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Applied Mathematics for the Analysis of Biomedical Data : Models, Methods, and MATLAB

Applied Mathematics for the Analysis of Biomedical Data : Models, Methods, and MATLAB

autor:
Peter J. Costa
 
editor:
Wiley
 
edição:
1
 
ano de publicação:
2017
 
idioma:
Inglês
 
ISBN:
9781119269502
 
nº de páginas:
448
 
formato:
ileio (leitura online e APP)
 

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 computingmethods to provide insight into the behavior of biological systems. The author draws upon hisexperience in academia, industry, and government–sponsored research as well as his expertisein MATLAB to produce a suite of computer programs with applications in epidemiology,machine learning, and biostatistics. These models are derived from real–world data andconcerns. Among the topics included are the spread of infectious disease (HIV/AIDS) througha population, statistical pattern recognition methods to determine the presence of disease in adiagnostic 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 referencefor industrial scientists, biostatisticians, product development scientists, and practitionerswho use mathematical models of biological systems in biomedical research, medical devicedevelopment, and pharmaceutical submissions.

PETER J. COSTA, PhD, is Senior Applied Mathematician at Hologic Incorporated in Marlborough, MA. Dr. Costa is the co-creator of MATLAB's Symbolic Math Toolbox. He has developed mathematical models for the spread of HIV, the outbreak of AIDS, the transmission of an infectious respiratory disease throughout a population, and the diagnosis of cervical cancer. His research interests include scientific computing and mathematical biology. He received a PhD in Applied Mathematics from the University of Massachusetts at Amherst.

Edit

Preface xi

Acknowledgements xiii

About the Companion Website xv

Introduction xvii

1 Data 1

1.1 Data Visualization, 1

1.2 Data Transformations, 3

1.3 Data Filtering, 7

1.4 Data Clustering, 17

1.5 Data Quality and Data Cleaning, 25

References, 28

2 Some Examples 29

2.1 Glucose–Insulin Interaction, 30

2.2 Transition from HIV to AIDS, 33

2.3 Real-Time Polymerase Chain Reaction, 37

References, 45

Further Reading, 45

3 SEIR Models 47

3.1 Practical Applications of SEIR Models, 50

References, 88

Further Reading, 90

4 Statistical Pattern Recognition and Classification 93

4.1 Measurements and Data Classes, 94

4.2 Data Preparation, Normalization, and Weighting Matrix, 98

4.3 Principal Components, 104

4.4 Discriminant Analysis, 107

4.5 Regularized Discriminant Analysis and Classification, 112

4.6 Minimum Bayes Score, Maximum Likelihood, and Minimum Bayes Risk, 116

4.7 The Confusion Matrix, Receiver–Operator Characteristic Curves, and Assessment Metrics, 122

4.8 An Example, 127

4.9 Nonlinear Methods, 131

References, 139

Further Reading, 140

5 Biostatistics and Hypothesis Testing 141

5.1 Hypothesis Testing Framework, 142

5.2 Test of Means, 157

5.3 Tests of Proportions, 179

5.4 Tests of Variances, 212

5.5 Other Hypothesis Tests, 232

References, 268

Further Reading, 270

6 Clustered Data and Analysis of Variance 271

6.1 Clustered Matched-Pair Data and Non-Inferiority, 273

6.2 Clustered Data, Assessment Metrics, and Diagnostic Likelihood Ratios, 278

6.3 Relative Diagnostic Likelihood Ratios, 286

6.4 Analysis of Variance for Clustered Data, 291

6.5 Examples for Anova, 300

6.6 Bootstrapping and Confidence Intervals, 314

References, 316

Further Reading, 316

Appendix: Mathematical Matters 317

Glossary of MATLAB Functions 335

Index 407

Informação indisponível
Pessoal
Tipo de licença Permissão de impressão
Acesso Perpétuo não permitido


Leitura online: um utilizador por sessão (sem simultaneidade)
Leitura offline (com a APP): máximo de 2 dispositivos em simultâneo

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