README.md

In jiezhou-2/imediation: Individual Mediation Analysis

imediation

The goal of imediation is to provide an easy access to the individual mediation effects in complicated multivariates situation.

Installation

Install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("jiezhou-2/imediation")

The main function in this package is

ime(index,u,AA,data,form,type)

which outputs the individual mediation effects for given mediator.

(1) index specifies the mediator of interest.  The p mediators are indexed by 1,2,...p respectively.

(2) Vector u specifies the state of treatment and other mediators, where 0 stands for no treatment, 1  treatment.


(3) AA is a p by p (0,1)-matrix specifying the causal relationships among mediators. The parents of mediator i are represented by the nonzero entry in ith row of AA.  If AA=0, which means no causality is available,  then direct individual mediation effect is computed othewise total individual mediation effect is computed. 


(4) data is a n by (p+q+2) matrix where the first column is treatment, the last column is the outcome, the 2 to (p+1) columns represent the mediators, the (p+2) to (p+q+1) columns represent the confounders.    


(5) form is a list with 2 compoents. The first is a vector where 0 in entry j means no interaction between treatment and mediator j in the outcome model, 1 means there is interaction between treatment and mediator j in the outcome model. The second component is a symmetrical p by p matrix. If the (i,j) entry is 1, then there is interaction between mediator i and mediator j in the outcome model. If (i,j) entry is 0, then there is no interaction between mediator i and mediator j in the outcome model. 


(6) type has two options, one is "continuous", which means outcome will by modeled by normal regression,  the other is "binomial", which means outcome will by modeled by logistic regression. In formar case, mediation effect is measured by the difference of outcome. In later case, mediation effect is measured by odds ratio. 

library(imediation)
library(igraph)
#> 
#> Attaching package: 'igraph'
#> The following objects are masked from 'package:stats':
#> 
#>     decompose, spectrum
#> The following object is masked from 'package:base':
#> 
#>     union

Causal relationships among mediators for the following examples.

#adjacency matrix
AA=matrix(0,nrow = 4,ncol =4)
A=matrix(c(0,1,0,0),nrow=2)
AA[c(2,3,4),1]=1
AA[4,c(1,2,3)]=1
AA[2:3,2:3]=A
#create graph
g1=graph_from_adjacency_matrix(adjmatrix = t(AA))
plot.igraph(g1)

Mediation model with 2 continuous mediators and binary treatment and outcome: Main-effect model

#data generation
size=200
 treatment=sample(x=c(0,1), size = size, replace = T,prob = c(0.5, 0.5))
  mediator=matrix(nrow = size, ncol = 2)
  error=matrix(nrow = size,ncol = 2)
  for (i in 1:size) {
    error[i,]=rnorm(n=2, mean=0, sd = 0.5)
  }

  mediator[,1]=0.5*treatment+error[,1]
  mediator[,2]=0.5*treatment+0.5*mediator[,1]+error[,2]
      expp=rep(0,size)
      p=rep(0,size)
      outcome=rep(0,size)
      for (i in 1:size) {
        expp[i]=0.5*treatment[i]+0.5*sum(mediator[i,])
        p[i]=exp(expp[i])/(1+exp(expp[i]))
        outcome[i]=rbinom(n=1,size=1,p=p[i])
      }
  data1=cbind(treatment,mediator,outcome)
  colnames(data1)=c("treatment",paste("mediator",1:2, sep = ""), "outcome")

#computation of mediation effects
form=vector( "list",2)
form[[1]]=rep(0,2)
form[[2]]=matrix(0,nrow = 2, ncol = 2)
ime(index=1,u=c(0,0),AA=AA,data = data1,form = form,type = "binomial")
#> [1] 1.349322
ime(index=2,u=c(0,0),AA=AA,data = data1,form = form,type = "binomial")
#> [1] 1.32038

Mediation model with 2 continuous mediators and binary treatment and outcome: treatment-mediator-interaction-effect model

#data generation
size=200
 treatment=sample(x=c(0,1), size = size, replace = T,prob = c(0.5, 0.5))
  mediator=matrix(nrow = size, ncol = 2)
  error=matrix(nrow = size,ncol = 2)
  for (i in 1:size) {
    error[i,]=rnorm(n=2, mean=0, sd = 0.5)
  }

  mediator[,1]=0.5*treatment+error[,1]
  mediator[,2]=0.5*treatment+0.5*mediator[,1]+error[,2]
      expp=rep(0,size)
      p=rep(0,size)
      outcome=rep(0,size)
      for (i in 1:size) {
        expp[i]=0.5*treatment[i]+0.5*sum(mediator[i,])+0.5*treatment[i]*mediator[i,1]
        p[i]=exp(expp[i])/(1+exp(expp[i]))
        outcome[i]=rbinom(n=1,size=1,p=p[i])
      }
  data2=cbind(treatment,mediator,outcome)
  colnames(data2)=c("treatment",paste("mediator",1:2, sep = ""), "outcome")
  head(data2)
#>      treatment  mediator1  mediator2 outcome
#> [1,]         1  0.4503669  0.2223242       1
#> [2,]         1 -0.6076851  0.1594417       0
#> [3,]         0  0.1173414  0.6627321       1
#> [4,]         0  0.1463012  1.1573888       0
#> [5,]         1  0.7552818  0.9626471       1
#> [6,]         0 -0.2085252 -0.4782378       1

#computation of mediation effects
form=vector( "list",2)
form[[1]]=c(0,0)
form[[2]]=matrix(0,nrow = 2, ncol = 2)
ime(index=1,u=c(0,0),AA=AA,data = data1,form = form,type = "binomial")
#> [1] 1.349144
ime(index=2,u=c(0,0),AA=AA,data = data1,form = form,type = "binomial")
#> [1] 1.320973

Mediation model with 2 continuous mediators and binary treatment and outcome: mediator-mediator-interaction-effect model

#data generation
size=200
 treatment=sample(x=c(0,1), size = size, replace = T,prob = c(0.5, 0.5))
  mediator=matrix(nrow = size, ncol = 2)
  error=matrix(nrow = size,ncol = 2)
  for (i in 1:size) {
    error[i,]=rnorm(n=2, mean=0, sd = 0.5)
  }

  mediator[,1]=0.5*treatment+error[,1]
  mediator[,2]=0.5*treatment+0.5*mediator[,1]+error[,2]
      expp=rep(0,size)
      p=rep(0,size)
      outcome=rep(0,size)
      for (i in 1:size) {
        expp[i]=0.5*treatment[i]+0.5*sum(mediator[i,])+0.5*mediator[i,2]*mediator[i,1]
        p[i]=exp(expp[i])/(1+exp(expp[i]))
        outcome[i]=rbinom(n=1,size=1,p=p[i])
      }
  data3=cbind(treatment,mediator,outcome)
  colnames(data3)=c("treatment",paste("mediator",1:2, sep = ""), "outcome")
  head(data3)
#>      treatment  mediator1     mediator2 outcome
#> [1,]         1 -0.1720938  0.3106310828       0
#> [2,]         0 -0.2900611 -0.2384122361       1
#> [3,]         0  0.2186295 -0.0004080681       1
#> [4,]         1  0.5222557  0.8460590974       1
#> [5,]         1  0.2090281 -0.0363928413       0
#> [6,]         1 -0.7596459  0.3398389626       1

#computation of mediation effects
form=vector( "list",2)
form[[1]]=c(0,0)
form[[2]]=matrix(c(0,1,1,0),nrow = 2, ncol = 2)
ime(index=1,u=c(0,0),AA=AA,data = data1,form = form,type = "binomial")
#> [1] 1.367162
ime(index=2,u=c(0,0),AA=AA,data = data1,form = form,type = "binomial")
#> [1] 1.33784

jiezhou-2/imediation documentation built on Dec. 21, 2021, 12:04 a.m.