Statistical Bioinformatics E-Book

Jae K. Lee

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

Seitenzahl: 660

Veröffentlichungsjahr: 2011

Beschreibung

This book provides an essential understanding of statistical concepts necessary for the analysis of genomic and proteomic data using computational techniques. The author presents both basic and advanced topics, focusing on those that are relevant to the computational analysis of large data sets in biology. Chapters begin with a description of a statistical concept and a current example from biomedical research, followed by more detailed presentation, discussion of limitations, and problems. The book starts with an introduction to probability and statistics for genome-wide data, and moves into topics such as clustering, classification, multi-dimensional visualization, experimental design, statistical resampling, and statistical network analysis.

• Clearly explains the use of bioinformatics tools in life sciences research without requiring an advanced background in math/statistics
• Enables biomedical and life sciences researchers to successfully evaluate the validity of their results and make inferences
• Enables statistical and quantitative researchers to rapidly learn novel statistical concepts and techniques appropriate for large biological data analysis
• Carefully revisits frequently used statistical approaches and highlights their limitations in large biological data analysis
• Offers programming examples and datasets
• Includes chapter problem sets, a glossary, a list of statistical notations, and appendices with references to background mathematical and technical material
• Features supplementary materials, including datasets, links, and a statistical package available online

Statistical Bioinformatics is an ideal textbook for students in medicine, life sciences, and bioengineering, aimed at researchers who utilize computational tools for the analysis of genomic, proteomic, and many other emerging high-throughput molecular data. It may also serve as a rapid introduction to the bioinformatics science for statistical and computational students and audiences who have not experienced such analysis tasks before.

Leseprobe

Contents

PREFACE

CONTRIBUTORS

CHAPTER 1 ROAD TO STATISTICAL BIOINFORMATICS

CHALLENGE 1: MULTIPLE-COMPARISONS ISSUE

CHALLENGE 2: HIGH-DIMENSIONAL BIOLOGICAL DATA

CHALLENGE 3: SMALL-n AND LARGE-p PROBLEM

CHALLENGE 4: NOISY HIGH-THROUGHPUT BIOLOGICAL DATA

CHALLENGE 5: INTEGRATION OF MULTIPLE, HETEROGENEOUS BIOLOGICAL DATA INFORMATION

REFERENCES

CHAPTER 2 PROBABILITY CONCEPTS AND DISTRIBUTIONS FOR ANALYZING LARGE BIOLOGICAL DATA

2.1 INTRODUCTION

2.2 BASIC CONCEPTS

2.3 CONDITIONAL PROBABILITY AND INDEPENDENCE

2.4 RANDOM VARIABLES

2.5 EXPECTED VALUE AND VARIANCE

2.6 DISTRIBUTIONS OF RANDOM VARIABLES

2.7 JOINT AND MARGINAL DISTRIBUTION

2.8 MULTIVARIATE DISTRIBUTION

2.9 SAMPLING DISTRIBUTION

2.10 SUMMARY

CHAPTER 3 QUALITY CONTROL OF HIGH-THROUGHPUT BIOLOGICAL DATA

3.1 SOURCES OF ERROR IN HIGH-THROUGHPUT BIOLOGICAL EXPERIMENTS

3.2 STATISTICAL TECHNIQUES FOR QUALITY CONTROL

3.3 ISSUES SPECIFIC TO MICROARRAY GENE EXPRESSION EXPERIMENTS

3.4 CONCLUSION

REFERENCES

CHAPTER 4 STATISTICAL TESTING AND SIGNIFICANCE FOR LARGE BIOLOGICAL DATA ANALYSIS

4.1 INTRODUCTION

4.2 STATISTICAL TESTING

4.3 ERROR CONTROLLING

4.4 REAL DATA ANALYSIS

4.5 CONCLUDING REMARKS

ACKNOWLEDGEMENTS

REFERENCES

CHAPTER 5 CLUSTERING: UNSUPERVISED LEARNING IN LARGE BIOLOGICAL DATA

5.1 MEASURES OF SIMILARITY

5.2 CLUSTERING

5.3 ASSESSMENT OF CLUSTER QUALITY

5.4 CONCLUSION

REFERENCES

CHAPTER6 CLASSIFICATION: SUPERVISED LEARNING WITH HIGH-DIMENSIONAL BIOLOGICAL DATA

6.1 INTRODUCTION

6.2 CLASSIFICATION AND PREDICTION METHODS

6.3 FEATURE SELECTION AND RANKING

6.4 CROSS-VALIDATION

6.5 ENHANCEMENT OF CLASS PREDICTION BY ENSEMBLE VOTING METHODS

6.6 COMPARISON OF CLASSIFICATION METHODS USING HIGH-DIMENSIONAL DATA

6.7 SOFTWARE EXAMPLES FOR CLASSIFICATION METHODS

REFERENCES

CHAPTER 7 MULTIDIMENSIONAL ANALYSIS AND VISUALIZATION ON LARGE BIOMEDICAL DATA*

7.1 INTRODUCTION

7.2 CLASSICAL MULTIDIMENSIONAL VISUALIZATION TECHNIQUES

7.3 TWO-DIMENSIONAL PROJECTIONS

7.4 ISSUES AND CHALLENGES

7.5 SYSTEMATIC EXPLORATION OF LOW-DIMENSIONAL PROJECTIONS

7.6 ONE-DIMENSIONAL HISTOGRAM ORDERING

7.7 TWO-DIMENSIONAL SCATTERPLOT ORDERING

7.8 CONCLUSION

REFERENCES

CHAPTER 8 STATISTICAL MODELS, INFERENCE, AND ALGORITHMS FOR LARGE BIOLOGICAL DATA ANALYSIS

8.1 INTRODUCTION

8.2 STATISTICAL/PROBABILISTIC MODELS

8.3 ESTIMATION METHODS

8.4 NUMERICAL ALGORITHMS

8.5 EXAMPLES

8.6 CONCLUSION

REFERENCES

CHAPTER 9 EXPERIMENTAL DESIGNS ON HIGH-THROUGHPUT BIOLOGICAL EXPERIMENTS

9.1 RANDOMIZATION

9.2 REPLICATION

9.3 POOLING

9.4 BLOCKING

9.5 DESIGN FOR CLASSIFICATIONS

9.6 DESIGN FOR TIME COURSE EXPERIMENTS

9.7 DESIGN FOR eQTL STUDIES

REFERENCES

CHAPTER 10 STATISTICAL RESAMPLING TECHNIQUES FOR LARGE BIOLOGICAL DATA ANALYSIS

10.1 INTRODUCTION

10.2 RESAMPLING METHODS FOR PREDICTION ERROR ASSESSMENT AND MODEL SELECTION

10.3 FEATURE SELECTION

10.4 RESAMPLING-BASED CLASSIFICATION ALGORITHMS

10.5 PRACTICAL EXAMPLE: LYMPHOMA

10.6 RESAMPLING METHODS

10.7 BOOTSTRAP METHODS

10.8 SAMPLE SIZE ISSUES

10.9 LOSS FUNCTIONS

10.10 BOOTSTRAP RESAMPLING FOR QUANTIFYING UNCERTAINTY

10.11 MARKOV CHAIN MONTE CARLO METHODS

10.12 CONCLUSIONS

REFERENCES

CHAPTER 11 STATISTICAL NETWORK ANALYSIS FOR BIOLOGICAL SYSTEMS AND PATHWAYS

11.1 INTRODUCTION

11.2 BOOLEAN NETWORK MODELING

11.3 BAYESIAN BELIEF NETWORK

11.4 MODELING OF METABOLIC NETWORKS

REFERENCES

CHAPTER 12 TRENDS AND STATISTICAL

12.1 INTRODUCTION

12.2 ALLELES, LINKAGE DISEQUILIBRIUM, AND HAPLOTYPE

12.3 INTERNATIONAL HapMap PROJECT

12.4 GENOTYPING PLATFORMS

12.5 OVERVIEW OF CURRENT GWAS RESULTS

12.6 STATISTICAL ISSUES IN GWAS

12.7 HAPLOTYPE ANALYSIS

12.8 HOMOZYGOSITY AND ADMIXTURE MAPPING

12.9 GENE ´ GENE AND GENE ´ ENVIRONMENT INTERACTIONS

12.10 GENE AND PATHWAY-BASED ANALYSIS

12.11 DISEASE RISK ESTIMATES

12.12 META-ANALYSIS

12.13 RARE VARIANTS AND SEQUENCE-BASED ANALYSIS

12.14 CONCLUSIONS

ACKNOWLEDGMENTS

REFERENCES

CHAPTER 13 R AND BIOCONDUCTOR PACKAGES IN BIOINFORMATICS: TOWARD SYSTEMS BIOLOGY

13.1 INTRODUCTION

13.2 BRIEF OVERVIEW OF THE BIOCONDUCTOR PROJECT

13.3 EXPERIMENTAL DATA

13.4 ANNOTATION

13.5 MODELS OF BIOLOGICAL SYSTEMS

13.6 CONCLUSION

13.7 ACKNOWLEDGMENTS

REFERENCES

COLOR PLATE

INDEX

The cover figure signifies the statistical analysis and biological interpretation of high-throughput molecular data. It is the logo of Dr. John N. Weinstein’s former research group at the US National Cancer Institute (in which Dr. Jae Lee worked) and his current Genomics & Bioinformatics Group at the M. D. Anderson Cancer Center.

Copyright © 2010 Wiley-Blackwell. All rights reserved

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

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Statistical bioinformatics: a guide for life and biomedical science researchers/edited by Jae K. Lee. p. cm.

Includes bibliographical references and index. ISBN 978-0-471-69272-0 (cloth)

1. Bioinformatics—Statistical methods. I. Lee, Jae K.

QH324.2.S725 2010 570.285—dc22

2009024890

For Sue, Irene, and Kevin

PREFACE

This book has been constructed primarily as a textbook for a one- or two-semester course in statistical bioinformatics. We hope that it will first serve as a comprehensive introduction to a broad range of topics in this area for life science students and researchers who are motivated to learn statistical analysis concepts and techniques in bioinformatics. Statistical and quantitative science audiences who have not yet dealt with challenging statistical issues in recent information-rich biological and biomedical data analysis may also benefit from this book by efficiently reviewing the different statistical concepts and techniques in such analyses. In particular, the four separate blocks in this book—statistical foundation, high-dimensional analysis, advanced topics, and multigene systems analysis—can be somewhat independently studied and taught in a course based on relevant needs and time restrictions for an effective learning purpose.

A similar outline as organized in this book has been used for several years in a one-semester graduate course which is open to students with diverse backgrounds at the University of Virginia. By publishing this book, we felt that these contents could be significantly enhanced by direct contributions of more specialized experts in the broad field of bioinformatics. In this multiauthor book, we have yet tried to maintain the need of a high-level mathematical and statistical understanding at a minimum. Readers of this book are thus assumed to have not much more than a basic college calculus level of mathematical understanding. A knowledge of matrix algebra would also be useful but is not a prerequisite.

This book is certainly a tribute to the contributions and support of many people. Acknowledgments are first due to the succeeding life science editors of John Wiley & Sons: Luna Han, Thomas Moore, and Karen Chambers. Without their continuous support and encouragement, the publication of this book would not have been possible. Also, all the efforts made by the expert authors who were willing to participate in this book should be highly acknowledged for its successful completion. Finally, the students who have taken this initial course and provided valuable feedback on various topics in this area over the last several years are also significant contributors to the current form of the book. The preparation of this book was supported in part by the National Institutes of Health Research Grant R01 HL081690.

J. K. Lee

Division of Biostatistics and Epidemiology

Charlottesville, Virginia

CONTRIBUTORS

HongshikAhn, Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY, USA

Merav Bar, Fred Hutchinson Cancer Research Center, Program in Computational Biology, Division of Public Health Sciences, Seattle, WA, USA

Nabil Belacel, National Research Council Canada, Institute for Information Technology, Moncton, NB, Canada

Sooyoung Cheon, KU Industry-Academy Cooperation Group Team of Economics and Statistics, Korea University, Jochiwon 339–700, Korea

Hyung Jun Cho, Department of Statistics, Korea University, Seoul, Korea

Xiangqin Cui, Department of Biostatistics, University of Alabama, Birmingham, AL, USA

Miroslava Cupelovic-Culf, National Research Council Canada, Institute for Information Technology, Moncton, NB, Canada

Ginger Davis, Department of Systems and Information Engineering, University of Virginia, Charlottesville, VA, USA

Robert Gentleman, Fred Hutchinson Cancer Research Center, Program in Computational Biology, Division of Public Health Sciences, Seattle, WA, USA

Debashis Ghosh, Departments of Statistics and Public Health Sciences, Penn State University, University Park, PA, USA

Haseong Kim, Intelligent Systems and Networks Group, Department of Electrical and Electronic Engineering, Imperial College, London, UK

Youngchul Kim, Division of Biostatistics and Epidemiology, University of Virginia, Charlottesville, VA, USA

Michael Lawrence, Fred Hutchinson Cancer Research Center, Program in Computational Biology, Division of Public Health Sciences, Seattle, WA, USA

Jae K. Lee, Division of Biostatistics and Epidemiology, University of Virginia, Charlottesville, VA, USA

Seungyeoun Lee, Department of Applied Statistics, Sejong University, Seoul, Korea

Nolweim LeMeur, Fred Hutchinson Cancer Research Center, Program in Computational Biology, Division of Public Health Sciences, Seattle, WA, USA xiv CONTRIBUTORS

Karen Lostritto, Yale School of Public Health, Yale University, New Haven, CT, USA

Annette M. Molinaro, Yale School of Public Health, Yale University, New Haven, CT, USA

Hojin Moon, Department of Mathematics and Statistics, California State University, Long Beach, CA, USA

Annamalai Muthiah, Department of Systems and Information Science, University of Virginia, Charlottesville, VA, USA

Taesung Park, Department of Statistics, Seoul National University, Seoul, Korea

Jinwook Seo, Visual Processing Laboratory, School of Computer Science and Engineering, Seoul National University, Gwanak-gu, Seoul, Korea

Wonseok Seo, Department of Statistics, Korea University, Seoul, Korea

Ben Sheiderman, Human-Computer Interaction Lab & Department of Computer Science, University of Maryland, College Park, MD, USA

Ning Sun, Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT, USA

Muneesh Tewari, Fred Hutchinson Cancer Research Center, Program in Computational Biology, Division of Public Health Sciences, Seattle, WA, USA

Christa Wang, National Research Council Canada, Institute for Information Technology, Moncton, NB, Canada

Paul D. Williams, Department of Public Health Science, University of Virginia, Charlottesville, VA, USA

Hongyu Zhao, Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT, USA

CHAPTER 1

ROAD TO STATISTICAL BIOINFORMATICS

Jae K. Lee

Department of Public Health Science, University of Virginia,

Charlottesville, Virginia, USA

There has been a great explosion of biological data and information in recent years, largely due to the advances of various high-throughput biotechnologies such as mass spectrometry, high throughput sequencing, and many genome-wide SNP profiling, RNA gene expression microarray, protein mass spectrometry, and many other recent high-throughput biotechniques (Weinstein et al., 2002). Furthermore, powerful computing systems and fast Internet connections to large worldwide biological databases enable individual laboratory researchers to easily access an unprecedentedly huge amount of biological data. Such enormous data are often too overwhelming to understand and extract the most relevant information to each researcher’s investigation goals. In fact, these large biological data are information rich and often contain much more information than the researchers who have generated such data may have anticipated. This is why many major biomedical research institutes have made significant efforts to freely share such data with general public researchers. Bioinformatics is the emerging science field concerned with the development of various analysis methods and tools for investigating such large biological data efficiently and rigorously. This kind of development requires many different components: powerful computer systems to archive and process such data, effective database designs to extract and integrate information from various heterogeneous biological databases, and efficient analysis techniques to investigate and analyze these large databases. In particular, analysis of these massive biological data is extremely challenging for the following reasons.

CHALLENGE 1: MULTIPLE-COMPARISONS ISSUE

Analysis techniques on high-throughput biological data are required to carefully handle and investigate an astronomical number of candidate targets and possible mechanisms, most of which are false positives, from such massive data (Tusher et al., 2001). For example, a traditional statistical testing criterion which allows 5% false-positive error (or significance level) would identify ~500 false positives from 10K microarray data between two biological conditions of interest even though no real biologically differentially regulated genes exist between the two. If a small number of, for example, 100, genes that are actually differentially regulated exist, such real differential expression patterns will be mixed with the above 500 false positives without any a priori information to discriminate the true positives from the false positives. Then, confidence on the 600 targets that were identified by such a statistical testing may not be high. Simply tightening such a statistical criterion will result in a high false-negative error rate, without being able to identify many important real biological targets. This kind of pitfall, the so-called multiple-comparisons issue, becomes even more serious when biological mechanisms such as certain signal transduction and regulation pathways that involve multiple targets are searched from such biological data; the number of candidate pathway mechanisms to be searched grows exponentially, for example, 10! for 10-gene sequential pathway mechanisms. Thus, no matter how powerful a computer system can handle a given computational task, it is prohibitive to tackle such problems by exhaustive computational search and comparison for these kinds of problems. Many current biological problems have been theoretically proven to be NP (nonpolynomial) hard in computer science, implying that no finite (polynomial) computational algorithm can search all possible solutions as the number of biological targets involved in such a solution becomes too large. More importantly, this kind of exhaustive search is simply prone to the risk of discovering numerous false positives. In fact, this is one of the most difficult challenges in investigating current large biological databases and is why only heuristic algorithms that tightly control such a high false positive error rate and investigate a very small portion of all possible solutions are often sought for many biological problems. Thus, the success of many bioinformatics studies critically depends on the construction and use of effective and efficient heuristic algorithms, most of which are based on probabilistic modeling and statistical inference techniques that can maximize the statistical power of identifying true positives while rigorously controlling their false positive error rates.

CHALLENGE 2: HIGH-DIMENSIONAL BIOLOGICAL DATA

The second challenge is the high-dimensional nature of biological data in many bioinformatics studies. When biological data are simultaneously generated with many gene targets, their data points become dramatically sparse in the corresponding high-dimensional data space. It is well known that mathematical and computational approaches often fail to capture such high-dimensional phenomena accurately (Tamayo et al., 1999). For example, many statistical algorithms cannot easily move between local maxima in a high-dimensional space. Also, inference by combining several disjoint lower dimensional phenomena may not provide the correct understanding on the real phenomena in their joint, high-dimensional space. It is therefore important to understand statistical dimension reduction techniques that can reduce high-dimensional data problems into lower dimensional ones while the important variation of interest in biological data is preserved.

CHALLENGE 3: SMALL-n AND LARGE-p PROBLEM

The third challenge is the so-called “small-n and large-p” problem. Desired performance of conventional statistical methods is achieved when the sample size, namely n, of the data, the number of independent observations of event, is much larger than the number of parameters, say p, which need to be inferred by statistical inference (Jain et al., 2003). In many bioinformatics problems, this situation is often completely reversed. For example, in a microarray study, tens of thousands of gene transcripts’ expression patterns may become candidate prediction factors for a biological phenomenon of interest (e.g., tumor sensitivity vs. resistance to a chemotherapeutic compound) but the number of independent observations (e.g., different patient biopsy samples) is often at most a few tens or smaller. Due to the experimental costs and limited biological materials, the number of independent replicated samples can be sometimes extremely small, for example, two or three, or unavailable. In these cases, most traditional statistical approaches often perform very poorly. Thus, it is also important to select statistical analysis tools that can provide both high specificity and high sensitivity under these circumstances.

CHALLENGE 4: NOISY HIGH-THROUGHPUT BIOLOGICAL DATA

The fourth challenge is due to the fact that high-throughput biotechnical data and large biological databases are inevitably noisy because biological information and signals of interest are often observed with many other random or biased factors that may obscure main signals and information of interest (Cho and Lee, 2004). Therefore, investigations on large biological data cannot be successfully performed unless rigorous statistical algorithms are developed and effectively utilized to reduce and decompose various sources of error. Also, careful assessment and quality control of initial data sets is critical for all subsequent bioinformatics analyses.

CHALLENGE 5: INTEGRATION OF MULTIPLE, HETEROGENEOUS BIOLOGICAL DATA INFORMATION

The last challenge is the integration of information often from multiple heterogeneous biological and clinical data sets, such as large gene functional and annotation databases, biological subjects’ phenotypes, and patient clinical information. One of the main goals in performing high-throughput biological experiments is to identify the most important critical biological targets and mechanisms highly associated with biological subjects’ phenotypes, such as patients’ prognosis and therapeutic response (Pittman et al., 2004). In these cases, multiple large heterogeneous datasets need to be combined in order to discover the most relevant molecular targets. This requires combining multiple datasets with very different data characteristics and formats, some of which cannot easily be integrated by standard statistical inference techniques, for example, the information from genomic and proteomic expression data and reported pathway mechanisms in the literature. It will be extremely important to develop and use efficient yet rigorous analysis tools for integrative inference on such complex biological data information beyond the individual researcher’s manual and subjective integration.

In this book, we introduce the statistical concepts and techniques that can overcome these challenges in studying various large biological datasets. Researchers with biological or biomedical backgrounds may not be able, or may not need, to learn advanced mathematical and statistical techniques beyond the intuitive understanding of such topics for their practical applications. Thus, we have organized this book for life science researchers to efficiently learn the most relevant statistical concepts and techniques for their specific biological problems. We believe that this composition of the book will help nonstatistical researchers to minimize unnecessary efforts in learning statistical topics that are less relevant to their specific biological questions, yet help them learn and utilize rigorous statistical methods directly relevant to those problems. Thus, while this book can serve as a general reference for various concepts and methods in statistical bioinformatics, it is also designed to be effectively used as a textbook for a semester or shorter length course as below. In particular, the chapters are divided into four blocks of different statistical issues in analyzing large biological datasets (Fig. 1.1):

I.Statistical Foundation Probability theories (Chapter 2), statistical quality control (Chapter 3), statistical tests (Chapter 4)

II.High-Dimensional Analysis Clustering analysis (Chapter 5), classification analysis (Chapter 6), multidimensional visualization (Chapter 7)

IIIAdvanced Analysis Topics Statistical modeling (Chapter 8), experimental design (Chapter 9), statistical resampling methods (Chapter 10)

IVMultigene Analysis in Systems Biology Genetic network analysis (Chapter 11), genetic association analysis (Chapter 12), R Bioconductor tools in systems biology (Chapter 13)

Figure 1.1 Possible course structure.

The first block of chapters will be important, especially for students who do not have a strong statistical background. These chapters will provide general backgrounds and terminologies to initiate rigorous statistical analysis on large biological datasets and to understand more advanced analysis topics later. Students with a good statistical understanding may also quickly review these chapters since there are certain key concepts and techniques (especially in Chapters 3 and 4) that are relatively new and specialized for analyzing large biological datasets.

The second block consists of analysis topics frequently used in investigating high-dimensional biological data. In particular, clustering and classification techniques, by far, are most commonly used in many practical applications of high-throughput data analysis. Various multidimensional visualization tools discussed in Chapter 7 will also be quite handy in such investigations.

The third block deals with more advanced topics in large biological data analysis, including advanced statistical modeling for complex biological problems, statistical resampling techniques that can be conveniently used with the combination of classification (Chapter 6) and statistical modeling (Chapter 8) techniques, and experimental design issues in high-throughput microarray studies.

The final block contains concise description of the analysis topics in several active research areas of multigene network and genetic association analysis as well as the R Bioconductor software in systems biology analysis. These will be quite useful for performing challenging gene network and multigene investigations in the fast-growing systems biology field.

These four blocks of chapters can be followed with the current order for a full semester-length course. However, except for the first block, the following three blocks are relatively independent of each other and can be covered (or skipped for specific needs and foci under a time constraint) in any order, as depicted in Figure 1.1. We hope that life science researchers who need to deal with challenging analysis issues in overwhelming large biological data in their specific investigations can effectively meet their learning goals in this way.

REFERENCES

Cho, H., and Lee, J. K. (2004). Bayesian hierarchical error model for analysis of gene expression data. Bioinformatics,20(13): 2016–2025.

Jain, N., et al. (2003). Local-pooled-error test for identifying differentially expressed genes with a small number of replicated microarrays. Bioinformatics,19(15): 1945–1951.

Pittman, J., et al. (2004). Integrated modeling of clinical and gene expression information for personalized prediction of disease outcomes. Proc. Natl. Acad.Sci. U.S.A.,101(22): 8431–8436.

Tamayo, P., et al. (1999). Interpreting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation. Proc. Natl. Acad.Sci. U.S.A.,96(6): 2907–2912.

Tusher, V. G., Tibshirani, R., and Chu, G. (2001). Significance analysis of microarrays applied to the ionizing radiation response. Proc. Natl. Acad.Sci. U.S.A.,98(9): 5116–5121.

Weinstein, J. N., et al. (2002). The bioinformatics of microarray gene expression profiling. Cytometry,47(1): 46–49.