MarZIC estimates and tests the marginal mediation effects of
zero-inflated compositional mediators. It can be applied to microbiome
studies to estimate and test the marginal mediation effects of relative
abundances (RA). Let \(Y\), \(M\) and \(X\) denote the outcome, mediator (RA) and
the independent variable respectively. And let \(1_{(M>0)}\) denote the binary indicator
variable indicating whether \(M\) is
positive. MarZIC decomposes the mediation effect into two components of
which one is the total mediation effect going thru the continuous scale
of the mediator, denoted by NIE\(_1\)
and the other is the mediation effect going thru the binary change (from
zero to non-zero status) of the mediator, denoted by NIE\(_2\). For a microbiome data, let \(M_j\) denote the RA of the \(j\)th taxon/OTU/ASV. And let \(Z\) denote confounder variable (if any) and
\(Z\) could contain multiple variables.
The marginal outcome model for \(Y\)
is: \[
Y=\beta_0+\beta_1M_j+\beta_21_{M_j>0}+\beta_3X+\beta_4X1_{M_j>0}+\beta_5XM_j+\beta_6Z+\epsilon
\] The mean of \(M_j\) depends
on \(X\) and \(Z\) through the following equation: \[
\log \Bigg(\frac{E(M_j)}{1-E(M_j)}\Bigg)=\alpha_0 + \alpha_1X+\alpha_2Z
\] Let \(\Delta_j=P(M_j=0)\)
which is the probability of a structural zero (ie, true zero). We use
the following logistic model for this probability:
\[
\log\bigg(\frac{\Delta_j}{1-\Delta_j}\bigg)=\gamma_0 +
\gamma_1X+\gamma_2Z
\]
Typically, users just need to feed the first six inputs to the
function: Experiment_dat, lib_name,
y_name, x_name, conf_name and
taxa_of_interest.
MicrobData A dataset contains microbiome data. The
microbiome data could be relative abundance or absolute abundance.
Subjects with missing value will be removed during analysis.CovData A dataset contains outcome, library size and
covariates.lib_name Name of library size variable.y_name Name of outcome variablex_name Name of covariate of interestconf_name Name of confounders Defaule is NULL, meaning
no confounder.x4_inter Whether to include the interaction term \(\beta_4\). Default is TRUE.x5_inter Whether to include the interaction term \(\beta_5\). Default is TRUE.taxa_of_interest A character vector for taxa names
indicating taxa that should be analyzed. Default is “all”, meaning all
taxa should be included into analysis.mediator_mix_range Number of mixtures in mediator.
Default is 1, meaning no mixture.transfer_to_RA Logical variable indicating whether the
microbiome data should be transferred into relative abundance. Default
is TRUE. If FALSE, microbiome data will not be transferred (e.g., if the
input data is already RA data).num_cores Number of CPU cores to be used in
parallelization task.adjust_method P value adjustment method. Same as
p.adjust in R. Default is “fdr”.fdr_rate FDR cutoff for significance. Default is
0.05.taxDropThresh The threshold of dropping taxon due to
high zero percentage. Default is 0.9, meaning taxon will be dropped for
analysis if zero percentage is higher than 90%.taxDropCount The threshold of dropping taxon due to not
enough non-zero observation counts. Default is 4 *
(length(conf_name)+2), meaning taxon will be dropped if non-zero
observation is less than four times of the total number of covariates
(including the independent variable) plus intercept.zero_prop_NIE2 The threshold of zero percentage for
calculating NIE2. Default is 0.1, meaning NIE2 will be calculated for
taxon with zero percentage greater than 10%.zero_count_NIE2 The threshold of zero counts for
calculating NIE2. Default is 4 * (length(conf_name)+2), meaning NIE2
will be calculated for taxon with zero counts greater than four times of
number of covariates plus 1.SDThresh The threshold of dropping taxon due to low
coefficient of variation (CV) to avoid constant taxon. Default is 0.05,
meaning any taxon has CV less than 0.05 will be dropped.SDx The threshold of stopping analysis due to low CV of
covariate of interest. Default is 0.05, meaning when CV of covariate of
interest is less than 0.05, the analysis will be stopped.SDy The threshold of stopping analysis due to low CV of
outcome. Default is 0.05, meaning when CV of outcome is less than 0.05,
the analysis will be stopped.A list of 4 datasets containing the results
for NIE1, NIE2, NDE, and
NIE. Each dataset has row representing each taxon, 6
columns for Estimates, Standard Error,
Lower bound for 95% Confidence Interval,
Upper bound for 95% Confidence Interval,
Adjusted p value, Significance indicator.
## A make up example with 1 taxon and 100 subjects.
set.seed(1)
nSub <- 200
nTaxa <- 10
## generate covariate of interest X
X <- rbinom(nSub, 1, 0.5)
## generate confounders
conf1<-rnorm(nSub)
conf2<-rbinom(nSub,1,0.5)
## generate mean of each taxon. All taxon are having the same mean for simplicity.
mu <- exp(-5 + X + 0.1 * conf1 + 0.1 * conf2) /
(1 + exp(-5 + X + 0.1 * conf1 + 0.1 * conf2))
phi <- 10
## generate true RA
M_taxon<-t(sapply(mu,function(x) dirmult::rdirichlet(n=1,rep(x*phi,nTaxa))))
P_zero <- exp(-3 + 0.3 * X + 0.1 * conf1 + 0.1 * conf2) /
(1 + exp(-3 + 0.3 * X + 0.1 * conf1 + 0.1 * conf2))
non_zero_ind <- t(sapply(P_zero,function(x) 1-rbinom(nTaxa,1,rep(x,nTaxa))))
True_RA<-t(apply(M_taxon*non_zero_ind,1,function(x) x/sum(x)))
## generate outcome Y based on true RA
Y <- 1 + 100 * True_RA[,1] + 5 * (True_RA[,1] > 0) + X + conf1 + conf2 + rnorm(nSub)
## library size was set to 10,000 for all subjects for simplicity.
libsize <- 10000
## generate observed RA
observed_AA <- floor(M_taxon*libsize*non_zero_ind)
observed_RA <- t(apply(observed_AA,1,function(x) x/sum(x)))
colnames(observed_RA)<-paste0("rawCount",seq_len(nTaxa))
CovData <- cbind(Y = Y, X = X, libsize = libsize, conf1 = conf1, conf2 = conf2)Above steps could be ignored if a SummarizedExperiment object is
already available. Suppose we’re interested in the mediation effects of
rawCount1, rawCount2, and
rawCount3, the analysis could be done as:
## run the analysis
res <- MarZIC(
MicrobData = observed_RA,
CovData = CovData,
lib_name = "libsize",
y_name = "Y",
x_name = "X",
conf_name = c("conf1","conf2"),
taxa_of_interest = c("rawCount1","rawCount2","rawCount3"),
num_cores = 1,
mediator_mix_range = 1
)The results contain 4 datasets for NIE\(_1\), NIE\(_2\), NDE, NIE, respectively. The NIE\(_1\), for example, could be extracted by:
NIE1 <- res$NIE1_saveThe significant result could be extracted by:
subset(NIE1, significance == TRUE)
#> est se CI low CI up p value unadj p value adj
#> rawCount1 7.138202 1.666013 3.872816 10.40359 1.830673e-05 5.492018e-05
#> significance
#> rawCount1 TRUEFrom the result, we can find that rawCount1 is an
significant mediator of mediating the effect of \(X\) on \(Y\).
Wu et al.(2022) MarZIC: A Marginal Mediation Model for Zero-Inflated Compositional Mediators with Applications to Microbiome Data. Genes 2022, 13, 1049.
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