statistical methods for microbiome data analysis

Statistical Methods for Microbiome DataAnalysis

Hongzhe [email protected], http://statgene.med.upenn.edu

University of Pennsylvania Perelman School of Medicine

April 25, 2012

Outline of My Talk

Outline

� Microbiome, Diseases, Technologies and Data

� Methods for Microbiome Data Analysis

� Kernel-based Regression Methods for Testing the Effect ofMicrobiome Composition on an Outcome

� Sparse Dirichlet-multinomial Regression for SimultaneousSelection of Microbiome-associated Covariates and TheirAffected Taxa

� Future Work

H.Li (Penn) Microbiome data analysis April 25, 2012 2 / 42

Microbiome, Diseases, Technologies and Data

The Human Microbiome

� Microbiome as extended human genome� 1013 human cells vs 1014 bacterial cells� Consist of Prokaryotes, Archaea, Fungi,

and Viruses� More than 3× 106 genes provided by our

gut microbiome� Distinctive microbiomes at different body

sites (GI, lung, skin etc.)� The human microbiome may explain the

missing link between genetic variation anddisease

� The human microbiome in health� Digestive enzyme activity� Synthesis of vitamins� Interaction with the immune system� Protection from pathogens, etc.

External auditory canal

Gastrointestinal tract

Hair on the head

Nostril

Skin

Firmicutes

Actinobacteria

Bacteroidetes

Cyanobacteria

Fusobacteria

Proteobacteria

Mouth

Penis Vagina

Oesophagus

Nat Rev Microbiol. 2011 Apr;9(4):279-90.



Microbiome and Human DiseasesGut-brain hypothesis1. Autism�C. bolteae / clostridia sporesMechanism unkown2. Mood: depression, anxiety

Hygiene hypothesis:Exagerrated innate immune responseUpregulation of regulatory T cellsafter capture of Ags by DCs�Bifidobacteria, Gram +ve organisms�Clostridia

Peripheral vascular disease

Inflammatory bowel disease

�Bacteroidetes and �Actinobacteria in obese Altered energy / lipid metabolismHigher relative abundance of glycoside hydrolases,carbohydrate-binding modules,glycosyltransferases, polysaccharide lyases, and carbohydrate esterases in the BacteroidetesTLR mediated

Hypertension / ischemicheartdisease

Biliary disease

Colon cancer

Altered xenobiotic / drug metabolism

Diet high in red meat and animal fatLow SCFA / butyrateHigh fecal fatsLow vitamin absorption� 7α dehydroxylating bacteria:cholic acid�deoxycholic acid (co-carcinogen)Low in H2S metabolizing bacteria

Obesity / metabolic syndrome

Asthma / atopy

e.g. Paracetamol metabolism:� predose urinary p-cresol sulfate leads to � postdose urinaryacetaminophen sulfate : acetaminophen glucuronide.Bacterially mediated p-cresol generation and competitiveo-sulfonation of p-cresol reduces the effective systemic capacityto sulfonate acetaminophen.

Hygiene hypothesisAltered immune response: TLR signalingLess microbial diversityActivation of specific species: for example, Escherichia

Result of metabolic syndromeAltered lipid deposition / metabolism

Altered enterohepatic circulation of bile

Kinross et al. Genome Medicine 2011, 3:14



Technologies - Next Generation Sequencing

� 16S rRNA gene targeted sequencing� Structural component of the prokaryotic ribosome� Used as a molecular clock to identify phylogeny� Portions are constant, allowing amplification� Portions are variable, allowing identification

16S rRNA gene

100 nt

V1 V2 V3 V4 V5 V6 V7 V8 V9F27

454

F357

R534

R926

F968

R149

2

Amplicon 454 FLX Titanium readVariable region Length approx. 1.5kb

� Alternative: whole genome sequencing (shotgun metagenomics) (Qin etal Nature 2010; Arumugam et al Nature 2011).



16S Sequences Processing Pipeline

Extract DNA and PCR amplify with barcoded primer

Pool amplicons

Pyrosequenceamplicons using 454’s

GS FLX instrument

> AGTGAGAGAAGCAGGGTCGTAATGTT . . .> AGTGCGATGCGTAGGGTCGTAATGCG . . .

> AGTGCGATGCGTAGGGTCGTAATGTA . . .> AGTGGATGCTCT AGGGTCGTAATGCA . . .

> AGTGTCACGGTGAGGGTCGTAATGGG . . .> AGTGGATGCTCT AGGGTCGTAATGTT . . .> AGTGTCACGGTGAGGGTCGTAATGCC . . .> AGTGAGAGAAGCAGGGTCGTAATCAC . . .. . .

Quality control, assign sequences to samples using barcode and denoise

align to reference alignment (e.g., using PYNAST), infer phylogeny (FastTree)Thousands of OTUs,

100’s of samples

OTU1

OTU2

OTU3

OTU1OTU2

OTU3

OTUq

RDP classifier

Species level OTUs can be summarized into higher levels

Cluster sequences into OTUs (97% level),

Assign lineages by

OTU: Operational Taxonomic Unit



Penn Gut Microbiome Project - COMBO

� Cross-sectional study Of diet and stoolMicroBiOme composition (COMBO).

� Collaborators: Gary Wu and Jim Lewis(GI) and Rick Bushman (Microbiology).

� Data� 98 subjects/stool samples� ∼ 900, 000 high quality, partial ( 370bp)

16S rRNA gene sequences, 17, 303 OTUsat 97% similarity, 119 genera

� 214 nutrients (FFQ diet questionnaire),demographic data such as BMI.

� Goal: Assess the diet effect on gutmicrobiome composition; Assess theeffect of the microbiome on BMI afteradjusting for diet

Host lifestyle

Host pathobiology

Host environment

Transient communitymembers

Host immune system

Host physiology

Host genotype

Core human microbiome

Variable human microbiome

Nature 449, 804-810



Penn Gut Microbiome Project - Results

Wu, Chen et. al (Science 2011).

Peonidin, anthocyanidinM

alvidin, anthocyanidinPetunidin, anthocyanidinTotal anthocyanidinsDelphinidin, anthocyanidinPelargonidin, anthocyanidinPotassiumPotassium

w/o suppl.M

agnesiumM

agnesium w/o suppl.

Free Choline, choline−contrib. metabolite

Free Choline w/o suppl.Natural Food FolateAOAC fiberPantothenic Acid w/o suppl.Naringenin, flavanoneVitam

in E w/o vit. suppl. Proanthocyanidin, 4−6m

ersProanthocyanidin, trim

ersProanthocyanidin, 7−10m

ersCyanidin, anthocyanidinProanthocyanidin, polym

ersProanthocyanidin, dim

ersCatechin, flavan−3−olAlcoholPhenylalanine, Aspartam

eAspartic Acid, Aspartam

eAspartam

efort. foodsCaffeineRetinolRetinol Equivalents of Vit ATotal Folate post 1998Folate Equivalents, suppl. & fort. foodsRiboflavin B2 w/o vit. pillsHistidineThreonineM

ethionineLysineLeucineTyrosineValineIsoleucineProteinPhenylalanineSerineTryptophanG

lycineAlanineArginineAsparateCholine, PhosphatidylcholineCholine, Phosphatidylcholine w/o suppl.Total Choline, no betaineCholine w/o suppl.Sum

of Betaine & CholineCystineG

lutamate

ProlineVitam

in D w/o vit. pillsCholine, G

lycerophosphocholineCholine, PhosphocholinePhosphorousPhosphorous w/o suppl.CalciumCalcium

w/o vit. pillsDairy ProteinDairy CalciumAnim

al ProteinCholine, Sphingom

yelinCholesterolTaurinePalm

itoleic fatty acidHydroxyprolineAnim

al fatc9,t11 conjug diene isom

er 18:2 LinoleicPalm

itic fatty acidSaturated fatStearic fatty acidPalm

itelaidic trans fatty acidSodiumDihydrophylloquinone Vitam

in K1 Trans O

leic fatty acidTotal TransTotal Trans/Cis Trans LinoleicEicosenoic fatty acidG

amm

a Linolenic fatty acidG

amm

a linolenic fatty acidFructoseG

lucoseCarbohydratesTotal SugarsSucroseG

lycemic Index

Maltose

Eriodictyol, flavononeAdded G

erm from

wheatsVitam

in E, Food Fortification

* * * * * * * * ** * * * * * * *

** * * * * * *

* * * ** * * * * * * * * * * * * * *

* * * * * *

* **

* * ** * * * * * * * * *

* * * ***

* * * ** * ** *

* * * * * * * * * ** * * * * ** * * * * * * * * * *

* * ** *

* * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** ** * *

**

* * * * * * * ** * * * * * * * * * *

* * * * * * * *

BacteroidesPrevotella−0.2

00.2

Spearman Correlation

PhylumFirm

icutesBacteroidetesActinobacteriaProteobacteria

Amino Acidsand

Choline

Fiberand

Plant DerivedCom

pounds

Fats

Carbohydrates

Fig. 1



COMBO OTU Abundance Table

4030 . . . . . .4023 . . . . .4013 . . . . .4005 . . . . .3085 . . . . .3079 . . . . .3072 . . . . .3065 . . . . .3057 . . . . .3050 . . . . .3044 . . . . .3038 . . . . .3030 . . . . .3023 . . . . .3016 . . . . .3009 . . . . .3001

OTU abundances for the gut microbiome0 2 4 6 8 10

Log2

Actinobacteria Bacteroidetes Firmicutes Fusobacteria Proteobacteria TM7

ID

count



Data Summarization and Statistical ChallengesData: n samples, q OTUs.

� LEVEL I: count data and phylogenetic tree (T )

yi = {yi1, · · · , yiq}, i = 1, · · · , n

� LEVEL II: proportion data and phylogenetic tree (T )

pi = {pi1, · · · , piq}, i = 1, · · · , n;

q∑j=1

pij = 1

� LEVEL III: distances between microbiome samples

dij = f(yi,yj , T ), i, j = 1, · · · , n

Statistical challenges

Phylogenetic information, count data and over-dispersion, dependencystructures of composition data etc.


Methods for Microbiome Data Analysis Kernel-based Score Test

Methods for Microbiome Data Analysis

Kernel-based Regression Methods and a Generalized UniFrac Distance(Chen and Li (2012): Bioinformatics, in revision.)



Notations and Problem Setup

Data

� yi: outcome (binary/continuous)

� xi = (xi1, · · · , xip): p covariates

� zi = (zi1, · · · , ziq): q OTUs on a phylogenetic tree (q large)

Goal

� Test the effect of z on y after adjusting for the effects of x.

Method

� Semi-parametric regression: g(µi;xi, zi) = xTi β + h(zi)

� µi: mean of the outcome variable� g(.): link function� h(z): modeled non-parametrically

� The goal becomes testing h(z) = 0



Kernel-based Estimation and Test

(Wahba 1990, Vapnik 1998, Schølkopf 2002, Liu et. al 2007,2008 )

Let h(.) ∈ HK , the function space generated by a kernel function K(., .). Liu et.al connected the kernel-based semi-parametric regression model to a generalizedmixed effects model:

g(µi) = xTi β + hi,

where β are fixed effects and h ∼ N(0, τK) are subject-specific random effects.

Testing h(z) = 0 is equivalent to the variance component test:

H0 : h(z) = 0⇔ H0 : τ = 0.

Score statistic

Q =1

2φ(y − µ̂0)TK(y − µ̂0)

The distribution of Q can be approximated by a scaled χ2 distribution.



Kernels for Microbiome Data

� Kernel as a similarity measure and create kernel from distance:

K = −1

2(I − 11′

n)D2(I − 11′

n),

where D is the distance matrix. It is easy to verify: D2ij = Kii +Kjj − 2Kij .

� The key is to use a distance that characterizes well the relationshipbetween microbiome samples.

� UniFrac distance is the most popular distance measure, but we willimprove on it.



UniFrac Distance (Knight 2005, 2007)

Unweighted UniFrac distance: the fraction of the branch length of the tree that is

unique to any community.

Unique Fraction (UniFrac) metric

• A branch length-based, qualitative phylogenetic β diversity measure

• Distance = fraction of the total branch length that is unique to any sample

A. Identical sequence sets: all seqs in red + blue set. 100% branch length shared (purple). UniFrac score = 0.

C. Unrelated sequence sets: seqs in red have no close relatives in blue. 0% branch length shared. UniFrac score = 1.

B. Related sequence sets: seqs in red have relatives in blue. ~50% branch length shared. UniFrac score = 0.5.

Red vs YellowShared=OrangeUniFrac = 0.3

Red vs BlueShared=PurpleUniFrac = 0.7

Yellow vs BlueShared=GreenUniFrac = 0.6

R YR

B

Y

B

0

0

0

.3

.3

.7

.7

.6

.6

R

Y

B

Distance Matrix Cluster of environments

D. UniFrac distances can be measured beween each pair of sequence sets on a single tree. The resulting distance matrix of pairwise distances can be used for clustering, PCoA, and other multivariate analyses.

Lozupone and Knight. UniFrac: a new phylogenetic method for comparing microbial communities. AEM, 2005.

� Most efficient in detecting thedifference in communitymembership

� Also difference in rare lineages,differs in probability of being pickedup by the sequencing machine

Weighted UniFrac distance:

Formula

dW =

m∑i=1

bi

∣∣∣pAi − pBi ∣∣∣m∑i=1

bi

∣∣∣pAi + pBi

∣∣∣� Most efficient in detecting

difference in abundant lineages

� Absolute difference puts too muchweight on abundant lineages



Generalized UniFrac Distances

(Chen and Li, 2012 Bioinformatics, revision)

Weighted and unweighted UniFrac place too much emphasis either onabundant lineages or rare lineages. We propose generalized UniFracdistance to fill the holes.

Generalized UniFrac Distance

d(α) =

m∑i=1

bi(pAi + pBi )α

∣∣∣∣pAi − pBipAi + pBi

∣∣∣∣m∑i=1

bi(pAi + pBi )α

,

where α ∈ [0, 1] controls the weight. From α = 1 to 0, more emphasis isplaced on low abundance lineages. When α = 1, d(α) is reduced to dW ;When α = 0 and pi = I(pi > 0), d(α) is reduced to dU .



Simulation

� Proportions are generated from a DirichletDistribution

(pi1, pi2, · · · , piq) ∼ D(π1, π2, · · · , πq, θ)

� Counts are generated from a Multinomial Distribution

(zi1, zi2, · · · , ziq) ∼M(pi1, pi2, · · · , piq, ni)

� Outcome depends on the underlying proportions of aselected OTU cluster

yi ∼ N(

qs∑j=1

αsjpisj , 1) OR

yi ∼ B(1,1

1 + exp{−∑qsj=1 αsjpisj}

)



Power Comparison - Binary Outcome

n = 100. An OTU cluster affects a disease outcome.

Effect

Pow

er

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

Cluster 12 (19.4%)

●

●

●

●

●

●

●

●

●

●

Cluster 4 (1.5%)

●

●

●

●

●

●

●

●

●

●

2 4 6 8 10

Cluster 13 (5.7%)

●

●

●

●

●

●

●

●

●

●

Cluster 19 (0.3%)

●

●

●

●

●

●

●

●

●

●

2 4 6 8 10

Kernel type● dW d(0.5) d(0) dU L



Power Comparison - Continuous Outcome

n = 100. An OTU cluster affects a quantitative trait.

Effect

Pow

er

0.2

0.4

0.6

0.8

1.0

0.2

0.4

0.6

0.8

1.0

Cluster 12 (19.4%)

●

●

●

●

●

●

●

● ● ●

Cluster 4 (1.5%)

●

●

●

●

●

●

●

●

●

●

2 4 6 8 10

Cluster 13 (5.7%)

●

●

●

●

●

●

●

● ● ●

Cluster 19 (0.3%)

●

●

●

●

●

●

●

●

●

●

2 4 6 8 10

Kernel type● dW d(0.5) d(0) dU L



Application to COMBO Data

Microbiome’s effects on BMI (n = 98).

Kernel type dW d(0.5) d(0) dU

p-value (original scale) 0.22 0.03 4.3E-5 6.7E-6p-value (dichotomized by 25) 0.21 0.02 7.9E-5 4.2E-5

Fat intake is a confounding factor, since it is correlated with both BMI(r = 0.32, p = 0.001) and microbiome composition (p < 0.05). Kernel-basedscore test after adjusting for fat intake:

Kernel type dW d(0.5) d(0) dU

p-value (microbiome) 0.36 0.11 6.5E-3 3.3E-3p-value (fat) 0.001 0.006 0.012 0.036

Conclusion: Microbiome composition can affect BMI independent of fat intake.


Methods for Microbiome Data Analysis Sparse Dirichlet-multinomial regression

Methods for Microbiome Data Analysis

Sparse Dirichlet-multinomial Regression for Taxon-level Analysis(Chen and Li (2012): Annals of Applied Statistics, in revision)



Notations and Problem Setup

Data

� yi = (yi1, · · · , yiq): q OTU counts

� xi = (xi1, · · · , xip): p covariates/nutrients

Goal

� Select covariates and their affected OTUs - an association graph.

Method� Sparse regression model

� Probability distribution for the count data� Link function that connects the counts to covariates� Penalty function used to induce sparsity



Overdispersion of OTU Counts



Dirichlet-Multinomial DistributionA compound distribution

fDM (y1, y2, · · · , yq;γ) =

∫fM (y1, y2, · · · , yq;π)fD(π;γ)dπ

� OTU counts follow a Multinomial distribution

fM (y1, y2, · · · , yq;π) =

(y+y

) q∏j=1

πyjj , y+ =

q∑j=1

yj

� OTU composition follows a Dirichlet distribution

fD(π1, π2, · · · , πq;γ) =Γ(γ+)∏qj=1 Γ(γj)

q∏j=1

πγj−1j , γ+ =

q∑j=1

γj

q OTUs ⇒ q free parameters γ1, γ2, · · · , γq. γj ∝ E(Yj) and γ+ =∑qj=1 γj

controls the degree of overdispersion.H.Li (Penn) Microbiome data analysis April 25, 2012 24 / 42


Link Function

Effects of covariates on jth OTU:

γj(xi;βj∗) = exp(βj0 +

p∑k=1

βjkxik),

βjk indicates the strength of kth covariate on jth OTU, βj0 determinesthe baseline abundance of jth OTU. β: q × (p+ 1) coefficient matrix.

βq0 βq1 … … βqk … … βqp

… … … … … … … …

βj0 βj1 … … βjk … … βjp

… … … … … … … …

β10 β11 … … β1k … … β1p

β*0 β*1 β*k β*p

βq*

βj*

β1*

γq(xi; βq*)

γj(xi; βj*)

γ1(xi; β1*)

Intercept k th nutrient

j th OTU



Likelihood Ratio Test (LRT)

Log-likelihood function

l(β;Y,X) =

n∑i=1

Γ̇

q∑j=1

γj(xi;βj∗)

− Γ̇

q∑j=1

yij +

q∑j=1

γj(xi;βj∗)

+

q∑j=1

{Γ̇(yij + γj(xi;βj∗)

)− Γ̇

(γj(xi;βj∗)

)} .LRT for kth covariate effect

H0 : β1k = · · · = βqk = 0 vs H1 : (β1k, · · · , βqk) ∈ IRq\0.

H0 : βjk = 0.



Likelihood Ratio Test (LRT) cont’d

� Application� LRT can be used for testing the association of a covariate with the overall

microbiome composition.

� Limitations� It does not tell which OTUs account for the association� If only a few OTUs are effected, LRT can be less powerful due to large DFs� Multiple testing problems especially with multiple correlated covariates

� Alternative� Variable selection approach based on penalization.


Penalized Maximum Likelihood Estimation (PMLE)Goal: select microbiome-associated covariates - nonzero columns of βand their associated OTUs - nonzero βjk in the selected columns.

βq0 βq1 … … βqk … … βqp

… … … … … … … …

βj0 βj1 … … βjk … … βjp

… … … … … … … …

β10 β11 … … β1k … … β1p

β*0 β*1 β*k β*p

βq*

βj*

β1*

γq(xi; βq*)

γj(xi; βj*)

γ1(xi; β1*)

Intercept k th nutrient

j th OTU

Penalized likelihood estimation: β̂ = argmin pl(β;Y,X, c, λ)

pl(β;Y,X, c, λ) = −l(β;Y,X) +

sparse group l1︷︸︸︷cλ

p∑k=1

√q ‖β∗k‖2︸︷︷︸

group l1

+ (1− c)λp∑k=1

‖β∗k‖1︸︷︷︸l1

,

‖β∗k‖2 =

√√√√ q∑j=1

β2kj , ‖β∗k‖1 =

q∑j=1

|βkj |.


Block Coordinate Gradient Descent Algorithm

(Tseng 2007, Meier 2008)

Step Algorithm

1 Let β ∈ IRq×(p+1) be an initial parameter vector2 For k = 0, · · · , p

d← arg mind|d∗t=0,t6=k{plQ(d)}if d 6= 0α← line searchβ ← β + αdend

end3 Repeat step 2 until some convergence criterion is met

An inexact line search using the Armijo rule is performed. Let α(t) be the largest value in

{α0δl}l≥0 such that pl(β̂(t)

+ α(t)d(t))− pl(β̂(t)) ≤ α(t)σ∆(t), where 0 < δ < 1, 0 < σ < 1,

α0 > 0, and ∆(t) is the improvement in the objective function pl(β) using a linear

approximation.



Simulation Strategy

� Two growth models

� Exponential growth: πij =exp{βj0+

∑pk=1 βjkxik}∑q

j=1 exp{βj0+∑p

k=1 βjkxik}� Linear growth: πij =

βj0+∑p

k=1 βjkxik∑qj=1(βj0+

∑pk=1 βjkxik)

� Counts are generated by

f∗DM (y1, y2, ..., yq ;π, θ) =(y+y

)∏qj=1

∏yjk=1{πj(1− θ) + (k − 1)θ}∏y+

k=1{1− θ + (k − 1)θ},

θ is the overdispersion parameter.

� 100 samples, ∼ 5000 reads each sample, 40 genus-level OTUs, 100covariates, 4 relevant covariates with each affecting 4 OTUs.θ = 0.025.

� Evaluate selection performance using Recall, Precision and F1 measure.



Simulation - PMLE (DM vs D vs M, SGL vs L)DM - Dirichlet-multinomial; D - Dirichlet; M - Multinomial regression models

SGL - sparse group l1 penalty; L - l1 penalty. The tuning parameters are selected

based on BIC with the coefficients re-estimated.

Mea

sure

0.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

Recall Precision F1

Within−group

Group

DM−L DM−SGL D−L D−SGL M−L M−SGL



Simulation - PMLE (Model Misspecification)

DM - Dirichlet-multinomial; D - Dirichlet; M - Multinomial regression models

SGL - sparse group l1 penalty; L - l1 penalty.M

easu

re 0.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

Recall

Exponentialgrowth

Lineargrowth

Precision

Exponentialgrowth

Lineargrowth

F1

Exponentialgrowth

Lineargrowth

Within−group

Group

DM−L DM−SGL D−L D−SGL M−L M−SGL



Results of COMBO - Nutrients Selected

30 common genera, 118 nutrients ⇒ 11 nutrients and 13 genera.

� The tuning parameters areselected based on BIC

� A total of 41 genus-nutrientassociations are selected

� Spearman rank correlationtest does not select anyassociations after Bonferronicorrection (FWER=0.05) orFDR control (FDR=0.05).

Alistipes

Oscillibacter

Bacteroides

Faecalibacterium

Subdoligranulum

Odoribacter

Parabacteroides

Naringenin,flavanone

ParasutterellaRuminococcus

Eriodictyol,flavonone

Prevotella

Barnesiella

Phascolarctobacterium

Coprococcus

Taurine

AddedGerm from

wheats

Choline,Phosphatidylcholine

Maltose

Methionine

Sucrose

Polyunsaturatedfat

Vitamin E

AnimalProtein





Alistipes

Oscillibacter

Bacteroides

Faecalibacterium

Subdoligranulum

Odoribacter

Parabacteroides




Prevotella

Barnesiella


Coprococcus

Taurine

AddedGerm from

wheats


Maltose

Methionine

AnimalProtein

Polyunsaturatedfat

Vitamin E

Sucrose





Alistipes

Oscillibacter

Bacteroides

Faecalibacterium

Subdoligranulum

Odoribacter

Parabacteroides




Prevotella

Barnesiella


Coprococcus

Taurine

AddedGerm from

wheats


Maltose

Methionine

Sucrose

Polyunsaturatedfat

Vitamin E

AnimalProtein





Odoribacter

Bacteroides

Alistipes

Faecalibacterium

Parabacteroides

Barnesiella

Subdoligranulum

Parasutterella

Oscillibacter Vitamin E

AddedGerm from

wheats

Polyunsaturatedfat

PrevotellaRuminococcus


Methionine

Coprococcus

Maltose

Taurine


PhascolarctobacteriumEriodictyol,flavonone

Sucrose

AnimalProtein



Results of COMBO Data Analysis - Model Fit 1

Fit the DM model with the selected 41 coefficients and compare it to the model

with intercepts only (null model). The log likelihood for the two models are

−60082 and −60202, respectively. ∆ = 120.

0 20 40 60 80 100

020

4060

8010

0

Model fitting with selected coefficients

Observed counts

Fitt

ed c

ount

s

r2= 0.79

0 20 40 60 80 100

020

4060

8010

0

Model fitting with intercepts only

Observed counts

Fitt

ed c

ount

s

r2= 0.70



Results of COMBO Data Analysis - Model Fit 2

The counts generated by DM model with fitted coefficients look morerealistic than the counts generated by Multinomial model.

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Real microbiome data Dirichlet-multinomial model Multinomial model



Summary

� Kernel-based regression methods for testing the significance ofmicrobiome composition on an outcome� Phylogenetic information can be readily incorporated into kernels� Adjusting the effects of other covariates is natural� Extension: tune α and get a valid p-value

� Sparse Dirichlet-multinomial regression model for selectingmicrobiome-associated covariates and their affected OTUs� Dirichlet-multinomial model is used to account for overdispersion of OTU

counts� Sparse group l1 penalty is used for simultaneous selection of both

covariates and OTUs� Extension: incorporate the phylogenetic tree information by imposing a

smoothness penalty (Chen and Li, 2012 Biostatistics, in revision)


Future work

Future Direction

� Modeling phylogenetic information, overdispersion and excessive zerosunder a common framework

� Dissecting the relationship between host genotypes, microbiome anddisease

� Correlating different microbial communities: bacterial, fungi, archealand viral communities

� Computational and statistical analysis of shotgun metagenomic data� Assembly, taxonomic classification, function prediction, etc.� Modeling the metagenome using Latent Dirichlet Allocation (LDA)

� Integrating metagenomics, meta-transcriptomics and meta-proteomics


Future work

Acknowledgements

Many thanks to:

� Jun Chen, PhD student

� Rick Bushman, PhD (Microbiology)

� Gary Wu, MD (Gastroenterology)

� James Lewis, MD (Gastroenterology)

� People in their labs.


Future work

Thank you!


statistical methods for microbiome data analysis

Documents