1. A Microbial Interdependence Association Test in Longitudinal Study Huilin Li Ph.D. Division of Biostatistics Department of Population Health
Thanks Justin for organizing this wonderful session. Today I am going to talk about how to utilize the repeated microbial samples to investigate the microbial interdependence and test its association with treatment group or any continuous trait.
between, recently a great nu
mber of longitudinal or time series microbial studies have provided great challenages and opportunities to investigate the
me! It’s a nice session. Thanks XX and Michael for the nice introduction which make my work easier. Today I would like to share a recent research project in my group. It is … The paper is currently under review, but the software is available in my webpage.
In microbiome research, I think one of the most important questions is which microbes are associated with our research interest. Considering there are tens and hundreds microbes live on our human body, to answer this question, people need to conduct a microbiome-wide association study.
2018 JSM
Vancouver, Canada

2. Importance of Longitudinal Microbiome Studies
The microbiome is dynamic, with interacting microbial species.
the microbial system changes over time
can be disturbed by factors such as diet, drugs, and the environment
Sampling microbial communities repeatedly over time provides the opportunities to study
their response to and recovery from disturbance
Stability and resilience
species interdependent relationship
As Susan mentioned, it is particularly of importance to conduct the longitudinal micorbiome studies. One big difference between microbiome data and genomic data is that microbiome is dynamic. The microbial species do not exist in isolation but instead form complex ecological interaction webs. There are massive competing and cooperating. They act as integrated microbial commuity. the microbial system changes from infancy through adulthood and can be disturbed by factors such as diet, drugs, and the environment12.
A microbiota community hosts a vast number of species that do not exist in isolation but instead form complex ecological interaction webs11. All of the species need to compete for space and resources, although some have mutualistic interactions that involve the exchange of metabolic products for the benefit of both. Unlike the human genome, which is relatively static through the lifespan,

3. Longitudinal/Time series Analysis
Review paper:
Faust K, Lahti L, Gonze D, de Vos W, Raes J. (2015). Metagenomics meets time series analysis: unraveling microbial community dynamics. Curr Opin Microbiol 25: 56–66.
Time Series Analysis– to reveal the trend, periodicity and predictability
V Bucci, et al. (2016) MDSINE: Microbial Dynamical Systems INference Engine for microbiome time-series analyses. Genome biology 17 (1), 121
Network Analysis—to construct taxon co-occurrence, interaction network
SPIEC-EASI: ZD Kurtz, et al. (2015) Sparse and compositionally robust inference of microbial ecological networks  - PLoS computational biology, 11(5) :e
David LA, Materna AC, Friedman J, Campos-Baptista MI, Blackburn MC, Perrotta A, Erdman SE, Alm EJ: Host lifestyle affects human microbiota on daily timescales. Genome Biol 2014, 15:R89.
Longitudinal Statistical Modeling
Chen, E. Z., & Li, H A two-part mixed-effects model for analyzing longitudinal microbiome compositional data. Bioinformatics (Oxford, England), 32(17), 2611–7.
Fukuyama et al. (2017) Multidomain analyses of a longitudinal human microbiome intestinal cleanout perturbation experiment. PLOS Computational Biology, August 16.
The increased amount of longitudinal or time seeries microbial studies have called for the analytical tool development. Here I listed two well drafteed review papers. There they review different method and dicussed their potential for the moving the microbiome research forward. IN summary there are three kinds of techniques are available to analyze repeated microbial samples.

4. Motivating Example Study description: 7 mice in Control group
342 genus level taxa
8 mice in LDP group
7 time points within 5 weeks
In the following, I am going to introduce a real longitudinal microbiome study, moviated by it, we devleoped our proposed test. This is a longitudinal mice study, to goal of it is to examine the effect of low-dose penicillin on the gut microbiome structure and metabolic phenotypes. Here is just a small portion of the whole experiment. We have two groups of the germ-free mice, the cecal microbiota collected from the conventional control donors and low-dose penicillian donors were transferred to those two group of germ-free mice seperately. Fecal samples from those mice were collected in 7 consecutive time points across their first 5 week life.
Ref: Cox, L. M., et al. (2014). Altering the intestinal microbiota during a critical developmental window has lasting metabolic consequences. Cell, 158(4), 705–721.

5. Motivating Example
IN this fiugre, the mean relative abundnacne of the major genus-level taxa in contorl and LDP groups over time are presented. Visually, we can observe the different dynamic changes of the gut microbial community between two groups.

6. Static Method
To compare changing trends of microbial structure between groups
Focus on the location difference and change
In the original paper, we explored the different microbial structures between the groups using PCoA method, it confirmed the group difference in the microbial profile at each time point by PERMAnova test. In the figures, the location of each sample has been draw in the coordinates of the first three principle components. By observing the PCoA figures in a row by the observed times, we can see the difference between two recipient groups remain, while each receipient group moves towards their donor sample along the time. However, you can see overall this analysis focus on the location difference and change.
Ref: Cox, L. M., et al. (2014). Altering the intestinal microbiota during a critical developmental window has lasting metabolic consequences. Cell, 158(4), 705–721.

7. Research Hypothesis
We hypothesize that prior antibiotic exposure disturbed the microbial interdependent structure following the transfer and colonization of the new hosts.

8. A Non-parametric Microbial Interdependence Test (NMIT)
NMIT is a non-parametric distance based test for group comparison on microbial temporal intedependenceraction in longitudinal study design
Our test is simple and powerful, it is a non.
I has two major steps:

9. A Non-parametric Microbial Interdependence Test (NMIT)
Component 1. we capture the individual microbial dependencies over time by performing pair-wise correlation analysis within each subject using the longitudinal microbial measurements.
Component 2. we test whether the correlation structure is different between groups or associated with an interested outcome or not using permutation MANOVA (Anderson, 2001; McArdle & Anderson,
2001; Tang et al. 2016).
Our test is simple and powerful, it is a non.
I has two major steps:

10. NMIT step 1: taxon screening
Step 1: screening criteria at genus level
Relative abundance > 0.1% in at least 20% of the total samples.
34 major taxa were retained
Since the microbiome data is generated from 16S sequencing method, we analyze it at the genus level.
First of all, the relative abundances are obtained at the
genus level for each subject.
Then we only kept the taxxa with relative abundance >0.1% in at least 20% of the total samples. Finally, there are 34
and 34 selected dominant taxa are retained in this
example after filtering (relative abundance > 0.1% in ≥20% of
all samples).

11. NMIT step 2: temporal correlation analysis
For each mouse, calculate the correlation (Kendall’s tau) between any two taxa over observation time.
For each subject, we have a 34 by 34 correlation matrix

12. NMIT step 3: distance between taxa temporal correlations
Step 3: distance between temporal correlations
Calculate distance (Frobenius norm) between two mice’s taxa temporal correlation matrices
The heat map shows that the within-group distances are smaller than the between group distances.

13. NMIT step 4: permutation MANOVA
X: 𝑁×𝑝 covariate matrix
𝐻=𝑋( 𝑋 𝑇 𝑋 ) −1 𝑋 𝑇 projection matrix
D = 𝑑 𝑖𝑖 ′ : 𝑁×𝑁 distance matrix
𝐴= 𝑎 𝑖𝑖 ′ = − 𝑑 𝑖𝑖 ′ 2 /2 : 𝑁×𝑁 adjacent matrix
𝐺=(𝐼− 11 𝑇 /𝑛)𝐴(1− 11 𝑇 /𝑛): centroid matrix
Pseudo-F statistics:
𝐹= 𝑡𝑟(𝐻𝐺𝐻) 𝑡𝑟[(𝐼−𝐻)𝐺(𝐼−𝐻)] .
In this new two –stage test, we would like to address the following issues.
Permute subject label to calculate the null distribution of Pseudo-F statistics (Anderson, M.J. 2001)

14. Simulation Studies Simulation Setup:
Num. of subject: N = 7, 10,13 in each group
Num. of time points: T = 8, 12, 16
Num. of taxa: 34
Correlation types: Pearson’s rho, Kendall’s tau, maximal information coefficient (MIC)
Distance measures: Frobenius, Maximum, Infinity, Spectral
In this new two –stage test, we would like to address the following issues.

15. Simulation Studies Data-generating procedure:
For each taxon, fit marginal distribution by zero-inflated negative binomial distribution.
Estimate edge connection probability in LDA and control group and denote them by 𝑝 1 𝑎𝑛𝑑 𝑝 0 respectively
Denote 𝑝 0 = 𝑝 0 and 𝑝 1 =(1−𝜆) 𝑝 0 +𝜆 𝑝 1 .
𝜆 (between 0 and 1) control group similarity
Individual temporal correlation matrix are generated by 𝑝 0 and 𝑝 1
Taxa counts are generated by NORmal-To Anything (NORTA) procedure.
In this new two –stage test, we would like to address the following issues.

16. Simulation results for different correlation types—Type I error
Correlation type: Pearson’s rho, Kendall’s tau, MIC
Distance measure: Frobenius
𝜆 (between 0 and 1) controls group similarity
Empirical type I error T 8 12 16 N 7 10 13
Pearson
0.053
0.051
0.040
0.044
0.052
0.060
0.056
0.046
Kendall
0.047
0.045
0.042
MIC
0.039
0.059
0.043
0.050
In this new two –stage test, we would like to address the following issues.

17. Simulation results for different correlation types--Power
Distance measure: Frobenius
𝜆 (between 0 and 1) controls group similarity

18. Simulation results for different distance measures—Type I error
Correlation type:, Kendall’s tau
Distance measure: Frobenius, Maximum, Infinity, Spectral
𝜆 (between 0 and 1) controls group similarity
Empirical type I error T 8 12 16 N 7 10 13
Frobenius
0.051
0.044
0.047
0.043
0.05
0.039
0.056
0.052
Maximum
0.053
0.057
0.045
0.042
0.058
0.065
Infinity
0.034
0.040
0.041
0.04
0.049
Spectral
0.038
0.046
In this new two –stage test, we would like to address the following issues.

19. Simulation results for different distance measures--Power
Distance measure: Frobenius
𝜆 (between 0 and 1) controls group similarity

20. Early childhood antibiotics and the microbiome (ECAM)
Real Data Analysis
Early childhood antibiotics and the microbiome (ECAM)
Study desgin:
42 newborn babies were monitored for one year
Delivery type: 18 Cesarean section vs. 24 Vaginal
Gender: 14 Female vs. 28 Male
Ever use antibiotics: 19 Yes vs. 23 No
Unbalanced design for microbiome samples
Extra samples are collected before and after antibiotics usage
Total 505 samples and 498 genus level taxa
Num. of time points: median = 12,
min = 7, max = 17
Distance measure: Frobenius
𝜆 (between 0 and 1) controls group similarity

21. Early childhood antibiotics and the microbiome (ECAM)
Real Data Analysis
Early childhood antibiotics and the microbiome (ECAM)
Research question: Does overall microbiome interdependence different between Cesarean section and Vaginal delivery babies after controlling gender and antibiotics usage?
MINT PMANOVA table DF SS MS F
p value
Delivery Type 1
114.9
1.72
0.001
Gender
61.1
0.91
0.692
Antibiotics
67.9
1.02
0.406
Residuals 38
2536.7
66.8
Total 41
2780.6
Distance measure: Frobenius
𝜆 (between 0 and 1) controls group similarity

22. Summary Non-parametric Microbial interdependence test (NMIT)
NMIT is designed for longitudinal microbial study
NMIT tests overall interdependence structure
NMIT is a non-parametric distance based test
NMIT allows both balanced and unbalanced design
NMIT can adjust confounders
Assumptions:
NMIT assumes subjects are exchangeable (independent)
NMIT assumes taxa correlation do not change over time
REF: Zhang Y, Han SW, Cox LM., and Li H. (2017) A Multivariate Distance Based Test on Microbial Temporal Interaction Group Comparison. Genetic Epidemiology.
Dr. Yilong Zhang

23. Acknowledgements
The study is funded by NIH R01 DK Collaborators:
He is an established researcher in microbiology and infectious diseases. In 2015, he was selected to be in the TIME 100 Most Influential People in the world
Dr. Martin Blaser and people in his lab
Dr. Zhiheng Pei and people in his lab