Analyzing the Large Number of Variables in

This book grew out of an online interactive offered through statcourse.com, and it soon became apparent to the author that the course was too limited in terms of time and length in light of the broad backgrounds of the enrolled students. The statisticians who took the course needed to be brought up to speed both on the biological context as well as on the specialized statistical methods needed to handle large arrays. Biologists and physicians, even though fully knowledgeable concerning the procedures used to generate microaarrays, EEGs, or MRIs, needed a full introduction to the resampling methods-the bootstrap, decision trees, and permutation tests, before the specialized methods applicable to large arrays could be introduced. As the intended audience for this book consists both of statisticians and of medical and biological research workers as well as all those research workers who make use of satellite imagery including agronomists and meteorologists, the book provides a step-by-step approach to not only the specialized methods needed to analyze the data from microarrays and images, but also to the resampling methods, step-down multi-comparison procedures, multivariate analysis, as well as data collection and pre-processing. While many alternate techniques for analysis have been introduced in the past decade, the author has selected only those techniques for which software is available along with a list of the available links from which the software may be purchased or downloaded without charge. Topical coverage includes: very large arrays; permutation tests; applying permutation tests; gathering and preparing data for analysis; multiple tests; bootstrap; applying the bootstrap; classification methods; decision trees; and applying decision trees.

Phillip I. Good, PhD, is Operations Manager at Information Research, a consulting firm specializing in statistical solutions for private and public organizations. He has published more than thirty scholarly works and more than six hundred popular articles. Dr. Good is the author of Introduction to Statistics Through Resampling Methods and R/S-PLUS and Introduction to Statistics Through Resampling Methods and Microsoft Office Excel, and coauthor of Common Errors in Statistics (and How to Avoid Them), Third Edition, all published by Wiley.

Preface	p. xi
Very Large Arrays	p. 1
Applications	p. 1
Problems	p. 2
Solutions	p. 2
Permutation Tests	p. 5
Two-Sample Comparison	p. 5
Blocks	p. 7
k-Sample Comparison	p. 8
Computing The p-Value	p. 9
Monte Carlo Method	p. 10
An R Program	p. 11
Multiple-Variable Comparisons	p. 11
Euclidean Distance Matrix Analysis	p. 12
Hotelling's T²	p. 13
Mantel's U	p. 14
Combining Univariate Tests	p. 15
Gene Set Enrichment Analysis	p. 16
Categorical Data	p. 17
Software	p. 19
Summary	p. 20
Applying the Permutation Test	p. 23
Which Variables Should Be Included?	p. 24
Single-Value Test Statistics	p. 26
Categorical Data	p. 26
A Multivariate Comparison Based on a Summary Statistic	p. 26
A Multivariate Comparison Based on Variants of Hotelling's T ²	p. 28
Adjusting for Covariates	p. 29
Pre-Post Comparisons	p. 31
Choosing a Statistic: Time-Course Microarrays	p. 32
Recommended Approaches	p. 35
To Learn More	p. 35
Biological Background	p. 37
Medical Imaging	p. 37
Ultrasound	p. 38
EEG/MEG	p. 39
Magnetic Resonance Imaging	p. 41
MRI	p. 41
fMRI	p. 42
Positron Emission Tomography	p. 44
Microarrays	p. 44
To Learn More	p. 47
Multiple Tests	p. 49
Reducing the Number of Hypotheses to Be Tested	p. 50
Normalization	p. 50
Selection Methods	p. 52
Univariate Statistics	p. 52
Which Statistic?	p. 54
Heuristic Methods	p. 55
Which Method?	p. 59
Controlling the Over All Error Rate	p. 59
An Example: Analyzing Data from Microarrays	p. 60
Controlling the False Discovery Rate	p. 61
An Example: Analyzing Time-Course Data from Microarrays	p. 62
Gene Set Enrichment Analysis	p. 63
Software for Performing Multiple Simultaneous Tests	p. 67
AFNI	p. 67
Cyber-T	p. 68
dChip	p. 68
ExactFDR	p. 69
GESS	p. 69
Haplo View	p. 69
MatLab	p. 69
R	p. 70
SAM	p. 70
ParaSam	p. 71
Summary	p. 72
To Learn More	p. 72
The Bootstrap	p. 73
Samples and Populations	p. 73
Precision of an Estimate	p. 74
R Code	p. 77
Applying the Bootstrap	p. 78
Bootstrap Reproducibility Index	p. 79
Estimation in Regression Models	p. 80
Confidence Intervals	p. 82
Testing for Equivalence	p. 83
Parametric Bootstrap	p. 84
Blocked Bootstrap	p. 85
Balanced Bootstrap	p. 85
Adjusted Bootstrap	p. 86
Which Test?	p. 87
Determining Sample Size	p. 88
Establish a Threshold	p. 89
Validation	p. 90
Cluster Analysis	p. 92
Correspondence Analysis	p. 94
Building a Model	p. 96
How Large Should The Samples Be?	p. 98
Summary	p. 99
To Learn More	p. 99
Classification Methods	p. 101
Nearest Neighbor Methods	p. 101
Discriminant Analysis	p. 102
Logistic Regression	p. 103
Principal Components	p. 103
Naive Bayes Classifier	p. 104
Heuristic Methods	p. 104
Decision Trees	p. 105
A Worked-Through Example	p. 106
To Learn More	p. 99
Which Algorithm Is Best for Your Application?	p. 108
Some Further Comparisons	p. 111
Validation Versus Cross-validation	p. 112
Improving Diagnostic Effectiveness	p. 113
Boosting	p. 113
Ensemble Methods	p. 113
Random Forests	p. 114
Software for Decision Trees	p. 116
Summary	p. 117
Applying Decision Trees	p. 119
Photographs	p. 119
Ultrasound	p. 121
MRI Images	p. 122
EEGs and EMGs	p. 124
Misclassification Costs	p. 125
Receiver Operating Characteristic	p. 126
When the Categories Are As Yet Undefined	p. 127
Unsupervised Principal Components Applied to fMRI	p. 127
Supervised Principal Components Applied to Microarrays	p. 129
Ensemble Methods	p. 131
Maximally Diversified Multiple Trees	p. 131
Putting It All Together	p. 133
Summary	p. 135
To Learn More	p. 135
Glossary of Biomedical Terminology	p. 137
Glossary of Statistical Terminology	p. 141
Appendix: An R Primer	p. 153
Getting Started	p. 153
R Functions	p. 155
Vector Arithmetic	p. 156
Store and Retrieve Data	p. 156
Storing and Retrieving Files from Within R	p. 156
The Tabular Format	p. 157
Comma Separated Format	p. 158
Resampling	p. 159
The While Command	p. 159
Expanding R's Capabilities	p. 161
Downloading Libraries of R Functions	p. 161
Programming Your Own Functions	p. 161
Bibliography	p. 165
Author Index	p. 175
Subject Index	p. 181
Table of Contents provided by Ingram. All Rights Reserved.

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Analyzing the Large Number of Variables in Biomedical and Satellite Imagery

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