Skip to main content

Mediation Analysis of Microbiome Data and Detection of Causality in Microbiome Studies

  • Chapter
  • First Online:
Inflammation, Infection, and Microbiome in Cancers

Part of the book series: Physiology in Health and Disease ((PIHD))

Abstract

Microbiome research has basically focused on three factors: environment, microbiome, and host. The interactions among these three factors are dynamic and complicated. Three general hypotheses have been developed to detect these interactions. Among these hypotheses, testing the mediated effects of environmental factors and host mediated by microbiome is the most often designed, because mediation analysis of the human microbiome in these dynamic and very complicated relationships could potentially provide insights into the role of the microbiome in health and the etiology of disease and, more importantly, lead to novel clinical interventions by modulating the microbiome.

However, microbiome data are high-dimensional, structured as phylogenetic tree, sparse, non-normally distributed, and are often characterized by the presence of a large portion of zero values and hence are skewed to the right and heteroscedastic. Thus, the suitable methods for mediation analysis of microbiome data are rare. Several methods for mediation analysis of microbiome data were just developed in most current years. In this book chapter, we first introduce traditional mediation models and mediation models in omics studies as backgrounds and then focus on describing and reviewing specifically designed mediation models in microbiome studies. Traditional mediation models include two broad types of frameworks for mediation analysis: one is structural equation modeling (SEM)-based mediation analysis, which covers “product method” or “product of coefficients method” and “difference of coefficients method”, respectively. Another is counterfactual-based mediation analysis, which uses “potential outcomes” or “counterfactual outcomes” method.

The data features and statistical issues of microbiome studies are more similar to those in other omics studies, such as high dimensionality and sparsity; thus the mediation models from omics studies provide more insights and motivations to develop the mediation models in microbiome studies, such as how to test multiple putative mediators simultaneously using permutation (MultiMed), how to reduce high-dimensional mediators through regularization or penalization (HIMA), and how to transform high-dimensional mediators into low-dimensional and uncorrelated mediators using the spectral decomposition (CausalMM). This book chapter mainly aims to introduce seven specifically designed mediation models in microbiome studies. They are (1) distance-based omnibus test of mediation effect (MedTest), (2) multivariate omnibus distance mediation analysis (MODIMA), (3) causal compositional mediation model (CCMM), (4) isometric log-ratio transformation for microbiome mediation (IsometricLRTMM), (5) sparse microbial causal mediation model (SparseMCMM), (6) mediation analysis for zero-inflated mediators (MedZIM), and (7) nonparametric entropy mediation (NPEM). All these models were developed to target specific data structure and features of microbiome data (e.g., dimensionality, compositionality, sparsity, zero-inflated) through either SEM-based or counterfactual-based mediation frameworks. We complete this chapter with comments on current mediation models for microbiome data analysis and how to understand establishing causality in microbiome studies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aitchison J (1982) The statistical analysis of compositional data. J R Stat Soc Ser B Methodol 44(2):139–177

    Google Scholar 

  • Alwin DF, Hauser RM (1975) The decomposition of effects in path analysis. Am Sociol Rev 40(1):37–47

    Article  Google Scholar 

  • Arthur JC, Gharaibeh RZ, Uronis JM, Perez-Chanona E, Sha W, Tomkovich S, Mühlbauer M, Fodor AA, Jobin C (2013) VSL#3 probiotic modifies mucosal microbial composition but does not reduce colitis-associated colorectal cancer. Sci Rep 3:2868–2868

    Article  PubMed  PubMed Central  Google Scholar 

  • Balke A, Pearl J (1995) Counterfactuals and policy analysis in structural models. Proceedings of the Eleventh conference on Uncertainty in artificial intelligence. Morgan Kaufmann, Montreal, QC, pp 11–18

    Google Scholar 

  • Baron RM, Kenny DA (1986) The moderator–mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. J Pers Soc Psychol 51(6):1173–1182

    Article  CAS  PubMed  Google Scholar 

  • Bentler PM, Weeks DG (1982) 34 multivariate analysis with latent variables. In: Handbook of statistics, vol 2. Elsevier, Amsterdam, pp 747–771

    Google Scholar 

  • Bernstein S (2019) David Lewis’ theories of causation and their influence. In: Becker K, Thomson ID (eds) The Cambridge history of philosophy, 1945–2015. Cambridge University Press, Cambridge

    Google Scholar 

  • Billheimer D, Guttorp P, Fagan WF (2001) Statistical interpretation of species composition. J Am Stat Assoc 96(456):1205–1214

    Article  Google Scholar 

  • Blalock HME (1971) Causal models in the social sciences. Aldine-Atherton, Chicago

    Google Scholar 

  • Bobko P, Rieck A (1980) Large sample estimators for standard errors of functions of correlation coefficients. Appl Psychol Meas 4(3):385–398

    Article  Google Scholar 

  • Boca SM, Sinha R, Cross AJ, Moore SC, Sampson JN (2014) Testing multiple biological mediators simultaneously. Bioinformatics 30(2):214–220

    Article  CAS  PubMed  Google Scholar 

  • Bollen KA, Stine R (1990) Direct and indirect effects: classical and bootstrap estimates of variability. Sociol Methodol 20:115–140

    Article  Google Scholar 

  • Brehm JW, Cohen AR (1962) Explorations in cognitive dissonance. Wiley, New York

    Book  Google Scholar 

  • Briggs R (2012) Interventionist counterfactuals. Philos Stud 160(1):139–166

    Article  Google Scholar 

  • Browne MW (1984) Asymptotically distribution-free methods for the analysis of covariance structures. Br J Math Stat Psychol 37(1):62–83

    Article  PubMed  Google Scholar 

  • Carter KM, Lu M, Jiang H, An L (2020) An information-based approach for mediation analysis on high-dimensional metagenomic data. Front Genet 11:148

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Cheng PW (1997) From covariation to causation: a causal power theory. Psychol Rev 104(2):367–405

    Article  Google Scholar 

  • Cho I, Yamanishi S, Cox L, Methé BA, Zavadil J, Li K, Gao Z, Mahana D, Raju K, Teitler I, Li H, Alekseyenko AV, Blaser MJ (2012) Antibiotics in early life alter the murine colonic microbiome and adiposity. Nature 488:621

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Clogg CC, Petkova E, Shihadeh ES (1992) Statistical methods for analyzing collapsibility in regression models. J Educ Stat 17(1):51–74

    Article  Google Scholar 

  • Cole SR, Hernán MA (2002) Fallibility in estimating direct effects. Int J Epidemiol 31(1):163–165

    Article  PubMed  Google Scholar 

  • Cole DA, Maxwell SE (2003) Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling. J Abnorm Psychol 112(4):558–577

    Article  PubMed  Google Scholar 

  • D’Ariano GM (2018) Causality re-established. arXiv:1804.10810v1 [quant-ph]

    Google Scholar 

  • De Maesschalck R, Jouan-Rimbaud D, Massart DL (2000) The mahalanobis distance. Chemom Intell Lab Syst 50(1):1–18

    Article  Google Scholar 

  • Duncan OD (1966) Path analysis: sociological examples. Am J Sociol 72(1):1–16

    Article  Google Scholar 

  • Efron B, Tibshirani R (1986) [Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy]: rejoinder. Stat Sci 1(1):77

    Google Scholar 

  • Egozcue JJ, Pawlowsky-Glahn V, Mateu-Figueras G, Barcelo-Vidal C (2003) Isometric logratio transformations for compositional data analysis. Math Geol 35(3):279–300

    Article  Google Scholar 

  • Fan J, Lv J (2008) Sure independence screening for ultrahigh dimensional feature space. J R Stat Soc Ser B 70(5):849–911

    Article  Google Scholar 

  • Farzan SF, Korrick S, Li Z, Enelow R, Gandolfi AJ, Madan J, Nadeau K, Karagas MR (2013) In utero arsenic exposure and infant infection in a United States cohort: a prospective study. Environ Res 126:24–30

    Article  CAS  PubMed  Google Scholar 

  • Fischbach MA (2018) Microbiome: focus on causation and mechanism. Cell 174(4):785–790

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fiske ST, Kenny DA, Taylor SE (1982) Structural models for the mediation of salience effects on attribution. J Exp Soc Psychol 18(2):105–127

    Article  Google Scholar 

  • Fornell C (1983) Issues in the application of covariance structure analysis: a comment. J Consum Res 9(4):443–448

    Article  Google Scholar 

  • Fosen J, Ferkingstad E, Borgan O, Aalen OO (2006) Dynamic path analysis-a new approach to analyzing time-dependent covariates. Lifetime Data Anal 12(2):143–167

    Article  PubMed  Google Scholar 

  • Freedman D (1999) From association to causation: some remarks on the history of statistics. J Soc Fr Stat 40(3):5–32

    Google Scholar 

  • Freedman LS, Schatzkin A (1992) Sample size for studying intermediate endpoints within intervention trials or observational studies. Am J Epidemiol 136(9):1148–1159

    Article  CAS  PubMed  Google Scholar 

  • Goodman LA (1960) On the exact variance of products. J Am Stat Assoc 55(292):708–713

    Article  Google Scholar 

  • Graf RG, Alf EF (1999) Correlations redux: asymptotic confidence limits for partial and squared multiple correlations. Appl Psychol Meas 23(2):116–119

    Article  Google Scholar 

  • Grubbs FE (1950) Sample criteria for testing outlying observations. Ann Math Stat 21(1):27–58

    Article  Google Scholar 

  • Hamidi B, Wallace K, Alekseyenko AV (2019) MODIMA, a method for multivariate omnibus distance mediation analysis, allows for integration of multivariate exposure-mediator-response relationships. Genes (Basel) 10(7):524

    Article  CAS  Google Scholar 

  • Hayes AF (2013) Introduction to mediation, moderation, and conditional process analysis. Guilford Press, New York

    Google Scholar 

  • Hempel C (1965) Aspects of scientific explanation and other essays in philosophy of science. Free Press, New York

    Google Scholar 

  • Hijazi RH, Jernigan RW (2009) Modelling compositional data using Dirichlet regression models. J Appl Prob Stat 4(1):77–91

    Google Scholar 

  • Holland PW (1986) Statistics and causal inference. J Am Stat Assoc 81(396):945–960

    Article  Google Scholar 

  • Holland PW (1988) Causal Inference, path analysis, and recursive structural equations models. Sociol Methodol 18:449–484

    Article  Google Scholar 

  • Huang Y-T, Pan W-C (2016) Hypothesis test of mediation effect in causal mediation model with high-dimensional continuous mediators. Biometrics 72(2):402–413

    Article  PubMed  Google Scholar 

  • Huang Y-T, Liang L, Moffatt MF, Cookson WOCM, Lin X (2015) iGWAS: integrative genome-wide association studies of genetic and genomic data for disease susceptibility using mediation analysis. Genet Epidemiol 39(5):347–356

    Article  PubMed  PubMed Central  Google Scholar 

  • Illari P, Russ F (2014) Causality: philosophical theory meets scientific practice. Oxford University Press, Oxford

    Google Scholar 

  • Imai K, Keele L, Tingley D (2010a) A general approach to causal mediation analysis. Psychol Methods 15(4):309–334

    Article  PubMed  Google Scholar 

  • Imai K, Keele L, Yamamoto T (2010b) Identification, inference and sensitivity analysis for causal mediation effects. Stat Sci 25:51–71

    Article  Google Scholar 

  • James LR, Brett JM (1984) Mediators, moderators, and tests for mediation. J Appl Psychol 69(2):307–321

    Article  Google Scholar 

  • Jöreskog KG (1970) A general method for analysis of covariance structures. Biometrika 57(2):239–251

    Article  Google Scholar 

  • Jöreskog KG (1973) A general method for estimating a linear structural equation system. Structural equation models in the social sciences. Seminar Press, New York

    Google Scholar 

  • Judd CM, Kenny DA (1981a) Estimating the effects of social interventions. Cambridge University Press, New York

    Google Scholar 

  • Judd CM, Kenny DA (1981b) Process analysis: estimating mediation in treatment evaluations. Eval Rev 5(5):602–619

    Article  Google Scholar 

  • Kant I (1781) The critique of pure reason. Cambridge University Press, Cambridge

    Google Scholar 

  • Keesling JW (1972) Maximum likelihood approaches to causal flow analysis. Department of Education, University of Chicago, Chicago

    Google Scholar 

  • Kenny DA, Kashy DA, Bolger N (1998) Data analysis in social psychology. In: The handbook of social psychology, vol 1–2, 4th edn. McGraw-Hill, New York, NY, pp 233–265

    Google Scholar 

  • Koh H (2018) Adaptive statistical methods for microbiome association studies. New York University, New York

    Google Scholar 

  • Leong C (2019) Microbiota and diet in infants and young children. University of Otago, Otago

    Google Scholar 

  • Lewis D (1973a) Counterfactuals. Blackwell, Harvard University Press, Oxford, Cambridge. Reissued by Blackwell Publishers 2001

    Google Scholar 

  • Lewis D (1973b) Counterfactuals and comparative possibility. J Philos Log 2:418–446

    Article  Google Scholar 

  • Lewis DK (1973c) Causation. J Philos 70(17):556–567

    Article  Google Scholar 

  • Li H (2019) Statistical and computational methods in microbiome and metagenomics. In: Balding D, Moltke I, Marioni J (eds) Handbook of statistical genomics: two volume set. Wiley, New York, pp 977–550

    Chapter  Google Scholar 

  • Li Z, Liyanage JS, O’Malley AJ, Datta S, Gharaibeh RZ, Jobin C, Wu Q, Coker MO, Hoen AG, Christensen BC, Madan JC, Karagas MR (2019) Mediation analysis for zero-inflated mediators with applications to microbiome data. arXiv preprint. arXiv:1906.09175

    Google Scholar 

  • Li Z, Liyanage JS, O’Malley AJ, Datta S, Gharaibeh RZ, Jobin C, Coker MO, Hoen AG, Christensen BC, Madan JC, Karagas MR (2020) MedZIM: mediation analysis for Zero-Inflated Mediators with applications to microbiome data. arXiv:1906.09175v2

    Google Scholar 

  • Lin W, Shi P, Feng R, Li H (2014) Variable selection in regression with compositional covariates. Biometrika 101(4):785–797

    Article  Google Scholar 

  • Lipton R, Ødegaard T (2005) Causal thinking and causal language in epidemiology: it’s in the details. Epidemiol Perspect Innov 2:8–8

    Article  PubMed  PubMed Central  Google Scholar 

  • Mackie JL (1965) Causes and conditions. Am Philos Q 2(4):245–264

    Google Scholar 

  • MacKinnon D (2008) Introduction to statistical mediation analysis. Psychology Press, New York

    Google Scholar 

  • Mackinnon DP, Dwyer JH (1993) Estimating mediated effects in prevention studies. Eval Rev 17(2):144–158

    Article  Google Scholar 

  • Mackinnon DP, Warsi G, Dwyer JH (1995) A simulation study of mediated effect measures. Multivar Behav Res 30(1):41–41

    Article  Google Scholar 

  • MacKinnon DP, Lockwood C, Hoffman J (1998) A new method to test for mediation. The annual meeting of the Society for Prevention Research. Park City, UT

    Google Scholar 

  • MacKinnon DP, Krull JL, Lockwood CM (2000) Equivalence of the mediation, confounding and suppression effect. Prev Sci 1(4):173–181

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • MacKinnon DP, Lockwood CM, Hoffman JM, West SG, Sheets V (2002) A comparison of methods to test mediation and other intervening variable effects. Psychol Methods 7(1):83–104

    Article  PubMed  PubMed Central  Google Scholar 

  • MacKinnon DP, Lockwood CM, Brown CH, Wang W, Hoffman JM (2007) The intermediate endpoint effect in logistic and probit regression. Clin Trials 4(5):499–513

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • MacMahon B, Pugh TF (1970) Epidemiology, principles and methods. Little, Brown, Boston

    Google Scholar 

  • Mahalanobis PC (1936) On the generalized distance in statistics. Proc Natl Insti Sci India 2:49–55

    Google Scholar 

  • McArdle JJ, McDonald RP (1984) Some algebraic properties of the Reticular Action Model for moment structures. Br J Math Stat Psychol 37(2):234–251

    Article  PubMed  Google Scholar 

  • McGuigan K, Langholtz B (1988) A note on testing mediation paths using ordinary least-squares regression. Unpublished note.

    Google Scholar 

  • Menzies P (2014) Counterfactual theories of causation. Stanford Encyclopedia of Philosophy

    Google Scholar 

  • Muthén B (1983) Latent variable structural equation modeling with categorical data. J Econ 22(1):43–65

    Article  Google Scholar 

  • Muthén B (1984) A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika 49(1):115–132

    Article  Google Scholar 

  • Nadeau KC, Li Z, Farzan S, Koestler D, Robbins D, Fei DL, Malipatlolla M, Maecker H, Enelow R, Korrick S, Karagas MR (2014) In utero arsenic exposure and fetal immune repertoire in a US pregnancy cohort. Clinical immunology 155(2):188–197

    Article  CAS  PubMed  Google Scholar 

  • Neyman J (1923) Sur les applications de la théorie des probabilités aux experiences agricoles: essai des principes. Rocz Nauk Rol 10:1–51 (in Polish). English translation by D. Dabrowska and T Speed, 1990. Stat Sci 1995: 1463–1980

    Google Scholar 

  • Norton JD (2003) Causation as folk science. In: Price H, Corry R (eds) Philosophers’ imprint, vol 3. Oxford University Press, Oxford

    Google Scholar 

  • Novick LR, Cheng PW (2004) Assessing interactive causal influence. Psychol Rev 111(2):455–485

    Article  PubMed  Google Scholar 

  • Pearl J (1998) Graphs, causality, and structural equation models. Sociol Methods Res 27(2):226–284

    Article  Google Scholar 

  • Pearl J (2001) Direct and indirect effects. Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence. Morgan Kaufmann, Seattle, pp 411–420

    Google Scholar 

  • Pearl J (2009a) Causal inference in statistics: an overview. Stat Surv 3:96–146

    Article  Google Scholar 

  • Pearl J (2009b) Causality: models, reasoning, and inference. Cambridge University Press, New York

    Book  Google Scholar 

  • Pearl J (2010) An introduction to causal inference. Int J Biostat 6(2):7–7

    PubMed Central  Google Scholar 

  • Pearl J, Mackenzie D (2018) The book of why: the new science of cause and effect. Basic Books, New York

    Google Scholar 

  • Pearson K (1900) The grammar of science. Adam and Charles Black, London

    Google Scholar 

  • Planck M (1941) Der Kausalbegriff in der Physik (The causal term in physics). Verlag von S. Hirzel, Stuttgart

    Google Scholar 

  • Preacher KJ, Rucker DD, Hayes AF (2007) Addressing moderated mediation hypotheses: theory, methods, and prescriptions. Multivar Behav Res 42(1):185–227

    Article  Google Scholar 

  • Reza FM (1994) An introduction to information theory. Dover Publications, Inc., New York

    Google Scholar 

  • Robins JM, Greenland S (1992) Identifiability and exchangeability for direct and indirect effects. Epidemiology 3(2):143–155

    Article  CAS  PubMed  Google Scholar 

  • Rothman K (1976) Causes. Am J Epidemiol 104:587–592

    Article  CAS  PubMed  Google Scholar 

  • Rubin DB (1974) Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol 66(5):688–701

    Article  Google Scholar 

  • Rubin DB (2004) Direct and indirect causal effects via potential outcomes*. Scand J Stat 31(2):161–170

    Article  Google Scholar 

  • Rubin DB (2005) Causal Inference using potential outcomes. J Am Stat Assoc 100(469):322–331

    Article  CAS  Google Scholar 

  • Russell B (1912) On the notion of cause. Proc Aristot Soc 7:1–26

    Article  Google Scholar 

  • Schulfer AF, Schluter J, Zhang Y, Brown Q, Pathmasiri W, McRitchie S, Sumner S, Li H, Xavier JB, Blaser MJ (2019) The impact of early-life sub-therapeutic antibiotic treatment (STAT) on excessive weight is robust despite transfer of intestinal microbes. ISME J 13(5):1280–1292

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Scriven M (1962) Explanations, predictions, and laws. University of Minnesota Press, Minneapolis. Retrieved from the University of Minnesota Digital Conservancy. http://hdl.handle.net/11299/184631

  • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423

    Article  Google Scholar 

  • Shannon C (1949) Communication in the presence of noise. Proc IRE 37(1):10–21

    Article  Google Scholar 

  • Shannon C, Weaver W (1949) The mathematical theory of communication. University of Illinois Press, Urbana. 117 p

    Google Scholar 

  • Shi P, Zhang A, Li H (2016) Regression analysis for microbiome compositional data. Ann Appl Stat 10(2):1019–1040

    Article  Google Scholar 

  • Simon HA, Rescher N (1966) Cause and counterfactual. Philos Sci 33(4):323–340

    Article  Google Scholar 

  • Sobel ME (1982) Asymptotic confidence intervals for indirect effects in structural equation models. Sociol Methodol 13:290–312

    Article  Google Scholar 

  • Sohn MB, Li H (2019) Compositional mediation analysis for microbiome studies. Ann Appl Stat 13(1):661–681

    Article  Google Scholar 

  • Srinivasan A, Xue L, Zhan X (2019) Compositional knockoff filter for high-dimensional regression analysis of microbiome data. bioRxiv: 851337

    Google Scholar 

  • Stone JV (2015) Information theory: a tutorial introduction. Sebtel Press, Sheffield

    Google Scholar 

  • Susser M (1973) Causal thinking in the health sciences. concepts and strategies in epidemiology. Oxford University Press, New York

    Google Scholar 

  • Székely GJ, Rizzo ML (2018) Energy: e-statistics: multivariate inference via the energy of data. R Package Version 1.7-5

    Google Scholar 

  • Tang Z-Z, Chen G, Hong Q, Huang S, Smith HM, Shah RD, Scholz M, Ferguson JF (2019) Multi-omic analysis of the microbiome and metabolome in healthy subjects reveals microbiome-dependent relationships between diet and metabolites. Front Genet 10:454

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Tarka P (2018) An overview of structural equation modeling: its beginnings, historical development, usefulness and controversies in the social sciences. Qual Quant 52(1):313–354

    Article  PubMed  Google Scholar 

  • ter Horst HJ (1986) On Stieltjes integration in Euclidean space. J Math Anal Appl 114(1):57–74

    Article  Google Scholar 

  • Tingley D, Yamamoto T, Hirose K, Keele L, Imai K (2017) Mediation: R package for causal mediation analysis. https://cran.r-project.org/web/packages/mediation/vignettes/mediation.pdf

  • Valeri L, VanderWeele TJ (2013) Mediation analysis allowing for exposure-mediator interactions and causal interpretation: theoretical assumptions and implementation with SAS and SPSS macros. Psychol Methods 18(2):137–150

    Article  PubMed  PubMed Central  Google Scholar 

  • VanderWeele TJ (2009) Marginal structural models for the estimation of direct and indirect effects. Epidemiology 20(1):18–26

    Article  PubMed  Google Scholar 

  • VanderWeele TJ (2010) Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology 21(4):540–551

    Article  PubMed  PubMed Central  Google Scholar 

  • VanderWeele TJ (2013) A three-way decomposition of a total effect into direct, indirect, and interactive effects. Epidemiology 24(2):224–232

    Article  PubMed  PubMed Central  Google Scholar 

  • VanderWeele TJ (2014) A unification of mediation and interaction: a 4-way decomposition. Epidemiology 25(5):749–761

    Article  PubMed  PubMed Central  Google Scholar 

  • VanderWeele TJ (2015) Explanation in causal inference: methods for mediation and interaction. Oxford University Press, New York

    Google Scholar 

  • VanderWeele TJ (2016) Mediation analysis: a practitioner’s guide. Annu Rev Public Health 37:17–32

    Article  PubMed  Google Scholar 

  • VanderWeele T, Vansteelandt S (2009) Conceptual issues concerning mediation, interventions and composition. Stat Interface 2:457–468

    Article  Google Scholar 

  • VanderWeele TJ, Vansteelandt S (2010) Odds ratios for mediation analysis for a dichotomous outcome. Am J Epidemiol 172(12):1339–1348

    Article  PubMed  PubMed Central  Google Scholar 

  • Vansteelandt S (2012) Estimation of direct and indirect effects. In: Berzuini PDC, Bernardinelli L (eds) Causality: statistical perspectives and applications. Wiley, New York

    Google Scholar 

  • Walter J, Armet AM, Finlay BB, Shanahan F (2020) Establishing or exaggerating causality for the gut microbiome: lessons from human microbiota-associated rodents. Cell 180(2):221–232

    Article  CAS  PubMed  Google Scholar 

  • Wang Y-B, Chen Z, Goldstein JM, Buck Louis GM, Gilman SE (2019) A Bayesian regularized mediation analysis with multiple exposures. Stat Med 38(5):828–843

    Article  PubMed  Google Scholar 

  • Wang C, Hu J, Blaser MJ, Li H (2020) Estimating and testing the microbial causal mediation effect with high-dimensional and compositional microbiome data. Bioinformatics 36(2):347–355

    Article  CAS  PubMed  Google Scholar 

  • West SG, Aiken LS (1997) Toward understanding individual effects in multicomponent prevention programs: Design and analysis strategies. The science of prevention: methodological advances from alcohol and substance abuse research. American Psychological Association, Washington, DC, pp 167–209

    Google Scholar 

  • Wiley DE (1973) The identification problem for structural equation models with unmeasured variables. In: Duncan AGOD (ed) Structural equation models in the social sciences. Academic, New York, pp 69–84

    Google Scholar 

  • Woodworth RS (1928) Dynamic psychology. In: Murchison C (ed) Psychologies of 1925. Clark University Press, Worcester, MA, pp 111–126

    Google Scholar 

  • Wright S (1920) The relative importance of heredity and environment in determining the piebald pattern of guinea-pigs. Proc Natl Acad Sci U S A 6(6):320–332

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Wright S (1921) Correlation and causation. J Agric Res 20:557–585

    Google Scholar 

  • Wright S (1923) The theory of path coefficients a reply to Niles’s criticism. Genetics 8(3):239–255

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Wright S (1934) The method of path coefficients. Ann Math Stat 5(3):161–215

    Article  Google Scholar 

  • Wright RW (1988) Causation, responsibility, risk, probability, naked statistics, and proof: pruning the bramble bush by clarifying the concepts. Iowa Law Rev 73:1001–1077

    Google Scholar 

  • Wu GD, Chen J, Hoffmann C, Bittinger K, Chen YY, Keilbaugh SA, Bewtra M, Knights D, Walters WA, Knight R, Sinha R, Gilroy E, Gupta K, Baldassano R, Nessel L, Li H, Bushman FD, Lewis JD (2011) Linking long-term dietary patterns with gut microbial enterotypes. Science 334(6052):105–108

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Xia Y, Sun J (2017) Hypothesis testing and statistical analysis of microbiome. Genes Dis 4(3):138–148

    Article  PubMed  PubMed Central  Google Scholar 

  • Xia Y, Lu N, Zhang H, Gunzler D, Zubenko GS, Tu XM (2012a) Statistical methods and issues in the study of suicide. In: Lavigne J (ed) Frontiers in suicide risk: research, treatment and prevention. Nova Science, Hauppauge, pp 139–158

    Google Scholar 

  • Xia Y, Morrison-Beedy D, Ma J, Feng C, Cross W, Tu X (2012b) Modeling count outcomes from HIV risk reduction interventions: a comparison of competing statistical models for count responses. AIDS Res Treat 2012:Article ID 593569

    Google Scholar 

  • Xia Y, Sun J, Chen D-G (2018a) Compositional analysis of microbiome data. In: Statistical analysis of microbiome data with R. Springer Singapore, Singapore, pp 331–393

    Chapter  Google Scholar 

  • Xia Y, Sun J, Chen D-G (2018b) Introductory overview of statistical analysis of microbiome data. In: Statistical analysis of microbiome data with R, Singapore, Springer Singapore, pp 43–75

    Google Scholar 

  • Xia Y, Sun J, Chen D-G (2018c) Modeling zero-inflated microbiome data. In: Statistical analysis of microbiome data with R, Singapore, Springer Singapore, pp 453–496

    Google Scholar 

  • Xia Y, Sun J, Chen D-G (2018d) What are microbiome data? In: Statistical analysis of microbiome data with R. Springer Singapore, Singapore, pp 29–41

    Chapter  Google Scholar 

  • Xu L, Paterson AD, Turpin W, Xu W (2015) Assessment and selection of competing models for zero-inflated microbiome data. PLoS One 10(7):–e0129606

    Google Scholar 

  • Zhang C-H (2010) Nearly unbiased variable selection under minimax concave penalty. Ann Stat 38(2):894–942

    Article  Google Scholar 

  • Zhang Q (2019). High dimensional mediation analysis with applications to causal gene identification. bioRxiv: 497826

    Google Scholar 

  • Zhang C-H, Zhang SS (2014) Confidence intervals for low dimensional parameters in high dimensional linear models. J R Stat Soc Ser B (Stat Methodol) 76(1):217–242

    Article  Google Scholar 

  • Zhang H, Zheng Y, Zhang Z, Gao T, Joyce B, Yoon G, Zhang W, Schwartz J, Just A, Colicino E, Vokonas P, Zhao L, Lv J, Baccarelli A, Hou L, Liu L (2016) Estimating and testing high-dimensional mediation effects in epigenetic studies. Bioinformatics 32(20):3150–3154

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Zhang J, Wei Z, Chen J (2018) A distance-based approach for testing the mediation effect of the human microbiome. Bioinformatics 34(11):1875–1883

    Article  CAS  PubMed  Google Scholar 

  • Zhang H, Chen J, Li Z, Liu L (2019) Testing for mediation effect with application to human microbiome data. Stat Biosci:1–16

    Google Scholar 

  • Zheng P, Zeng B, Zhou C, Liu M, Fang Z, Xu X, Zeng L, Chen J, Fan S, Du X, Zhang X, Yang D, Yang Y, Meng H, Li W, Melgiri ND, Licinio J, Wei H, Xie P (2016) Gut microbiome remodeling induces depressive-like behaviors through a pathway mediated by the host’s metabolism. Mol Psychiatry 21(6):786–796

    Article  CAS  PubMed  Google Scholar 

  • Zitnik M, Nguyen F, Wang B, Leskovec J, Goldenberg A, Hoffman MM (2019) Machine learning for integrating data in biology and medicine: principles, practice, and opportunities. Inf Fusion 50:71–91

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

I would like to thank the anonymous reviewer whose expertise comments and suggestions helped to improve and clarify this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yinglin Xia .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The American Physiological Society

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Xia, Y. (2021). Mediation Analysis of Microbiome Data and Detection of Causality in Microbiome Studies. In: Sun, J. (eds) Inflammation, Infection, and Microbiome in Cancers. Physiology in Health and Disease. Springer, Cham. https://doi.org/10.1007/978-3-030-67951-4_16

Download citation

Publish with us

Policies and ethics