Introductory Overview of Statistical Analysis of Microbiome Data

In this chapter, we first introduce and discuss the themes and statistical hypotheses in human microbiome studies in Sect. 3.1. Then, we overview the classic statistical methods and models for microbiome studies in Sect. 3.2. In Sect. 3.3, we introduce the newly developed multivariate statistical methods. Section 3.4 introduces the compositional analysis of microbiome data. In Sect. 3.5, we discuss the longitudinal data analysis and causal inference in microbiome studies. In Sect. 3.6, we introduce some statistical packages for analyzing microbiome data. Finally, we cover the limitations of existing statistical methods and future development in Sect. 3.7.

[1]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[2]  T. Roane,et al.  Perturbation and restoration of the fathead minnow gut microbiome after low-level triclosan exposure , 2015, Microbiome.

[3]  Timothy J. Laurent,et al.  A Taxonomic Signature of Obesity in the Microbiome? Getting to the Guts of the Matter , 2014, PloS one.

[4]  Martin J Blaser,et al.  Community differentiation of the cutaneous microbiota in psoriasis , 2013, Microbiome.

[5]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[6]  Eric S. Lander,et al.  Natural history of the infant gut microbiome and impact of antibiotic treatment on bacterial strain diversity and stability , 2015, Science Translational Medicine.

[7]  W. Ledger,et al.  Complexities of the Uniquely Human Vagina , 2012, Science Translational Medicine.

[8]  Hongzhe Li,et al.  Power and sample-size estimation for microbiome studies using pairwise distances and PERMANOVA , 2015, Bioinform..

[9]  Jian Huang,et al.  SCAD-penalized regression in high-dimensional partially linear models , 2009, 0903.5474.

[10]  Simeone Marino,et al.  Mathematical modeling of primary succession of murine intestinal microbiota , 2013, Proceedings of the National Academy of Sciences.

[11]  N. Stenseth,et al.  Convergent temporal dynamics of the human infant gut microbiota , 2010, The ISME Journal.

[12]  C. Huh,et al.  Comparative Analysis of the Gut Microbiota in People with Different Levels of Ginsenoside Rb1 Degradation to Compound K , 2013, PloS one.

[13]  Liping Zhao,et al.  An opportunistic pathogen isolated from the gut of an obese human causes obesity in germfree mice , 2012, The ISME Journal.

[14]  Yinglin Xia,et al.  Intestinal epithelial vitamin D receptor deletion leads to defective autophagy in colitis , 2014, Gut.

[15]  Ping Liu,et al.  Structural changes of gut microbiota in a rat non-alcoholic fatty liver disease model treated with a Chinese herbal formula. , 2013, Systematic and applied microbiology.

[16]  R. Knight,et al.  Meta‐analyses of human gut microbes associated with obesity and IBD , 2014, FEBS letters.

[17]  David S. Wishart,et al.  INMEX—a web-based tool for integrative meta-analysis of expression data , 2013, Nucleic Acids Res..

[18]  Rafael A. Irizarry,et al.  Meta-analysis of gut microbiome studies identifies disease-specific and shared responses , 2017, Nature Communications.

[19]  Vanni Bucci,et al.  MDSINE: Microbial Dynamical Systems INference Engine for microbiome time-series analyses , 2016, Genome Biology.

[20]  G. Tseng,et al.  Comprehensive literature review and statistical considerations for GWAS meta-analysis , 2012, Nucleic acids research.

[21]  M. Gorzelak,et al.  Methods for Improving Human Gut Microbiome Data by Reducing Variability through Sample Processing and Storage of Stool , 2015, PloS one.

[22]  Fengzhu Sun,et al.  Variance adjusted weighted UniFrac: a powerful beta diversity measure for comparing communities based on phylogeny , 2011, BMC Bioinformatics.

[23]  Yan He,et al.  Comparison of microbial diversity determined with the same variable tag sequence extracted from two different PCR amplicons , 2013, BMC Microbiology.

[24]  Lu Wang,et al.  The NIH Human Microbiome Project. , 2009, Genome research.

[25]  Les Dethlefsen,et al.  The Pervasive Effects of an Antibiotic on the Human Gut Microbiota, as Revealed by Deep 16S rRNA Sequencing , 2008, PLoS biology.

[26]  N. Stenseth,et al.  Seasonal plankton dynamics along a cross-shelf gradient , 2006, Proceedings of the Royal Society B: Biological Sciences.

[27]  William A. Walters,et al.  QIIME allows analysis of high-throughput community sequencing data , 2010, Nature Methods.

[28]  George Sugihara,et al.  Detecting Causality in Complex Ecosystems , 2012, Science.

[29]  F. Turroni,et al.  Meta‐analysis of the human gut microbiome from urbanized and pre‐agricultural populations , 2017, Environmental microbiology.

[30]  William D. Shannon,et al.  Patterned progression of bacterial populations in the premature infant gut , 2014, Proceedings of the National Academy of Sciences.

[31]  Kyle Bittinger,et al.  Comparative metabolomics in vegans and omnivores reveal constraints on diet-dependent gut microbiota metabolite production , 2014, Gut.

[32]  Daniel B. DiGiulio,et al.  Development of the Human Infant Intestinal Microbiota , 2007, PLoS biology.

[33]  Curtis Huttenhower,et al.  Chapter 12: Human Microbiome Analysis , 2012, PLoS Comput. Biol..

[34]  D. Moher,et al.  Preferred reporting items for systematic reviews and meta-analyses: the PRISMA Statement , 2009, BMJ : British Medical Journal.

[35]  V. D’Argenio,et al.  Comparative Metagenomic Analysis of Human Gut Microbiome Composition Using Two Different Bioinformatic Pipelines , 2014, BioMed research international.

[36]  Nicholas Chia,et al.  Impact of demographics on human gut microbial diversity in a US Midwest population , 2016, PeerJ.

[37]  Kyu Ha Lee,et al.  Bayesian variable selection for multivariate zero-inflated models: Application to microbiome count data. , 2017, Biostatistics.

[38]  Runze Li,et al.  Statistical Challenges with High Dimensionality: Feature Selection in Knowledge Discovery , 2006, math/0602133.

[39]  David J. Edwards,et al.  Hypothesis Testing and Power Calculations for Taxonomic-Based Human Microbiome Data , 2012, PloS one.

[40]  Rafael Bargiela,et al.  Gut microbiota disturbance during antibiotic therapy: a multi-omic approach , 2012, Gut.

[41]  Lei Zhang,et al.  Negative binomial mixed models for analyzing microbiome count data , 2017, BMC Bioinformatics.

[42]  Jürg Bähler,et al.  Proportionality: A Valid Alternative to Correlation for Relative Data , 2014, bioRxiv.

[43]  Ruth Ley,et al.  Unravelling the effects of the environment and host genotype on the gut microbiome , 2011, Nature Reviews Microbiology.

[44]  D. Moher,et al.  Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement , 2009, BMJ : British Medical Journal.

[45]  H. Curtis.  What is normal vaginal flora? , 1997, Genitourinary medicine.

[46]  N. Yi,et al.  ZERO-INFLATED NEGATIVE BINOMIAL REGRESSION FOR DIFFERENTIAL ABUNDANCE TESTING IN MICROBIOME STUDIES , 2016 .

[47]  R. Knight,et al.  Microbial community resemblance methods differ in their ability to detect biologically relevant patterns , 2010, Nature Methods.

[48]  Nicholas A. Bokulich,et al.  Metabolic and metagenomic outcomes from early-life pulsed antibiotic treatment , 2015, Nature Communications.

[49]  R. Cook.  On the Interpretation of Regression Plots , 1994 .

[50]  Thomas P. Quinn,et al.  Differential proportionality –a normalization-free approach to differential gene expression , 2017, bioRxiv.

[51]  Dan R. Littman,et al.  Induction of Intestinal Th17 Cells by Segmented Filamentous Bacteria , 2009, Cell.

[52]  Mark D. Robinson,et al.  edgeR: a Bioconductor package for differential expression analysis of digital gene expression data , 2009, Bioinform..

[53]  S. Sereika,et al.  Vector Autoregressive Models and Granger Causality in Time Series Analysis in Nursing Research: Dynamic Changes Among Vital Signs Prior to Cardiorespiratory Instability Events as an Example , 2017, Nursing research.

[54]  William T. Langford,et al.  Biodiversity and species interactions: extending Lotka-Volterra community theory , 2003 .

[55]  Mark D. Robinson,et al.  Moderated statistical tests for assessing differences in tag abundance , 2007, Bioinform..

[56]  Juhee Lee,et al.  A Bayesian Semiparametric Regression Model for Joint Analysis of Microbiome Data , 2018, Front. Microbiol..

[57]  J. Sobel,et al.  Emerging role of lactobacilli in the control and maintenance of the vaginal bacterial microflora. , 1990, Reviews of infectious diseases.

[58]  Erik Kristiansson,et al.  Variability in Metagenomic Count Data and Its Influence on the Identification of Differentially Abundant Genes , 2017, J. Comput. Biol..

[59]  J. Clemente,et al.  Gut Microbiota from Twins Discordant for Obesity Modulate Metabolism in Mice , 2013, Science.

[60]  G. Wu,et al.  Diet and the intestinal microbiome: associations, functions, and implications for health and disease. , 2014, Gastroenterology.

[61]  M. Verdegem,et al.  The Colonization Dynamics of the Gut Microbiota in Tilapia Larvae , 2014, PloS one.

[62]  R. Knight,et al.  The Effect of Diet on the Human Gut Microbiome: A Metagenomic Analysis in Humanized Gnotobiotic Mice , 2009, Science Translational Medicine.

[63]  R. Knight,et al.  UniFrac: an effective distance metric for microbial community comparison , 2011, The ISME Journal.

[64]  R. Knight,et al.  UniFrac: a New Phylogenetic Method for Comparing Microbial Communities , 2005, Applied and Environmental Microbiology.

[65]  J. Ware,et al.  Applied Longitudinal Analysis , 2004 .

[66]  Statistical methods and issues in the study of suicide , 2012 .

[67]  Jun Lu,et al.  BMC Bioinformatics BioMed Central Methodology article Identifying differential expression in multiple SAGE libraries: an , 2005 .

[68]  Ji Zhu,et al.  A ug 2 01 0 Group Variable Selection via a Hierarchical Lasso and Its Oracle Property Nengfeng Zhou Consumer Credit Risk Solutions Bank of America Charlotte , NC 28255 , 2010 .

[69]  Marti J. Anderson,et al.  A new method for non-parametric multivariate analysis of variance in ecology , 2001 .

[70]  P. Diggle,et al.  Analysis of Longitudinal Data , 2003 .

[71]  N. Pillai,et al.  Dirichlet–Laplace Priors for Optimal Shrinkage , 2014, Journal of the American Statistical Association.

[72]  E. Plummer,et al.  A Comparison of Three Bioinformatics Pipelines for the Analysis ofPreterm Gut Microbiota using 16S rRNA Gene Sequencing Data , 2015 .

[73]  L. T. Angenent,et al.  Succession of microbial consortia in the developing infant gut microbiome , 2010, Proceedings of the National Academy of Sciences.

[74]  F. Bushman,et al.  Linking Long-Term Dietary Patterns with Gut Microbial Enterotypes , 2011, Science.

[75]  F. Bäckhed,et al.  Obesity alters gut microbial ecology. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[76]  Jean M. Macklaim,et al.  ANOVA-Like Differential Expression (ALDEx) Analysis for Mixed Population RNA-Seq , 2013, PloS one.

[77]  Liping Zhao,et al.  Strain-level dissection of the contribution of the gut microbiome to human metabolic disease , 2016, Genome Medicine.

[78]  Hongzhe Li,et al.  A two-part mixed-effects model for analyzing longitudinal microbiome compositional data , 2016, Bioinform..

[79]  Roberto Romero,et al.  Correction: The composition and stability of the vaginal microbiota of normal pregnant women is different from that of non-pregnant women , 2014, Microbiome.

[80]  Levi Waldron,et al.  Composition of the adult digestive tract bacterial microbiome based on seven mouth surfaces, tonsils, throat and stool samples , 2012, Genome Biology.

[81]  Richard A. Moore,et al.  Fusobacterium nucleatum infection is prevalent in human colorectal carcinoma. , 2012, Genome research.

[82]  Hongzhe Li,et al.  Disordered Microbial Communities in the Upper Respiratory Tract of Cigarette Smokers , 2010, PloS one.

[83]  Brian H. McArdle,et al.  FITTING MULTIVARIATE MODELS TO COMMUNITY DATA: A COMMENT ON DISTANCE‐BASED REDUNDANCY ANALYSIS , 2001 .

[84]  Jens Roat Kultima,et al.  Temporal and technical variability of human gut metagenomes , 2015, Genome Biology.

[85]  U. Nöthlings,et al.  Genome-wide association analysis identifies variation in vitamin D receptor and other host factors influencing the gut microbiota , 2016, Nature Genetics.

[86]  M. Robinson,et al.  Small-sample estimation of negative binomial dispersion, with applications to SAGE data. , 2007, Biostatistics.

[87]  Roberto Romero,et al.  The composition and stability of the vaginal microbiota of normal pregnant women is different from that of non-pregnant women , 2014, Microbiome.

[88]  Daniel B. Rowe,et al.  Multivariate Bayesian Statistics: Models for Source Separation and Signal Unmixing , 2002 .

[89]  Ker-Chau Li,et al.  Sliced Inverse Regression for Dimension Reduction , 1991 .

[90]  Tormod Næs,et al.  Characterizing mixed microbial population dynamics using time-series analysis , 2008, The ISME Journal.

[91]  Yan Wang,et al.  Predicting microbial interactions by using network-constrained regularization incorporating covariate coefficients and connection signs , 2015, 2015 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

[92]  Melissa J. Morine,et al.  The role of breast-feeding in infant immune system: a systems perspective on the intestinal microbiome , 2015, Microbiome.

[93]  N. Ho,et al.  metamicrobiomeR: an R package for analysis of microbiome relative abundance data using zero-inflated beta GAMLSS and meta-analysis across studies using random effect models , 2018, bioRxiv.

[94]  G. Weinstock,et al.  Hypothesis Testing of Metagenomic Data , 2015 .

[95]  Hui Zhang,et al.  Modeling longitudinal binomial responses: implications from two dueling paradigms , 2011 .

[96]  R. Knight,et al.  Dietary input of microbes and host genetic variation shape among-population differences in stickleback gut microbiota , 2015, The ISME Journal.

[97]  Jean Thioulouse,et al.  Simultaneous analysis of a sequence of paired ecological tables: A comparison of several methods , 2011, 1202.5473.

[98]  J. Harris,et al.  Zero-inflated negative binomial mixed model: an application to two microbial organisms important in oesophagitis , 2016, Epidemiology and Infection.

[99]  S. Y. Dennis.  On the hyper-Dirichlet type 1 and hyper-Liouville distributions , 1991 .

[100]  M. Pop,et al.  Robust methods for differential abundance analysis in marker gene surveys , 2013, Nature Methods.

[101]  V. Tremaroli,et al.  Dynamics and Stabilization of the Human Gut Microbiome during the First Year of Life. , 2015, Cell host & microbe.

[102]  R. Knight,et al.  Quantitative and Qualitative β Diversity Measures Lead to Different Insights into Factors That Structure Microbial Communities , 2007, Applied and Environmental Microbiology.

[103]  H. Ochman,et al.  Factors associated with the diversification of the gut microbial communities within chimpanzees from Gombe National Park , 2012, Proceedings of the National Academy of Sciences.

[104]  Tommi Vatanen,et al.  The dynamics of the human infant gut microbiome in development and in progression toward type 1 diabetes. , 2015, Cell host & microbe.

[105]  D. Littman,et al.  Segmented filamentous bacteria take the stage , 2010, Mucosal Immunology.

[106]  Jian Huang,et al.  A Selective Review of Group Selection in High-Dimensional Models. , 2012, Statistical science : a review journal of the Institute of Mathematical Statistics.

[107]  Susan Holmes,et al.  phyloseq: An R Package for Reproducible Interactive Analysis and Graphics of Microbiome Census Data , 2013, PloS one.

[108]  K. Pearson.  Mathematical contributions to the theory of evolution.—On a form of spurious correlation which may arise when indices are used in the measurement of organs , 1897, Proceedings of the Royal Society of London.

[109]  Gordon K. Smyth,et al.  limma: Linear Models for Microarray Data , 2005 .

[110]  Jizhong Zhou,et al.  Environmental filtering decreases with fish development for the assembly of gut microbiota. , 2016, Environmental microbiology.

[111]  Scott Powell,et al.  Stability and phylogenetic correlation in gut microbiota: lessons from ants and apes , 2014, Molecular ecology.

[112]  Liping Zhao.  The gut microbiota and obesity: from correlation to causality , 2013, Nature Reviews Microbiology.

[113]  N. Swenson.  Phylogenetic Beta Diversity Metrics, Trait Evolution and Inferring the Functional Beta Diversity of Communities , 2011, PloS one.

[114]  John D. Storey,et al.  Statistical significance for genomewide studies , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[115]  Yi Guo,et al.  Selecting a sample size for studies with repeated measures , 2013, BMC Medical Research Methodology.

[116]  J. Hanfelt,et al.  Bolus Weekly Vitamin D3 Supplementation Impacts Gut and Airway Microbiota in Adults With Cystic Fibrosis: A Double-Blind, Randomized, Placebo-Controlled Clinical Trial , 2018, The Journal of clinical endocrinology and metabolism.

[117]  Li Ma,et al.  A phylogenetic scan test on a Dirichlet-tree multinomial model for microbiome data , 2016, 1610.08974.

[118]  Yinglin Xia,et al.  Lack of Vitamin D Receptor Causes Dysbiosis and Changes the Functions of the Murine Intestinal Microbiome. , 2015, Clinical therapeutics.

[119]  Charles K. Fisher,et al.  Identifying Keystone Species in the Human Gut Microbiome from Metagenomic Timeseries Using Sparse Linear Regression , 2014, PloS one.

[120]  Jingming Ma,et al.  Modeling Count Outcomes from HIV Risk Reduction Interventions: A Comparison of Competing Statistical Models for Count Responses , 2012, AIDS research and treatment.

[121]  Matthew L. Jenior,et al.  Intra- and Interindividual Variations Mask Interspecies Variation in the Microbiota of Sympatric Peromyscus Populations , 2014, Applied and Environmental Microbiology.

[122]  J. Aitchison.  A new approach to null correlations of proportions , 1981 .

[123]  D. Relman,et al.  Incomplete recovery and individualized responses of the human distal gut microbiota to repeated antibiotic perturbation , 2010, Proceedings of the National Academy of Sciences.

[124]  J. Aitchison.  Principal component analysis of compositional data , 1983 .

[125]  L. Trippa,et al.  Bayesian Nonparametric Ordination for the Analysis of Microbial Communities , 2016, Journal of the American Statistical Association.

[126]  M. Rogosa,et al.  Species differentiation of human vaginal lactobacilli. , 1960, Journal of general microbiology.

[127]  Georg K Gerber,et al.  The dynamic microbiome , 2014, FEBS letters.

[128]  R. Rigby,et al.  Generalized additive models for location, scale and shape , 2005 .

[129]  R. Knight,et al.  Bacterial Community Variation in Human Body Habitats Across Space and Time , 2009, Science.

[130]  Hongzhe Li,et al.  VARIABLE SELECTION FOR SPARSE DIRICHLET-MULTINOMIAL REGRESSION WITH AN APPLICATION TO MICROBIOME DATA ANALYSIS. , 2013, The annals of applied statistics.

[131]  Rob Knight,et al.  Analysis of composition of microbiomes: a novel method for studying microbial composition , 2015, Microbial ecology in health and disease.

[132]  Brian J. Reich,et al.  MIMIX: A Bayesian Mixed-Effects Model for Microbiome Data From Designed Experiments , 2017, Journal of the American Statistical Association.

[133]  Heather K. Allen,et al.  Meta-analysis To Define a Core Microbiota in the Swine Gut , 2017, mSystems.

[134]  B. Birren,et al.  Genomic analysis identifies association of Fusobacterium with colorectal carcinoma. , 2012, Genome research.

[135]  Anders F. Andersson,et al.  Short-Term Antibiotic Treatment Has Differing Long-Term Impacts on the Human Throat and Gut Microbiome , 2010, PloS one.

[136]  Martin Hartmann,et al.  Introducing mothur: Open-Source, Platform-Independent, Community-Supported Software for Describing and Comparing Microbial Communities , 2009, Applied and Environmental Microbiology.

[137]  Hongyu Zhao,et al.  A Dirichlet‐tree multinomial regression model for associating dietary nutrients with gut microorganisms , 2017, Biometrics.

[138]  Susan P. Holmes,et al.  Waste Not , Want Not : Why Rarefying Microbiome Data is Inadmissible . October 1 , 2013 , 2013 .

[139]  Georg K. Gerber,et al.  Longitudinal Microbiome Data Analysis , 2015 .

[140]  R. Dennis Cook,et al.  Testing predictor contributions in sufficient dimension reduction , 2004, math/0406520.

[141]  M A Krohn,et al.  The normal vaginal flora, H2O2-producing lactobacilli, and bacterial vaginosis in pregnant women. , 1993, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[142]  Hongzhe Li,et al.  Associating microbiome composition with environmental covariates using generalized UniFrac distances , 2012, Bioinform..

[143]  C. Xiang,et al.  Human Intestinal Lumen and Mucosa-Associated Microbiota in Patients with Colorectal Cancer , 2012, PloS one.

[144]  Lusheng Huang,et al.  Uncovering the composition of microbial community structure and metagenomics among three gut locations in pigs with distinct fatness , 2016, Scientific Reports.

[145]  Yinglin Xia,et al.  Hypothesis testing and statistical analysis of microbiome , 2017, Genes & diseases.

[146]  Gregory B. Gloor,et al.  Compositional analysis: a valid approach to analyze microbiome high-throughput sequencing data. , 2016, Canadian journal of microbiology.

[147]  Liping Zhao,et al.  Structural segregation of gut microbiota between colorectal cancer patients and healthy volunteers , 2011, The ISME Journal.

[148]  R. Rigby,et al.  Generalized Additive Models for Location Scale and Shape (GAMLSS) in R , 2007 .

[149]  Gregory B Gloor,et al.  Expanding the UniFrac Toolbox , 2016, PloS one.

[150]  R. Knight,et al.  Meta-analyses of studies of the human microbiota , 2013, Genome research.

[151]  Gunnar Rätsch,et al.  Ecological Modeling from Time-Series Inference: Insight into Dynamics and Stability of Intestinal Microbiota , 2013, PLoS Comput. Biol..

[152]  Wei Xu,et al.  Assessment and Selection of Competing Models for Zero-Inflated Microbiome Data , 2015, PloS one.

[153]  James F. Meadow,et al.  Microbiota of the indoor environment: a meta-analysis , 2015, Microbiome.

[154]  Mihai Pop,et al.  Statistical Methods for Detecting Differentially Abundant Features in Clinical Metagenomic Samples , 2009, PLoS Comput. Biol..

[155]  L. Ursell,et al.  Gut Microbiomes of Malawian Twin Pairs Discordant for Kwashiorkor , 2013, Science.

[156]  S. Kelley,et al.  The Gut Microbiome Is Altered in a Letrozole-Induced Mouse Model of Polycystic Ovary Syndrome , 2016, PloS one.

[157]  Timothy L. Tickle,et al.  Dysfunction of the intestinal microbiome in inflammatory bowel disease and treatment , 2012, Genome Biology.

[158]  Haema Nilakanta,et al.  A review of software for analyzing molecular sequences , 2014, BMC Research Notes.

[159]  Vera Pawlowsky-Glahn,et al.  It's all relative: analyzing microbiome data as compositions. , 2016, Annals of epidemiology.

[160]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[161]  Eric Z. Chen,et al.  Inflammation, Antibiotics, and Diet as Environmental Stressors of the Gut Microbiome in Pediatric Crohn's Disease. , 2015, Cell host & microbe.

[162]  Jenny Tung,et al.  Social networks predict gut microbiome composition in wild baboons , 2015, eLife.

[163]  J. Gordon,et al.  A humanized gnotobiotic mouse model of host-archaeal-bacterial mutualism. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[164]  Xiangrong Yin,et al.  Sequential sufficient dimension reduction for large p, small n problems , 2015 .

[165]  A. Stapleton,et al.  Inverse association of H2O2-producing lactobacilli and vaginal Escherichia coli colonization in women with recurrent urinary tract infections. , 1998, The Journal of infectious diseases.

[166]  J. Lewis,et al.  Food and the gut microbiota in inflammatory bowel diseases: a critical connection , 2012, Current opinion in gastroenterology.

[167]  Davis J. McCarthy,et al.  Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation , 2012, Nucleic acids research.

[168]  Patrick D. Schloss,et al.  Looking for a Signal in the Noise: Revisiting Obesity and the Microbiome , 2016, mBio.

[169]  Cédric Notredame,et al.  How should we measure proportionality on relative gene expression data? , 2016, Theory in Biosciences.

[170]  Georg K. Gerber,et al.  Inferring Dynamic Signatures of Microbes in Complex Host Ecosystems , 2012, PLoS Comput. Biol..

[171]  R. Knight,et al.  Diversity, stability and resilience of the human gut microbiota , 2012, Nature.

[172]  Hongzhe Li,et al.  A Logistic Normal Multinomial Regression Model for Microbiome Compositional Data Analysis , 2013, Biometrics.

[173]  D. Nicolae,et al.  Mixed Effect Dirichlet-Tree Multinomial for Longitudinal Microbiome Data and Weight Prediction , 2017, 1706.06380.

[174]  J. Gordon,et al.  Gnotobiotic zebrafish reveal evolutionarily conserved responses to the gut microbiota. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[175]  K. Gerald van den Boogaart,et al.  Analyzing Compositional Data with R , 2013 .

[176]  V. Pawlowsky-Glahn,et al.  Compositional data analysis : theory and applications , 2011 .

[177]  Eric J. Alm,et al.  Two dynamic regimes in the human gut microbiome , 2017, PLoS Comput. Biol..

[178]  Jun Sun,et al.  Exploring gut microbes in human health and disease: Pushing the envelope , 2014, Genes & diseases.

[179]  Kung-Sik Chan,et al.  The effect of climate variation on agro-pastoral production in Africa. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[180]  William D. Shannon,et al.  Statistical Object Data Analysis of Taxonomic Trees from Human Microbiome Data , 2012, PloS one.

[181]  J. Viktor.  Statistical analysis and modelling of gene count data in metagenomics , 2017 .

[182]  N. Stenseth,et al.  From patterns to processes and back: analysing density-dependent responses to an abiotic stressor by statistical and mechanistic modelling , 2005, Proceedings of the Royal Society B: Biological Sciences.

[183]  D. Mackinnon.  Introduction to Statistical Mediation Analysis , 2008 .

[184]  B. White,et al.  Fecal microbiomes of non‐human primates in Western Uganda reveal species‐specific communities largely resistant to habitat perturbation , 2014, American journal of primatology.

[185]  W. D. de Vos,et al.  Associations between the human intestinal microbiota, Lactobacillus rhamnosus GG and serum lipids indicated by integrated analysis of high-throughput profiling data , 2013, PeerJ.

[186]  J. Aitchison.  Reducing the dimensionality of compositional data sets , 1984 .

[187]  Jun Chen,et al.  An omnibus test for differential distribution analysis of microbiome sequencing data , 2018, Bioinform..

[188]  Marina Vannucci,et al.  An integrative Bayesian Dirichlet-multinomial regression model for the analysis of taxonomic abundances in microbiome data , 2017, BMC Bioinformatics.

[189]  C. Quince,et al.  Dirichlet Multinomial Mixtures: Generative Models for Microbial Metagenomics , 2012, PloS one.

[190]  Jeffrey I. Gordon,et al.  Reciprocal Gut Microbiota Transplants from Zebrafish and Mice to Germ-free Recipients Reveal Host Habitat Selection , 2006, Cell.

[191]  Martin J. Blaser,et al.  Antibiotics, birth mode, and diet shape microbiome maturation during early life , 2016, Science Translational Medicine.

[192]  W. Huber,et al.  which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. MAnorm: a robust model for quantitative comparison of ChIP-Seq data sets , 2011 .

[193]  R. Cook.  Graphics for regressions with a binary response , 1996 .

[194]  Jasmine Chong,et al.  MicrobiomeAnalyst: a web-based tool for comprehensive statistical, visual and meta-analysis of microbiome data , 2017, Nucleic Acids Res..

[195]  Chittaranjan S. Yajnik,et al.  Molecular Characterization and Meta-Analysis of Gut Microbial Communities Illustrate Enrichment of Prevotella and Megasphaera in Indian Subjects , 2016, Front. Microbiol..

[196]  Zaid Abdo,et al.  Temporal Dynamics of the Human Vaginal Microbiota , 2012, Science Translational Medicine.

[197]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .

[198]  Jun Zhu,et al.  Succession in the Gut Microbiome following Antibiotic and Antibody Therapies for Clostridium difficile , 2012, PloS one.

[199]  P. Turnbaugh,et al.  Microbial ecology: Human gut microbes associated with obesity , 2006, Nature.

[200]  N. Sewankambo,et al.  HIV-1 infection associated with abnormal vaginal flora morphology and bacterial vaginosis , 1997, The Lancet.

[201]  W. Huber,et al.  Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2 , 2014, Genome Biology.

[202]  V. Pawlowsky-Glahn,et al.  Modeling and Analysis of Compositional Data , 2015 .