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In this book, the authors aim to provide the step-by-step procedures to perform data analysis of microbiome data by way of the R programming language. The book provides some bioinformatic and statistical foundations of data analysis because microbiome data are complicated and analysis of microbiome data is still very challenging. To strike a balance, authors briefly introduce concepts, backgrounds, statistical method developments in the beginning three chapters before illustrating the applications in real data (Chap. 4-12).

Dr. Yinglin Xia is a Research Associate Professor at the Department of Medicine, the University of Illinois at Chicago, USA. He was a R esearch Assistant Professor in the Department of Biostatistics and Computational Biology at the University of Rochester, Rochester, NY. Dr. Xia has worked on a variety of research projects and clinical trials in microbiome, gastroenterology, oncology, immunology, psychiatry, sleep, neuroscience, HIV, mental health, public health, social and behavioral sciences, as well as nursing caregiver. He has published more than 100 papers in peer-reviewed journals on Statistical Methodology, Clinical Trial, Medical Statistics, Biomedical Sciences, and Social and Behavioral sciences. He serves the editorial board of 9 scientific journals. Dr. Xia is well versed in the design and analysis in the areas of longitudinal data, mediation and moderation analyses, multilevel clustered-data, zero-inflated count data, mixed-effects model, GEE, structural equation model, meta-analysis, and ROC curve. He has successfully applied his statistical knowledge, modeling and programming skills to study designs and data analysis in biomedical research and clinical trials. He has been involved as a co-investigator or statistician in numerous NIH, CDC, and other grants. Three grants he designed on microbiome studies were funded by NIH and other funding agencies. His recent papers on microbiome data analysis are well received by peers.

Dr. Jun Sun is a tenured Professor of Medicine at the University of Illinois at Chicago, USA. She is an elected fellow of American Gastroenterological Associate (AGA). Her research interests are host–microbiome interactions in inflammation and cancer. Her key achievements include (1) characterization of vitamin D receptor regulation of gut microbiome in intestinal homeostasis and inflammation, (2) identification of dysbiosis and intestinal dysfunction in amyotrophic lateral sclerosis (ALS), (3) characterization of bacteria in regulating intestinal stem cells, and (4) identification and characterization of the Salmonella effector protein AvrA in host–bacterial interactions. Dr. Sun has published over 160 scientific articles in peer-reviewed journals, including Gut, Cell Stem Cells, Nature Genetics, JBC, American Journal of Pathology, American Journal of Physiology-GI. She is the leading editor of three books, including a recent Nature/Springer book entitled Mechanisms Underlying Host-Microbiome Interactions in Pathophysiology of Human Diseases. This book has shown a novel theme and multiple disciplinary topics of microbiome research for broad audience. She is in the editorial board of more than 10 peer-reviewed international scientific journals. She services study sections for the NIH, American Cancer Society, and other national and international research foundations. She is the Chair-elected for the AGA microbiome section. Her research is supported by the NIH, DOD, and other research awards. Dr. Sun is a believer of scientific art and artistic science. She enjoys writing her science papers in English and poems in Chinese. She teaches her medical fellows biomedical knowledge and also the way to translate the Chinese poems. In addition to her research papers and books, her poetry collection《让时间停留在这一刻》“Let time stay still at this moment”, is published in January 2018 by Chinese Literature and History Press.

Prof. Ding-Geng Chen is a fellow of the American Statistical Association and currently the Wallace Kuralt distinguished Professor at the University of North Carolina at Chapel Hill, USA and an extraordinary Professor at University of Pretoria, South Africa. He was a Professor at the University of Rochester and the Karl E. Peace endowed eminent scholar chair in biostatistics at Georgia Southern University. He is also a senior consultant for biopharmaceuticals and government agencies with extensive expertise in clinical trial biostatistics and public health statistics. Professor Chen has written more than 150 referred publications and co-authored/co-edited 23 books on biostatistical clinical trial methodology, meta-analysis, causal-inference and data analytics, and public health statistics.

1 Bioinformatic Analysis of Microbiome Data . . . . . . . . . . . . . . . . . . 1
1.1 Introduction to Microbiome Study . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 What Is the Human Microbiome? . . . . . . . . . . . . . . . . 1
1.1.2 Microbiome Research and DNA Sequencing . . . . . . . . 2
1.2 Introduction to Phylogenetics. . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 16S rRNA Sequencing Approach . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 The Advantages of 16S rRNA Sequencing . . . . . . . . . 5
1.3.2 Bioinformatic Analysis of 16S rRNA Sequencing
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Shotgun Metagenomic Sequencing Approach . . . . . . . . . . . . . . 12
1.4.1 Definition of Metagenomics . . . . . . . . . . . . . . . . . . . . 12
1.4.2 Advantages of Shotgun Metagenomic Sequencing . . . . 13
1.4.3 Bioinformatic Analysis of Shotgun Metagenomic
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Bioinformatics Data Analysis Tools . . . . . . . . . . . . . . . . . . . . . 18
1.5.1 QIIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.2 mothur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.3 Analyzing 16S rRNA Sequence Data Using QIIME
and Mothur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 What Are Microbiome Data? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Microbiome Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Microbiome Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 Microbiome Data Are Structured as a Phylogenetic
Tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Feature-by-Sample Contingency Table . . . . . . . . . . . . . 30
2.2.3 OTU Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.4 Taxa Count Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.5 Taxa Percent Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 Features of Microbiome Data . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.1 Microbiome Data Are Compositional. . . . . . . . . . . . . . 34
2.3.2 Microbiome Data Are High Dimensional and
Underdetermined . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.3 Microbiome Data Are Over-Dispersed . . . . . . . . . . . . . 36
2.3.4 Microbiome Data Are Often Sparse
with Many Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4 An Example of Over-Dispersed and Zero-Inflated
Microbiome Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Challenges of Modeling Microbiome Data . . . . . . . . . . . . . . . . 38
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Introductory Overview of Statistical Analysis of Microbiome
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1 Research Themes and Statistical Hypotheses in Human
Microbiome Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Classic Statistical Methods and Models in Microbiome
Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.1 Classic Statistical Tests . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.2 Multivariate Statistical Tools . . . . . . . . . . . . . . . . . . . . 46
3.2.3 Over-Dispersed and Zero-Inflated Models . . . . . . . . . . 47
3.3 Newly Developed Multivariate Statistical Methods . . . . . . . . . . 48
3.3.1 Dirichlet-Multinomial Model . . . . . . . . . . . . . . . . . . . . 48
3.3.2 UniFrac Distance Metric Family . . . . . . . . . . . . . . . . . 49
3.3.3 Multivariate Bayesian Models . . . . . . . . . . . . . . . . . . . 50
3.3.4 Phylogenetic LASSO and Microbiome . . . . . . . . . . . . 51
3.4 Compositional Analysis of Microbiome Data . . . . . . . . . . . . . . 52
3.5 Longitudinal Data Analysis and Causal Inference in
Microbiome Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.1 Standard Longitudinal Models . . . . . . . . . . . . . . . . . . . 54
3.5.2 Newly Developed Over-Dispersed and Zero-Inflated
Longitudinal Models. . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5.3 Regression-Based Time Series Models. . . . . . . . . . . . . 57
3.5.4 Detecting Causality: Causal Inference
and Mediation Analysis of Microbiome Data . . . . . . . . 59
3.5.5 Meta-analysis of Microbiome Data . . . . . . . . . . . . . . . 60
3.6 Introduction of Statistical Packages . . . . . . . . . . . . . . . . . . . . . 62
3.7 Limitations of Existing Statistical Methods and Future
Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4 Introduction to R, RStudio and ggplot2 . . . . . . . . . . . . . . . . . . . . . 77
4.1 Introduction to R and RStudio . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1.1 Installing R, RStudio, and R Packages . . . . . . . . . . . . . 78
4.1.2 Set Working Directory in R . . . . . . . . . . . . . . . . . . . . 79
4.1.3 Data Analysis Through RStudio . . . . . . . . . . . . . . . . . 80
4.1.4 Data Import and Export . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.5 Basic Data Manipulation . . . . . . . . . . . . . . . . . . . . . . . 87
4.1.6 Simple Summary Statistics . . . . . . . . . . . . . . . . . . . . . 93
4.1.7 Other Useful R Functions . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Introduction to the dplyr Package . . . . . . . . . . . . . . . . . . . . . . 102
4.3 Introduction to ggplot2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3.1 ggplot2 and the Grammar of Graphics . . . . . . . . . . . . . 110
4.3.2 Simplify Specifications in Creating a Plot Using
ggplot() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.3.3 Creating a Plot Using ggplot() . . . . . . . . . . . . . . . . . . 115
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5 Power and Sample Size Calculations for Microbiome Data . . . . . . 129
5.1 Hypothesis Testing and Power Analysis . . . . . . . . . . . . . . . . . . 129
5.1.1 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.1.2 Power Analysis and Sample Size Calculation . . . . . . . . 132
5.2 Power Analysis for Testing Differences in Diversity
Using T-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.2.1 Power Formula for Continuous Outcome . . . . . . . . . . . 134
5.2.2 Diversity Data for ALS Study . . . . . . . . . . . . . . . . . . . 137
5.2.3 Calculating Power or Sample Size Using R Function
power.t.test() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.3 Power Analysis for Comparing Diversity Across More
than Two Groups Using ANOVA . . . . . . . . . . . . . . . . . . . . . . 143
5.3.1 Hypothesis and Theory of Power for One-Way
ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.3.2 Calculating Power or Sample Size Using R Function
pwr.avova.test() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.4 Power Analysis for Comparing a Taxon of Interest Across
Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.4.1 Hypothesis and Basic Power and Sample Size
Formulas for Comparing Proportions . . . . . . . . . . . . . . 146
5.4.2 Power Analysis Using R Function
power.prop.test() . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.4.3 Power Analysis Using v2 Test and Fisher
Exact Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.5 Comparing the Frequency of All Taxa Across Groups
Using Dirichlet-Multinomial Model . . . . . . . . . . . . . . . . . . . . . 154
5.5.1 Multivariate Hypothesis Testing
and Dirichlet-Multinomial Model . . . . . . . . . . . . . . . . 154
5.5.2 Power and Sample Size Calculations Under Dirichlet-
Multinomial Model. . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.5.3 Power and Size Calculations Using HMP Package . . . . 157
5.5.4 Effect Size Calculation Using HMP Package . . . . . . . . 164
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6 Community Diversity Measures and Calculations . . . . . . . . . . . . . . 167
6.1 Vdr−/− Mice Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.2 Introduction to Community Diversities . . . . . . . . . . . . . . . . . . . 167
6.2.1 Alpha Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2.2 Beta Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2.3 Gamma Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.3 Alpha Diversity Measures and Calculations . . . . . . . . . . . . . . . 169
6.3.1 Chao 1 Richness Index and Number of Taxa . . . . . . . . 169
6.3.2 Shannon-Wiener Diversity Index . . . . . . . . . . . . . . . . . 173
6.3.3 Simpson Diversity Index. . . . . . . . . . . . . . . . . . . . . . . 174
6.3.4 Pielou’s Evenness Index . . . . . . . . . . . . . . . . . . . . . . . 177
6.3.5 Make a Dataframe of Diversity Indices . . . . . . . . . . . . 178
6.4 Beta Diversity Measures and Calculations . . . . . . . . . . . . . . . . 180
6.4.1 Binary Similarity Coefficients: Jaccard
and Sørensen Indices . . . . . . . . . . . . . . . . . . . . . . . . . 182
6.4.2 Distance (Dissimilarity) Coefficients:
Bray-Curtis Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
7 Exploratory Analysis of Microbiome Data and Beyond . . . . . . . . . 191
7.1 Datasets from Mice and Human. . . . . . . . . . . . . . . . . . . . . . . . 191
7.1.1 Vdr−/− Mice Data Set . . . . . . . . . . . . . . . . . . . . . . . . . 191
7.1.2 Cigarette Smokers Data Set. . . . . . . . . . . . . . . . . . . . . 191
7.2 Exploratory Analysis with Graphic Summary . . . . . . . . . . . . . . 192
7.2.1 Plot Richness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
7.2.2 Plot Abundance Bar . . . . . . . . . . . . . . . . . . . . . . . . . . 193
7.2.3 Plot Heatmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
7.2.4 Plot Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.2.5 Plot Phylogenetic Tree . . . . . . . . . . . . . . . . . . . . . . . . 199
7.3 Clustering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
7.3.1 Introduction to Clustering, Distance
and Ordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
7.3.2 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
7.4 Ordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.4.1 Principal Component Analysis (PCA) . . . . . . . . . . . . . 209
7.4.2 Principal Coordinate Analysis (PCoA) . . . . . . . . . . . . . 214
7.4.3 Non-metric Multidimensional Scaling (NMDS) . . . . . . 220
7.4.4 Correspondence Analysis (CA) . . . . . . . . . . . . . . . . . . 223
7.4.5 Redundancy Analysis (RDA) . . . . . . . . . . . . . . . . . . . 227
7.4.6 Constrained Correspondence Analysis (CCA). . . . . . . . 236
7.4.7 Constrained Analysis of Principal Coordinates
(CAP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
7.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
8 Univariate Community Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
8.1 Comparisons of Diversities Between Two Groups. . . . . . . . . . . 251
8.1.1 Two-Sample Welch’s t-Test . . . . . . . . . . . . . . . . . . . . 251
8.1.2 Wilcoxon Rank Sum Test . . . . . . . . . . . . . . . . . . . . . . 254
8.2 Comparisons of a Taxon of Interest Between Two Groups . . . . 256
8.2.1 Comparison of Relative Abundance Using
Wilcoxon Rank Sum Test . . . . . . . . . . . . . . . . . . . . . . 256
8.2.2 Comparison of Present or Absent Taxon
Using Chi-Square Test . . . . . . . . . . . . . . . . . . . . . . . . 260
8.3 Comparisons Among More than Two Groups
Using ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
8.3.1 One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
8.3.2 Pairwise and Tukey Multiple Comparisons . . . . . . . . . 270
8.4 Comparisons Among More than Two Groups
Using Kruskal-Wallis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
8.4.1 Kruskal-Wallis Test . . . . . . . . . . . . . . . . . . . . . . . . . . 273
8.4.2 Compare Diversities Among Groups . . . . . . . . . . . . . . 274
8.4.3 Find Significant Taxa Among Groups . . . . . . . . . . . . . 277
8.4.4 Multiple Testing and E-value, FWER and FDR . . . . . . 278
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
9 Multivariate Community Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . 285
9.1 Hypothesis Testing Among Groups Using Permutational
Multivariate Analysis of Variance (PERMANOVA) . . . . . . . . . 285
9.1.1 Introduction of PERMANOVA . . . . . . . . . . . . . . . . . . 285
9.1.2 Implementing PERMANOVA Using
Vegan Package. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
9.1.3 Implementing Pairwise Permutational MANOVA
Using RVAideMemoire Package . . . . . . . . . . . . . . . . . 297
9.1.4 Test Group Homogeneities Using the Function
betadisper() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
9.2 Hypothesis Tests Among Group-Differences Using Mantel
Test (MANTEL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
9.2.1 Introduction of Mantel and Partial Mantel Tests
for Dissimilarity Matrices . . . . . . . . . . . . . . . . . . . . . . 304
9.2.2 Illustrating Mantel Test Using Vegan Package . . . . . . . 306
9.3 Hypothesis Tests Among-Group Differences
Using ANOSIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
9.3.1 Introduction of Analysis of Similarity
(ANOSIM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
9.3.2 Illustrating Analysis of Similarity (ANOSIM)
Using Vegan Package . . . . . . . . . . . . . . . . . . . . . . . . . 313
9.4 Hypothesis Tests of Multi-response Permutation Procedures
(MRPP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
9.4.1 Introduction of MRPP . . . . . . . . . . . . . . . . . . . . . . . . 316
9.4.2 Illustrating MRPP Using Vegan Package . . . . . . . . . . . 317
9.5 Compare Microbiome Communities Using the GUniFrac
Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
9.5.1 Introduction to UniFrac, Weighted UniFrac
and Generalized UniFrac Distance Metrics . . . . . . . . . . 320
9.5.2 Breast Milk Data Set . . . . . . . . . . . . . . . . . . . . . . . . . 322
9.5.3 Comparing Microbiome Communities Using
the GUniFrac Package . . . . . . . . . . . . . . . . . . . . . . . . 323
9.6 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
10 Compositional Analysis of Microbiome Data . . . . . . . . . . . . . . . . . 331
10.1 Introduction to Compositional Analysis . . . . . . . . . . . . . . . . . . 331
10.1.1 What Are Compositional Data? . . . . . . . . . . . . . . . . . . 331
10.1.2 Aitchison Simplex . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
10.1.3 Problems with Standard Statistical Methods . . . . . . . . . 332
10.1.4 Statistical Analysis of Compositional Data . . . . . . . . . . 334
10.2 Why Microbiome Dataset Can Be Treated
as Compositional? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
10.3 Exploratory Compositional Data Analysis . . . . . . . . . . . . . . . . 349
10.3.1 Compositional Biplot . . . . . . . . . . . . . . . . . . . . . . . . . 349
10.3.2 Compositional Scree Plot . . . . . . . . . . . . . . . . . . . . . . 356
10.3.3 Compositional Cluster Dendrogram . . . . . . . . . . . . . . . 357
10.3.4 Compositional Barplot . . . . . . . . . . . . . . . . . . . . . . . . 358
10.4 Comparison Between the Groups Using ALDEx2 Package . . . . 361
10.4.1 Vdr Data Set of Fecal and Cecal Sites . . . . . . . . . . . . . 361
10.4.2 Compositional Data Analysis Using ALDEx2 . . . . . . . 361
10.4.3 Difference Plot, Effect Size and Effect Plot . . . . . . . . . 368
10.5 Proportionality: Correlation Analysis for Relative Data . . . . . . . 371
10.5.1 Correlation Analysis Is Not Appropriate for
Compositional Data . . . . . . . . . . . . . . . . . . . . . . . . . . 371
10.5.2 Introduction to Proportionality. . . . . . . . . . . . . . . . . . . 373
10.5.3 Illustrating Proportionality Analysis . . . . . . . . . . . . . . . 375
10.6 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
11 Modeling Over-Dispersed Microbiome Data . . . . . . . . . . . . . . . . . . 395
11.1 Count-Based Differential Abundance Analysis
of Microbiome Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
11.1.1 Biological and Technical Variations . . . . . . . . . . . . . . 396
11.1.2 Poisson Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
11.1.3 Negative Binomial Model . . . . . . . . . . . . . . . . . . . . . . 400
11.2 NB Model in edgeR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
11.2.1 Development of NB in the Setting of Genomic
Count Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
11.2.2 Dispersion Estimators of NB in edgeR . . . . . . . . . . . . 401
11.2.3 Hypothesis Testing in edgeR. . . . . . . . . . . . . . . . . . . . 403
11.3 The edgeR Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
11.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
11.3.2 Step-by-Step Implementing edgeR. . . . . . . . . . . . . . . . 408
11.4 NB Model in DESeq and DESeq2 . . . . . . . . . . . . . . . . . . . . . . 424
11.4.1 NB Model in DESeq . . . . . . . . . . . . . . . . . . . . . . . . . 424
11.4.2 NB Model in DESeq2 . . . . . . . . . . . . . . . . . . . . . . . . 425
11.5 The DESeq and DESeq2 Packages. . . . . . . . . . . . . . . . . . . . . . 427
11.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
11.5.2 Step-by-Step Implementing DESeq2 . . . . . . . . . . . . . . 428
11.6 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
12 Modeling Zero-Inflated Microbiome Data . . . . . . . . . . . . . . . . . . . . 453
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
12.2 Zero-Inflated Models: ZIP and ZINB . . . . . . . . . . . . . . . . . . . . 454
12.2.1 ZIP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
12.2.2 ZINB Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
12.2.3 Modeling Using ZIP and ZINB . . . . . . . . . . . . . . . . . . 457
12.3 Zero-Hurdle Models: ZHP and ZHNB . . . . . . . . . . . . . . . . . . . 465
12.3.1 ZHP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
12.3.2 ZHNB Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
12.3.3 Modeling ZHP and ZHNB . . . . . . . . . . . . . . . . . . . . . 468
12.3.4 Comparing Zero-Inflated and Zero-Hurdle Models . . . . 471
12.3.5 Interpreting Main Effects of Modeling Results . . . . . . . 477
12.3.6 Multiple Testing Issue and Adjusting P-Values . . . . . . 480
12.4 Zero-Inflated Beta Regression Model with Random Effects . . . . 481
12.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
12.4.2 ZIBR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
12.4.3 Hypothesis Testing of ZIBR . . . . . . . . . . . . . . . . . . . . 482
12.4.4 Modeling Using ZIBR . . . . . . . . . . . . . . . . . . . . . . . . 483
12.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
· · · · · · (收起)