathematical Matters

A.1 Linear Least Squares Fit

A.2 Elementary Matrix Theory

A.3 Elementary Probability Theory

References

Further Reading

Glossary of MATLAB Functions

Index

EULA

List of Tables

Introduction

Table 0.1

Table 0.2

Chapter 1

Table 1.1

Table 1.2

Chapter 2

Table 2.1

Table 2.2

Chapter 3

Table 3.1

Table 3.2

Table 3.3

Table 3.4

Table 3.5

Table 3.6

Table 3.7

Table 3.8

Table 3.9

Chapter 4

Table 4.1

Table 4.2

Table 4.3

Table 4.4a

Table 4.4b

Table 4.5

Table 4.6

Table 4.7

Chapter 5

Table 5.1

Table 5.2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

Table 5.8

Table 5.9

Table 5.10

Table 5.11

Table 5.12

Table 5.13

Table 5.14

Table 5.15

Table 5.16

Table 5.17

Table 5.18

Table 5.19

Table 5.20

Table 5.21

Table 5.22

Table 5.23

Table 5.24

Table 5.25

Table 5.26

Table 5.27

Table 5.28

Table 5.29

Table 5.30

Table 5.31

Chapter 6

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Table 6.6

Table 6.7

Table 6.8a

Table 6.8b

Table 6.8c

Table 6.9

Table 6.10

Table 6.11

Table 6.12

Table 6.13

Table 6.14a

Table 6.14b

Table 6.15

Table 6.16

Table 6.17

Table 6.18a

Table 6.18b

Table 6.18c

Table 6.18d

Table 6.19

Table 6.20

Table 6.21

Table 6.22

Table 6.23

Appendix

Table A.1

Guide

Cover

Table of Contents

Preface

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Preface

This is the book I wanted. Or rather I should write, this book would have greatly benefited a considerably younger me.

Just two months after completing my graduate studies, I began my career as a professional mathematician at a prestigious research laboratory. At that time, I was well prepared to prove theorems and to make complicated analytical computations. I had no clue, however, how to model and analyze data. It will come as no surprise, then, that I was not wildly successful in my first job.

But I did learn and mostly that I needed to devise a new approach and new set of tools to solve problems which engineers, physicists, and other applied scientists faced on a day–to–day basis. This book presents some of those tools. It is written with the “new approach” that I often learned the hard way over several decades.

The approach is deceptively simple. Mathematics needs to resemble the world and not the other way around. Most of us learn iteratively. We try something, see how well it works, identify the faults of the method, modify, and try the resulting variation. This is how industrial mathematics is successfully implemented. It has been my experience that the formula of data + mathematical model + computational software can produce insightful and even powerful results. Indeed, this process has been referred to as industrial strength mathematics.

This book and its complimentary exercises have been composed to follow this methodology. The reader is encouraged to “play around” with the data, models, and software to see where those steps lead. I have also tried to streamline the presentation, especially with respect to hypothesis testing, so that the reader can locate a technique which “everyone knows” but rarely writes down.

Most of all, I hope that the reader enjoys this book. Applied mathematics is not a joyless pursuit. Getting at the heart of a matter via mathematical principles has proven most rewarding for me. Please have some fun with this material.

Acknowledgements

There are 4,632 humans (and a few avians) who found their way into this book. In particular, I wish to thank (at least) the following people.

No two people were more influential and supportive in the development of this work than Anne R. Costa and Dr. William J. Satzer. Anne is my shining light and wife of 30 years. She is aptly named as she greets my typically outlandish suggestions “sweetheart, I have this idea …” with grace and aplomb. Her good humor and editorial skills polished the book's presentation and prevented several ghastly errors. Bill Satzer read through the entire manuscript, made many insightful recommendations, and helped give the book a coherent theme. He is due significantly more than my thanks.

Dr. Vladimir Krapchev (MIT) first introduced me to the delicate dance of mathematical models and data while Dr. Laurence Jacobs (ADK) showed me the power of computational software. Dr. Adam Feldman (Massachusetts General Hospital) and Dr. James Myrtle (who developed the PSA test) greatly enhanced my understanding of prostate specific antigen levels and the associated risk of prostate cancer. Dr. Clay Thompson (Creative Creek) and Chris Griffin (St. Jude's Medical) taught me how to program in MATLAB and create numerous data analysis and visualization tools. Thomas Lane and Dr. Thomas Bryan (both of The MathWorks) helped with subtle statistical and computational issues. Professor Charles Roth (Rutgers University) guided me through the mathematical model for real–time polymerase chain reaction. Victoria A. Petrides (Abbott Diagnostics) encouraged the development of outlier filtering and exact hypothesis testing methods. Michelle D. Mitchell helped to develop the HIV/AIDS SEIR model. William H. Moore (Northrup Grumman Systems) and Constantine Arabadjis taught me the fundamentals of the extended Kalman–Bucy filter and helped me implement an automated outbreak detection method. Dr. Robert Nordstrom (NIH) first introduced me to and made me responsible for the development of statistical pattern recognition techniques as applied to the detection of cervical cancer. His influence in this work cannot be overstated. Dr. Stephen Sum (infraredx) and Professor Gilda Garibotti (Centro Regional Universitario, Bariloche) were crucial resources in the refinement of pattern recognition techniques. Professor Rüdiger Seydel (Universität Köln) invited me to his department and his home so that I could give lectures on my latest developments. Dr. Cleve Moler (The MathWorks) contributed an elegant M–file (lambertw.m) for the computation of the Lambert W function. Professor Brett Ninness (University of Newcastle) permitted the use of his team's QPC package which allowed me to compute support vector machine boundaries. Sid Mayer (Hologic) and I discussed hypothesis testing methods until we wore out several white boards and ourselves. Professor Richard Ellis (University of Massachusetts) provided keen mathematical and personal insight.

For their ontological support and enduring friendship I thank Carmen Acuña, Gus & Mary Ann Arabadjis, Elizabeth Augustine & Robert Praetorius, Sylvan Elhay & Jula Szuster, Alexander & Alla Eydeland, Alfonso & Franca Farina, Vladimir & Tania Krapchev, Stephen & Claudia Krone, Bill & Carol Link, Jack & Lanette McGovern, Bill & Amy Moore, Ernest & Rae Selig, Jim Stefanis & Cindy Sacco, Rüdiger & Friederike Seydel, Uwe Scholz, Clay & Susan Thompson, and many others. To my family, including my parents (Marie and Peter), brothers (MD, Lorenzo, JC, and E), and sisters (V, Maria, Jaki, and Pam), thank you for understanding my decidedly different view of the world. To my nieces (Coral, Jamie, Jessica, Lauren, Natalie, Nicole, Shannon, Teresa, and Zoë the brave hearted) and nephews (Anthony, Ben, Dimitris, Jack, Joseph, Matthew, and Michael) this book explains, in part, why your old uncle is forever giving you math puzzles: Now go do your homework. A hearty thanks to my mates at the Atkinson Town Pool in Sudbury, Massachusetts. There is no better way to start the day than with a swim and a laugh. Special thanks to the Department of Mathematics & Statistics at the University of Massachusetts (Amherst) for educating and always welcoming me.

To everyone mentioned above, and a those (4562?) I have undoubtedly and inadvertently omitted, please accept my sincere gratitude. This work could not exist without your support.

All mistakes are made by me and me alone, without help from anyone.

P.J. Costa Hudson, MA