Yinglin Xia and Jun Sun

Bioinformatic and Statistical Analysis of Microbiome Data

From Raw Sequences to Advanced Modeling with QIIME 2 and R

Yinglin Xia

Department of Medicine, University of Illinois Chicago, Chicago, IL, USA

Jun Sun

Department of Medicine, University of Illinois Chicago, Chicago, IL, USA

ISBN 978-3-031-21390-8 e-ISBN 978-3-031-21391-5

https://doi.org/10.1007/978-3-031-21391-5

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To our late grandmothers:

Mrs. Zhong Yilan (钟宜兰), Mrs. Sun Zhangqiong (孙章琼), and Mrs. Zhong Yizhen (钟宜珍) for their deep, constant love and support.

Preface

Over the past two decades, microbiome research has received much attention across diverse fields and has become a topic of great scientific and public interests.

The microbiome is invisible but exists within a body space or a particular environment, but it is essential for development, immunity, and nutrition and can change our health status and progression of multiple diseases. The human microbiome has been described as an “essential organ” of the human body, “the invisible organ,” “the forgotten organ” and “the last human organ” under active research, which highlights the importance of the human microbiome in health.

Compared with other research fields, microbiome data are complicated and have several unique characteristics. Thus, choosing appropriate statistical test or method is a very important step for analysis of microbiome data. However, it is still a challenging task for those biomedical researchers without statistical background and for those biostatisticians who do not have research experiences in this field. An appropriate statistical test or method is chosen not only based on the assumptions and properties of the statistical methods but also based on sufficient knowledge of the type and unique characteristics of collected data and the objective of the study.

We have done pioneering work to establish the microbiome data statistics and analysis. In October 2018, we published Statistical Analysis of Microbiome Data with R (Springer Nature), where we described a framework of statistical analysis of microbiome data. As the first statistical analysis book in microbiome research, we have received positive feedback from the readers around the world and positive review by Biometrical Journal (Dr. Kim-Anh Lê Cao, Biometrical Journal, Vol. 61, 2019). In that book, we focused on statistical analysis of microbiome data and introduced bioinformatic analysis of microbiome data with one chapter. Bioinformatic analysis of microbiome data is also a very important topic in microbiome research. The quality of read counts generated by bioinformatic analysis will have a large impact on the quality of downstream statistical analysis of microbiome data. We believe that it is very important to describe the workflows from bioinformatic analysis to statistical analysis of microbiome data. Thus, since October 2018, right after publishing our first book on statistical analysis of microbiome data, we planned to write a new book for combined bioinformatic and statistical analysis of microbiome data. This idea was motivated by the readers of the 2018 book who asked us for providing more coverages of bioinformatic analysis.

Our current book was written under the framework to provide one of the most important workflows for microbiome data analysis: from 16S rRNA sequencing raw reads to statistical analysis. We aim to provide a comprehensive review on statistical theories and methods on microbiome data analysis and discuss the development of bioinformatic and biostatistical methods and models in microbiome research. Particularly, we aim to provide the step-by-step procedures to perform bioinformatic and statistical analysis of microbiome data.

Profiling of bacterial communities through bacterial 16S rRNA sequencing is one important approach for bioinformatic analysis of microbiome data, which this book focuses on. Another important approach for bioinformatic analysis of microbiome data is shotgun metagenomics. Shotgun metagenomics methods allow for direct whole-genome shotgun sequencing of the microbiome metagenomic DNA, which have significantly improved our understanding of microbial community composition in ecosystem (e.g., the human body).

The microbiome data are the collection of all microorganisms. Emerging evidence and needs have shown the importance of viruses, fungi, and other microbes. Although no standard approach as bacterial 16S rRNA sequencing is available for analysis of the viral community and profiling of viruses’ communities is still very challenging, however, in current years, several viral metagenomic data analysis tools have been developed to characterize different features of viruses, including viral discovery, virome composition analysis, taxonomy classification, and functional annotation. Although the beginning interests started from the 16S rRNA sequencing approach, we hope to have opportunities to discuss the other microbial data analysis and particularly profiling and analysis of viruses’ communities in the future.

Statistical tools for performing microbiome data analysis are now available in different languages and environments across different platforms, either in web-based or programming-based approaches. Obviously, R system and environment play a critical role in developing statistical methods and models for analyzing microbiome data. QIIME 2 is a bioinformatic analysis tool via wrapping other sequencing platforms and also provides basic statistical analysis. Because of its comprehensive features and documentation supporting, QIIME 2 is one of the most popular bioinformatic tools in analysis of microbiome data. Thus, in this book, we leverage the capabilities of R and QIIME 2 for bioinformatic and statistical analysis of microbiome data.

Our book with 18 chapters is organized in this way: in the beginning two chapters, we specially provide overview and introduction of QIIME 2 and R in analysis of microbiome data, respectively. Chapters 3 to 6 present bioinformatic analysis of microbiome data and mainly through QIIME 2.

Chapter 7 introduces the original Operational Taxonomic Unit (OTU) methods in numerical taxonomy and Chapter 8 describes a movement of moving beyond OTU methods that has arisen in microbiome research field. Chapters 9 to 18 present biostatistical analysis of microbiome data and mainly through R and also QIIME 2.

Chapter 3 describes the basic data processing in QIIME 2. Chapter 4 introduces how to build feature table and feature data from raw sequencing reads. Chapter 5 introduces assigning taxonomy and building phylogenetic tree. Chapter 6 introduces taxonomic classification of the representative sequences and how to cluster Operational Taxonomic Units (OTUs). Chapter 7 comprehensively describes the development of OTU methods in numerical taxonomy, which provides a theoretical background of the clustering-based OTU methods that are used in bioinformatic analysis of microbiome data. Chapter 8 describes a movement that moves beyond OTU methods arisen in microbiome research field, which provides a comprehensive review on bioinformatic analysis of microbiome data. Chapters 9 and 10 provide two basic statistical analyses of microbiome data: Chap. 9 introduces alpha diversity metrics and visualization, Chap. 10 introduces beta diversity metrics and ordination. Chapters 11 to 18 present more advanced statistical methods and models in microbiome research. Chapter 11 introduces nonparametric methods for multivariate analysis of variance in ecological and microbiome data and statistical testing of beta diversity in microbiome data. Chapter 12 discusses differential abundance analysis of microbiome data mainly through the metagenomeSeq package. Chapter 13 presents zero-inflated beta models for microbiome data. Chapter 14 introduces compositional data and specifically the newly developed models for compositional analysis of microbiome data. Chapter 15 introduces linear mixed-effects models and describes using them for analysis of longitudinal microbiome data. Chapter 16 describes generalized linear mixed models (GLMMs) including the brief history of generalized linear models and generalized nonlinear models, algorithms for fitting GLMMs, as well as statistical hypothesis testing and modeling in GLMMs. Chapter 17 specifically introduces the newly developed GLMMs for longitudinal microbiome data and adopting the GLMMs in other fields to analyze longitudinal microbiome data. Chapter 18 provides an overview of multivariate longitudinal microbiome data analysis and specifically introduces the newly developed non-parametric microbial interdependence test. The large P small N problem is also discussed in the last chapter of this book.

We hope the contents and organization of these chapters will provide a set of basic concepts of microbiome, a framework of bioinformatic and statistical analysis of microbiome data. We expect this book to be used by (1) graduate students who study bioinformatic and statistical analysis of microbiome data; (2) bioinformaticians and statisticians, working on microbiome projects, either for their own research or for their collaborative research for experimental design, grant application, and data analysis; and (3) researchers who investigate biomedical and biochemical projects with the microbiome, and multi-omics data analysis. The datasets and R and QIIME 2 commends used in this book are available from Springer’s website or by requesting to the first author: Yinglin Xia at yinglin.xia2007@gmail.com.

Yinglin Xia

Jun Sun

Chicago, IL, USA Chicago, IL, USA

May 2022

Acknowledgments

The authors wish to thank the editors and staff at Springer Nature for their feedback along the way of process to publishing. Very special thanks to Mrs. Merry Stuber, Senior Editor, New York, for her enthusiasm in supporting and guiding the present project from beginning to end. We also wish to thank Dr. Cherry Ma, Managing Editor, Dr. Yu Zhu, Senior Publisher, and Mrs. Emily Zhang, Editor, for their help in processing the book proposal review.

We thank the three anonymous reviewers for their positive reviews on this book proposal. Especially we thank the two anonymous reviewers for their very positive and constructive reviews on the first draft of this book. Their constructive feedback was helpful in improving our reversion of this book. Broadly, we greatly appreciate the developers of bioinformatic and statistical methods, models, and R packages and R system and environment in general. Without their great works, the book cannot be available in current breadth and scope. Our special thanks go to Dr. Joseph Paulson for sharing his research paper with us.

Our path to the current academic journey and success was paved by supports from families for generations. We all wish to express our deepest appreciation to our respective parents and parents-in-law – Xincui Wang, Qijia Xia, Xiao-Yun Fu, and Zong-Xiang Sun – and to our respective families – Yuxuan Xia and Jason Xia – for their love and support.

Yinglin’s grandmother Zhong Yilan (钟宜兰) was very kind and generous. She was always willing to help others and encouraged him to help people who were in need. She took care of Yinglin’s everyday life until he left his village to attend high school at county. Yinglin remember that his grandmother Zhong Yilan always brought him with her to visit their relatives before Yinglin attended school. Yinglin’s grandmother from his mother’s side Zhong Yizhen (钟宜珍) was very kind and skillful. When Yinglin was young, every year his grandmother Zhong Yizhen gave them delicious homemade foods, delicate hand-knitted straw hats, and hand-woven straw fan as gifts. She only had one daughter, Yinglin’s mother. She lived with Yinglin’s parents for several years at the late time of her life.

Jun’s grandmother Sun Zhangqiong (孙章琼) was positive, warm-hearted, and open-minded. In a traditional society, women’s role was narrowly defined around the family. However, she always encouraged her granddaughter to chase her dreams, to find her intellectual potential, and to work for the society. Her vision and value for life has a deep influence on Jun.

We would like to dedicate this book to our late grandmothers, Mrs. Zhong Yilan (钟宜兰), Mrs. Sun Zhangqiong (孙章琼), and Mrs. Zhong Yizhen (钟宜珍) for their deep, constant love and support. May this book honor their memory and legacy.

Finally, we would like to acknowledge the VA Merit Award 1101BX004824-01, the DOD grant W81XWH-20-1-0623 (BC191198), Crohn’s & Colitis Foundation Senior Research Award (902766), the NIDDK/National Institutes of Health grant R01 DK105118, and R01DK114126 to Jun Sun. The study sponsors play no role in the study design, data collection, analysis, and interpretation of data. The contents do not represent the views of the United States Department of Veterans Affairs or the United States Government.

Contents

1 Introduction to QIIME 2 1

1.1 Overview of QIIME 2 1

1.2 Core Concepts in QIIME 2 3

1.2.1 Artifacts 3

1.2.2 Visualizations 4

1.2.3 Semantic Type 4

1.2.4 Plugins 4

1.3 Install QIIME 2 5

1.4 Store and Track Data 7

1.5 Extract Data from QIIME 2 Archives 8

1.6 Summary 8

References 8

2 Introduction to R for Microbiome Data 11

2.1 Some Useful R Functions 11

2.1.1 Save Data into R Data Format 12

2.1.2 Read Back Data from R Data Format Files 14

2.1.3 Use Download.File() to Download File from Website 15

2.2 Some Useful R Packages for Microbiome Data 15

2.2.1 Readr 16

2.2.2 Ggpubr 17

2.2.3 Tidyverse 23

2.3 Specifically Designed R Packages for Microbiome Data 24

2.3.1 Phyloseq 24

2.3.2 Microbiome 34

2.3.3 ampvis2 47

2.3.4 curatedMetagenomicData 48

2.4 Some R Packages for Analysis of Phylogenetics 48

2.4.1 Ape 49

2.4.2 Phytools 50

2.4.3 Castor 52

2.5 BIOM Format and Biomformat Package 54

2.6 Creating Analysis Microbiome Dataset 57

2.7 Summary 61

References 61

3 Basic Data Processing in QIIME 2 65

3.1 Importing Data into QIIME 2 65

3.1.1 Import FASTA Format Data 66

3.1.2 Import FASTQ Format Data 69

3.1.3 Import Feature Table 73

3.1.4 Import Phylogenetic Trees 75

3.2 Exporting Data from QIIME 2 76

3.2.1 Export Feature Table 76

3.2.2 Export Phylogenetic Trees 77

3.3 Extracting Data from QIIME 2 Archives 77

3.3.1 Extract Data Using the Qiime Tools Export Command 78

3.3.2 Extract Data Using Unzip Program on macOS 78

3.4 Filtering Data in QIIME 2 79

3.4.1 Filter Feature Table 80

3.4.2 Taxonomy-Based Tables and Sequences Filtering 83

3.4.3 Filter Distance Matrices 86

3.5 Introducing QIIME 2 View 87

3.6 Communicating Between QIIME 2 and R 87

3.6.1 Export QIIME 2 Artifacts into R Using qiime2R Package 87

3.6.2 Prepare Feature Table and Metadata in R and Import into QIIME 2 90

3.7 Summary 92

References 92

4 Building Feature Table and Feature Representative Sequences from Raw Reads 95

4.1 Analyzing Demultiplexed Paired-End FASTQ Data 96

4.1.1 Prepare Sample Metadata 96

4.1.2 Prepare Raw Sequence Data 99

4.1.3 Import Data Files as Qiime Zipped Artifacts(.qza) 100

4.1.4 Examine and Visualize the Qualities of the Sequence Reads 101

4.2 Analyzing Demultiplexed Paired-End FASTQ Data Using DADA2 and q2-dada2 Plugin 103

4.2.1 Introduction to DADA2 and q2-dada2 Plugin 103

4.2.2 Denoise Sequences to Construct Feature Table and Feature Data with q2-dada2 Plugin 104

4.2.3 Summarize the Feature Table and Feature Data from q2-dada2 Plugin 108

4.3 Analyzing Multiplexed Paired-End FASTQ Data Using q2-dada2 Plugin 108

4.3.1 Prepare Sample Metadata 109

4.3.2 Prepare Raw Sequence Data 109

4.3.3 Import Data Files as Qiime Zipped Artifacts(.qza) 110

4.3.4 Demultiplexing Sequences 110

4.3.5 Summarize the Demultiplexing Results and Examine Quality of the Reads 112

4.4 Analyzing Demultiplexed Paired-End FASTQ Data Using Deblur and q2-deblur Plugin 113

4.4.1 Introduction to Deblur and q2-deblur Plugin 113

4.4.2 Process Initial Quality Filtering 114

4.4.3 Preliminary Works for Denoising with Deblur 114

4.4.4 Denoise Sequences with Deblur to Construct Feature Table and Feature Data 116

4.4.5 Summarize the Feature Table and Feature Data from Deblur 117

4.4.6 Remarks on DADA2 and Deblur 118

4.5 Summary 119

References 120

5 Assigning Taxonomy, Building Phylogenetic Tree 123

5.1 Assigning Taxonomy 123

5.1.1 Bioinformatics Tools and Reference Databases 123

5.1.2 QIIME 2-Formatted and Maintained Taxonomic Reference Databases 125

5.1.3 DADA2-Formatted and Maintained Taxonomic Reference Databases 128

5.1.4 Introduction to q2-Feature-Classifier 128

5.1.5 Assign Taxonomy Using the q2-Feature-Classifier 132

5.1.6 Remarks on Taxonomic Classification 135

5.2 Building Phylogenetic Tree 135

5.2.1 Introduction to Phylogenetic Tree 135

5.2.2 Build a Phylogenetic Tree Using the Alignment and Phylogeny Commands 136

5.2.3 Remarks on the Taxonomic and Phylogenetic Trees 138

5.3 Summary 141

References 141

6 Clustering Sequences into OTUs 147

6.1 Introduction to Clustering Sequences into OTUs 147

6.1.1 Merge Reads 148

6.1.2 Remove Non-biological Sequences 148

6.1.3 Trim Reads Length 148

6.1.4 Discard Low-Quality Reads 149

6.1.5 Dereplicate Sequences 149

6.2 Introduction to VSEARCH and q2-vsearch 149

6.3 Closed-Reference Clustering 150

6.3.1 Introduction 150

6.3.2 Implement Cluster-Features-Closed-Reference 150

6.3.3 Remarks on Closed-Reference Clustering 152

6.4 De Novo Clustering 153

6.4.1 Introduction 153

6.4.2 Implement Cluster-Features-De-Novo 153

6.4.3 Remarks on De Novo Clustering 154

6.5 Open-Reference Clustering 155

6.5.1 Introduction 155

6.5.2 Implement Cluster-Features-Open-Reference 155

6.5.3 Remarks on Open-Reference Clustering 156

6.6 Summary 157

References 157

7 OTU Methods in Numerical Taxonomy 161

7.1 Brief History of Numerical Taxonomy 162

7.2 Principles of Numerical Taxonomy 164

7.2.1 Definitions of Characters and Taxa 165

7.2.2 Sample Size Calculation: How Many Characters? 166

7.2.3 Equal Weighting Characters 169

7.2.4 Taxonomic Rank 169

7.3 Phenetic Taxonomy: Philosophy of Numerical Taxonomy 170

7.3.1 Phenetics: Numerical-Based Empiricism Versus Aristotle’s Essentialism 170

7.3.2 Classification: Inductive Theory Versus Darwin’ Theory of Evolution 173

7.3.3 Biological Classifications: Phenetic Approach Versus Cladistic Approach 174

7.4 Construction of Taxonomic Structure 176

7.4.1 Defining the Operational Taxonomic Units 177

7.4.2 Estimation of Taxonomic Resemblance 178

7.4.3 Commonly Clustering-Based OTU Methods 192

7.5 Statistical Hypothesis Testing of OTUs 208

7.5.1 Hypothesis Testing on Similarity Coefficients of OTUs 208

7.5.2 Hypothesis Testing on Clustering OTUs 209

7.6 Some Characteristics of Clustering-Based OTU Methods 210

7.6.1 Some Basic Questions in Numerical Taxonomy 211

7.6.2 Characteristics of Numerical Taxonomy 212

7.7 Summary 218

References 219

8 Moving Beyond OTU Methods 227

8.1 Clustering-Based OTU Methods in Microbiome Study 228

8.1.1 Common Clustering-Based OTU Methods 228

8.1.2 Hierarchical Clustering OTU Methods 229

8.1.3 Heuristic Clustering OTU Methods 230

8.1.4 Limitations of Clustering-Based OTU Methods 231

8.1.5 Purposes of Using OTUs in Microbiome Study 240

8.1.6 Defining Species and Species-Level Analysis 241

8.2 Moving Toward Single-Nucleotide Resolution-Based OTU Methods 250

8.2.1 Concept Shifting in Bioinformatic Analysis 250

8.2.2 Single-Nucleotide Resolution Clustering-Based OTU Methods 252

8.3 Moving Beyond the OTU Methods 254

8.3.1 Entropy-Based Methods: Oligotyping 255

8.3.2 Denoising-Based Methods 256

8.4 Discussion on Moving Beyond OTU Methods 267

8.4.1 Necessity of Targeting Single-Base Resolution 267

8.4.2 Possibility of Moving Beyond Traditional OTU Methods 268

8.4.3 Issues of Sub-OTU Methods 270

8.4.4 Prediction of Sequence Similarity to Ecological Similarity 271

8.4.5 Functional Analysis and Multi-omics Integration 271

8.5 Summary 273

References 273

9 Alpha Diversity 289

9.1 Abundance-Based Alpha Diversity Metrics 290

9.1.1 Chao 1 Richness and Abundance-Based Coverage Estimator (ACE) 290

9.1.2 Shannon Diversity 298

9.1.3 Simpson Diversity 300

9.1.4 Pielou’s Evenness 304

9.2 Phylogenetic Alpha Diversity Metrics 305

9.2.1 Phylogenetic Diversity 306

9.2.2 Phylogenetic Entropy 306

9.2.3 Phylogenetic Quadratic Entropy (PQE) 307

9.3 Exploring Alpha Diversity and Abundance 307

9.3.1 Heatmap 308

9.3.2 Boxplot 312

9.3.3 Violin Plot 316

9.4 Statistical Hypothesis Testing of Alpha Diversity 318

9.4.1 Summarize the Diversity Measures 319

9.4.2 Plot Histogram of the Diversity Distributions 319

9.4.3 Kruskal-Wallis Test 319

9.4.4 Perform Multiple Comparisons 321

9.5 Alpha Diversity Analysis in QIIME 2 322

9.5.1 Calculate Alpha Diversity Using Core-Metrics-Phylogenetic Method 322

9.5.2 Calculate Alpha Diversity Using Alpha Method 324

9.5.3 Calculate Alpha Diversity Using Alpha-Phylogenetic Method 326

9.5.4 Test for Differences of Alpha Diversity Between Groups 327

9.5.5 Alpha Rarefaction in QIIME 2 328

9.6 Summary 330

References 331

10 Beta Diversity Metrics and Ordination 335

10.1 Abundance-Based Beta Diversity Metrics 335

10.1.1 Bray-Curtis Dissimilarity 337

10.1.2 Jaccard Dissimilarity 339

10.1.3 Sørensen Dissimilarity 340

10.2 Phylogenetic Beta Diversity Metrics 342

10.2.1 Unweighted UniFrac 342

10.2.2 Weighted UniFrac 343

10.2.3 GUniFrac 344

10.2.4 pldist 344

10.2.5 Calculate (Un)Weighted UniFrac and GUniFrac Distances Using the GUniFrac Package 345

10.2.6 Remarks on Rarefaction for Alpha and Beta Diversity Analysis 348

10.3 Ordination Methods 349

10.3.1 Introduction to Ordination 349

10.3.2 Ordination Plots in the ampvis2 Package 352

10.3.3 Principal Component Analysis (PCA) 353

10.3.4 Principal Coordinate Analysis (PCoA) 359

10.3.5 Nonmetric Multidimensional Scaling (NMDS) 362

10.3.6 Correspondence Analysis (CA) 366

10.3.7 Detrended Correspondence Analysis (DCA) 371

10.3.8 Redundancy Analysis (RDA) 374

10.3.9 Canonical Correspondence Analysis (CCA) 377

10.4 Beta Diversity Metrics and Ordination in QIIME 2 381

10.4.1 Calculate Beta Diversity Measures 381

10.4.2 Explore Principal Coordinates (PCoA) Using Emperor Plots 382

10.5 Remarks on Ordination and Clustering 384

10.6 Summary 388

References 388

11 Statistical Testing of Beta Diversity 397

11.1 Introduction to Nonparametric MANOVA Using Permutation Tests 397

11.2 Analysis of Similarity (ANOSIM) 398

11.2.1 Introduction of ANOSIM 399

11.2.2 Perform ANOSIM Using the Vegan Package 401

11.2.3 Remarks on ANOSIM 404

11.3 Permutational MANOVA (PERMANOVA) 405

11.3.1 Introduction to PERMANOVA 405

11.3.2 Perform PERMANOVA Using the Vegan Package 409

11.3.3 Remarks on PERMANOVA 417

11.4 Analysis of Multivariate Homogeneity of Group Dispersions 418

11.4.1 Introduction to the Function betadisper() 418

11.4.2 Implement the Function betadisper() 419

11.5 Pairwise PERMANOVA 422

11.5.1 Introduction to Pairwise PERMMANOVA 422

11.5.2 Implement Pairwise PERMMANOVA Using the RVAideMemoire Package 423

11.6 Identify Core Microbial Taxa Using the Microbiome Package 426

11.7 Statistical Testing of Beta Diversity in QIIME 2 428

11.7.1 Significant Testing of Bray-Curtis Distance 429

11.7.2 Significant Testing of Jaccard Distance 430

11.7.3 Significant Testing of Unweighted UniFrac Distance 430

11.7.4 Significant Testing of Weighted UniFrac Distance 431

11.8 Summary 431

References 431

12 Differential Abundance Analysis of Microbiome Data 435

12.1 Zero-Inflated Gaussian (ZIG) and Zero-Inflated Log-Normal (ZILN) Mixture Models 436

12.1.1 Total Sum Scaling (TSS) 437

12.1.2 Cumulative Sum Scaling (CSS) 438

12.1.3 ZIG and ZILN Models 438

12.2 Implement ZILN via metagenomeSeq 440

12.3 Some Additional Statistical Tests in metagenomeSeq 453

12.3.1 Log-Normal Permutation Test of Abundance 453

12.3.2 Presence-Absence Testing of the Proportion/Odds 454

12.3.3 Discovery Odds Ratio Testing of the Proportion of Observed Counts 455

12.3.4 Perform Feature Correlations 455

12.4 Illustrate Some Useful Functions in metagenomeSeq 456

12.4.1 Access the MRexperiment Object 456

12.4.2 Subset the MRexperiment Object 457

12.4.3 Filter the MRexperiment Object or Count Matrix 458

12.4.4 Merge the MRexperiment Object 458

12.4.5 Call the Normalized Counts Using the cumNormMat() and MRcounts() 459

12.4.6 Calculate the Normalization Factors Using the calcNormFactors() 460

12.4.7 Access the Library Sizes Using the libSize() 460

12.4.8 Save the Normalized Counts Using the exportMat() 461

12.4.9 Save the Sample Statistics Using the exportStats() 461

12.4.10 Find Unique OTUs or Features 461

12.4.11 Aggregate Taxa 462

12.4.12 Aggregate Samples 463

12.5 Remarks on CSS Normalization, ZIG, and ZILN 465

12.6 Summary 466

References 467

13 Zero-Inflated Beta Models for Microbiome Data 469

13.1 Zero-Inflated Beta Modeling Microbiome Data 469

13.2 Zero-Inflated Beta Regression (ZIBSeq) 471

13.2.1 Introduction to ZIBseq 471

13.2.2 Implement ZIBseq 473

13.2.3 Remarks on ZIBSeq 479

13.3 Zero-Inflated Beta-Binomial Model (ZIBB) 480

13.3.1 Introduction to ZIBB 480

13.3.2 Implement ZIBB 483

13.3.3 Remarks on ZIBB 488

13.4 Summary 489

References 489

14 Compositional Analysis of Microbiome Data 491

14.1 Introduction to Compositional Data 492

14.1.1 What Are Compositional Data? 492

14.1.2 Microbiome Data Are Treated as Compositional 492

14.1.3 Aitchison Simplex 493

14.1.4 Challenges of Analyzing Compositional Data 494

14.1.5 Fundamental Principles of Compositional Data Analysis 495

14.1.6 The Family of Log-Ratio Transformations 496

14.1.7 Remarks on Log-Ratio Transformations 498

14.2 ANOVA-Like Compositional Differential Abundance Analysis 500

14.2.1 Introduction to ALDEx2 500

14.2.2 Implement ALDEx2 Using R 505

14.2.3 Remarks on ALDEx2 517

14.3 Analysis of Composition of Microbiomes (ANCOM) 518

14.3.1 Introduction to ANCOM 519

14.3.2 Implement ANCOM Using QIIME 2 520

14.3.3 Remarks on ANCOM 526

14.4 Analysis of Composition of Microbiomes-Bias Correction (ANCOM-BC) 528

14.4.1 Introduction to ANCOM-BC 528

14.4.2 Implement ANCOM-BC Using the ANCOMBC Package 532

14.4.3 Remarks on ANCOM-BC 547

14.5 Remarks on Compositional Data Analysis Approach 549

14.6 Summary 551

References 551

15 Linear Mixed-Effects Models for Longitudinal Microbiome Data 557

15.1 Introduction to Linear Mixed-Effects Models (LMMs) 558

15.1.1 Advantages and Disadvantages of LMMs 558

15.1.2 Fixed and Random Effects 559

15.1.3 Definition of LMMs 559

15.1.4 Statistical Hypothesis Tests 560

15.1.5 How to Fit LMMs 561

15.2 Identifying the Significant Taxa Using the nlme Package 563

15.2.1 Introduction to LMMs in Microbiome Research 563

15.2.2 Longitudinal Microbiome Data Structure 564

15.2.3 Fit LMMs Using the Read Counts as the Outcome 565

15.3 Modeling the Diversity Indices Using the lme4 and LmerTest Packages 570

15.3.1 Introduction to the lme4 and lmerTest Packages 571

15.3.2 Fit LMMs Using the Diversity Index as the Outcome 572

15.4 Implement LMMs Using QIIME 2 576

15.4.1 Introduction to the QIIME Longitudinal Linear-Mixed-Effects Command 576

15.4.2 Fit LMMs in QIIME 2 577

15.4.3 Perform Volatility Analysis 579

15.5 Remarks on LMMs 581

15.6 Summary 582

References 582

16 Introduction to Generalized Linear Mixed Models 587

16.1 Generalized Linear Models (GLMs) and Generalized Nonlinear Models (GNLMs) 588

16.2 Generalized Linear Mixed Models (GLMMs) 588

16.3 Model Estimation in GLMMs 590

16.4 Algorithms for Parameter Estimation in GLMMs 591

16.4.1 Penalized Quasi-Likelihood-Based Methods Using Taylor-Series Linearization 592

16.4.2 Likelihood-Based Methods Using Numerical Integration 593

16.4.3 Markov Chain Monte Carlo-Based Integration 595

16.4.4 IWLS and EM-IWLS Algorithms 596

16.5 Statistical Hypothesis Testing and Modeling in GLMMs 599

16.5.1 Model Selection in Statistics 599

16.5.2 Model Selection in Machine Learning 599

16.5.3 Information Criteria for Model Selection 600

16.5.4 Likelihood-Ratio Test 605

16.5.5 Vuong Test 607

16.6 Summary 608

References 608

17 Generalized Linear Mixed Models for Longitudinal Microbiome Data 615

17.1 Generalized Linear Mixed Models (GLMMs) in Microbiome Research 616

17.1.1 Data Transformation Versus Using GLMMs 617

17.1.2 Model Selection in Microbiome Data 618

17.1.3 Statistical Hypothesis Testing in Microbiome Data 619

17.2 Generalized Linear Mixed Modeling Using the glmmTMB Package 621

17.2.1 Introduction to glmmTMB 621

17.2.2 Implement GLMMs via glmmTMB 624

17.2.3 Remarks on glmmTMB 646

17.3 Generalized Linear Mixed Modeling Using the GLMMadaptive Package 647

17.3.1 Introduction to GLMMadaptive 647

17.3.2 Implement GLMMs via GLMMadaptive 647

17.3.3 Remarks on GLMMadaptive 659

17.4 Fast Zero-Inflated Negative Binomial Mixed Modeling (FZINBMM) 660

17.4.1 Introduction to FZINBMM 660

17.4.2 Implement FZINBMM Using the NBZIMM Package 664

17.4.3 Remarks on FZINBMM 668

17.5 Remarks on Fitting GLMMs 669

17.6 Summary 670

References 671

18 Multivariate Longitudinal Microbiome Models 675

18.1 Overview of Multivariate Longitudinal Microbiome Analysis 675

18.1.1 Multivariate Distance/Kernel-Based Longitudinal Models 676

18.1.2 Multivariate Integration of Multi-omics Methods 677

18.1.3 Univariate Analysis Versus Multivariate Analysis 678

18.2 Nonparametric Microbial Interdependence Test (NMIT) 678

18.2.1 Introduction to NMIT 679

18.2.2 Implement NMIT Using R 680

18.2.3 Implement NMIT Using QIIME 2 687

18.2.4 Remarks on NMIT 690

18.3 The Large P Small N Problem 692

18.4 Summary 693

References 693

Index 697

About the Authors

Yinglin Xia

is a Research Professor in the Department of Medicine at the University of Illinois Chicago (UIC). He was a Research Assistant Professor in the Department of Biostatistics and Computational Biology at the University of Rochester (Rochester, NY) before joining AbbVie (North Chicago, IL) as a Clinical Statistician. He joined UIC as a Research Associate Professor in 2015. Dr. Xia has successfully applied his statistical study design and data analysis skills to clinical trials, medical statistics, biomedical sciences, and social and behavioral sciences. He has published more than 140 statistical methodology and research papers in peer-reviewed journals. He serves on the editorial boards of several scientific journals including as an Associate Editor of Gut Microbes and has served as a reviewer for over 100 scientific journals. Dr. Xia has published three books on statistical analysis of microbiome and metabolomics data. He is the lead author of Statistical Analysis of Microbiome Data with R (Springer Nature, 2018), which was the first statistics book in microbiome study, Statistical Data Analysis of Microbiomes and Metabolomics (American Chemical Society, 2022), and An Integrated Analysis of Microbiomes and Metabolomics (American Chemical Society, 2022).A photo of Yinglin Xia.

Jun Sun

is a tenured Professor of Medicine at the University of Illinois Chicago. She is an elected fellow of the American Gastroenterological Association (AGA) and American Physiological Society (APS). She chairs the AGA Microbiome and Microbial Therapy section (2020–2022). She is an internationally recognized expert on microbiome and human diseases, such as vitamin D receptor in inflammation, dysbiosis, and intestinal dysfunction in amyotrophic lateral sclerosis (ALS). Her lab is the first to discover that chronic effects and molecular mechanisms of Salmonella infection and development of colon cancer. Dr. Sun has published over 210 scientific articles in peer-reviewed journals and 8 books on microbiome. She is on the editorial boards of more than 10 peer-reviewed international scientific journals and serves on the study sections for the national and international research foundations. Dr. Sun is a believer of scientific art and artistic science. She enjoys writing her science papers in English and poems in Chinese. Her poetry collection book《让时间停留在这一刻》(“Let Time Stay Still at This Moment”) was published in 2018.A photo of Jun Sun.