Description
Book SynopsisFeatures 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 governmentsponsored 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 realworld data and concerns. Among the topics included are the spread of infectious disease (HIV/AIDS) through a population, statistical pattern recognition methods
Table of Contents
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
