In AllanJe/multimediate: Causal mediation analysis in presence of multiple mediators uncausally related
Multiple mediation analysis
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
library(multimediate)
This function is based on the work presented in Jerolon et al 2020 and the R package mediation presented in Tingley et al 2014. Models supported by our R function are shown in the following table.
Models supported by multimediate.
Outcome
Mediators Linear Binary Ordered categorical Non-ordered categorical
Linear Ok Ok Ok Not yet
Binary (Probit) Ok Ok Ok Not yet
Ordered categorical Ok Ok Ok Not yet
Non-ordered categorical Not yet Not yet Not yet Not yet
Example 1
We will do a mediation analysis with the following model.
- Binary treatment : $T$
- Linear Outcome : $Y$
- Linear mediators : $M_1,M_2,M_3$
- Binary covariables : $C_1,C_2,C_3$
In this first example the covariable $C_1$ is affecting all three mediators and the outcome $Y$; the covariable $C_2$ is affecting $M_1$ and the outcome $Y$; and the covariable $C_3$ is affecting $M_2$ and the outcome $Y$ as described in the diagramm.
data(data1)
data1$Treatment=as.factor(data1$Treatment)
data1$C1=as.factor(data1$C1)
data1$C2=as.factor(data1$C2)
data1$C3=as.factor(data1$C3)
data1$M1=as.numeric(data1$M1)
data1$M2=as.numeric(data1$M2)
data1$M3=as.numeric(data1$M3)
data1$Outcome=as.numeric(data1$Outcome)
summary(data1)
The regression models are then as follows.
M1reg=lm(M1~ Treatment + C1 + C2, data=data1)
M2reg=lm(M2~ Treatment + C1 + C3, data=data1)
M3reg=lm(M3~ Treatment + C1 , data=data1)
Yreg=lm(Outcome~ Treatment + M1 + M2 + M3 + C1 + C2 + C3, data=data1)
Once the regressions are done, we can then proceed to the multiple mediation analysis using the multimediate function. Then display the results with the summary function.
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
True values of causal effects in data 1.
Total Effect Direct Effect Joint Indirect Effect Indirect Effect by M1 Indirect Effect by M2 Indirect Effect by M3
92 10 82 10 18 54
summary(med.analysis,opt="avg")
#plot(med.analysis)
Example 2
- Binary treatment : $T$
- Binary Outcome : $Y$
- Linear mediators : $M_1,M_2,M_3$
- Binary covariables : $C_1,C_2,C_3$
data(data2)
data2$Treatment=as.factor(data2$Treatment)
data2$C1=as.factor(data2$C1)
data2$C2=as.factor(data2$C2)
data2$C3=as.factor(data2$C3)
data2$M1=as.numeric(data2$M1)
data2$M2=as.numeric(data2$M2)
data2$M3=as.numeric(data2$M3)
data2$Outcome=as.factor(data2$Outcome)
summary(data2)
M1reg=lm(M1~ Treatment + C1, data=data2)
M2reg=lm(M2~ Treatment + C2, data=data2)
M3reg=lm(M3~ Treatment + C3, data=data2)
Yreg=glm(Outcome~ Treatment + M1 + M2 + M3 + C1 + C2 + C3, data=data2, family = binomial("logit"))
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95,fun=median)
True values of causal effects in data 2 on log OR scale.
Total Effect Direct Effect Joint Indirect Effect Indirect Effect by M1 Indirect Effect by M2 Indirect Effect by M3
1.311 0.71 0.601 0.195 0.19 0.216
summary(med.analysis,opt="avg",logit="all")
# summary(med.analysis,opt="avg",logit="effects")
# plot(med.analysis)
# summary(med.analysis,opt="avg",logit="OR")
#plot(med.analysis,logit = "OR")
#summary(med.analysis,opt="avg",logit="logOR")
#plot(med.analysis,logit = "logOR")
Example 3
- Binary treatment $T$
- Polytomic Outcome $Y$
- Linear mediators $M_1,M_2,M_3$
- Binary covariables $C_1,C_2,C_3$
data(data3)
data3$Treatment=as.factor(data3$Treatment)
data3$C1=as.factor(data3$C1)
data3$C2=as.factor(data3$C2)
data3$C3=as.factor(data3$C3)
data3$M1=as.numeric(data3$M1)
data3$M2=as.numeric(data3$M2)
data3$M3=as.numeric(data3$M3)
data3$Outcome=as.factor(data3$Outcome)
summary(data3)
M1reg=lm(M1~ Treatment + C1 + C3, data=data3)
M2reg=lm(M2~ Treatment + C1 + C2, data=data3)
M3reg=lm(M3~ Treatment + C2 + C3, data=data3)
library(MASS)
Yreg=polr(Outcome ~ Treatment + M1 + M2 + M3 + C1 + C2 + C3 , data = data3, method = "probit")
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=100,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=100,conf.level=0.95)
summary(med.analysis,opt="avg")
Values of causal effects in data 3.
Total Effect Direct Effect Joint Indirect Effect Indirect Effect by M1 Indirect Effect by M2 Indirect Effect by M3
2.21 0.5 1.71 0.32 0.44 0.60
summary(med.analysis,opt="avg")
Example 4
- Binary treatment $T$
- Linear Outcome $Y$
- Linear mediator $M_1$
- Binary mediator $,M_2$
- Polytomic mediator $M_3$
- Binary covariables $C_1,C_2,C_3$
data(data4)
data4$Treatment=as.factor(data4$Treatment)
data4$C1=as.factor(data4$C1)
data4$C2=as.factor(data4$C2)
data4$C3=as.factor(data4$C3)
data4$M1=as.numeric(data4$M1)
data4$M3=as.factor(data4$M3)
data4$M2=as.factor(data4$M2)
data4$Outcome=as.numeric(data4$Outcome)
summary(data4)
M1reg=lm(M1~ Treatment + C1 + C2 + C3, data = data4)
M2reg=glm(M2~ Treatment + C1 + C3, data = data4, family = binomial("probit"))
M3reg=polr(M3~Treatment + C2 + C3 , data = data4, method = "probit")
Yreg=lm(Outcome~ Treatment + M1 + M2 + M3 + C1 + C2 + C3, data=data4)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg,
treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
Values of causal effects in data 4.
Total Effect Direct Effect Joint Indirect Effect Indirect Effect by M1 Indirect Effect by M2 Indirect Effect by M3
57.68 10 47.48 34.2 0 13.48
summary(med.analysis,opt="avg")
Example 5
- Binary treatment $T$
- Survival Outcome $Y$
- Linear mediators $M_1,M_2,M_3$
data(data5)
# data5$Exposure=as.factor(data5$Exposure)
# data5$M1=as.numeric(data5$M1)
# data5$M3=as.numeric(data5$M3)
# data5$M2=as.numeric(data5$M2)
# data5$Outcome=as.numeric(data5$Outcome)
summary(data5)
modM1=lm(M1 ~ Exposure, data = data5)
modM2=lm(M2 ~ Exposure, data = data5)
modM3=lm(M3 ~ Exposure, data = data5)
lmodel.m=list(modM1,modM2, modM3)
library(timereg)
model.y=aalen(Surv(surv_time, event) ~ const(Exposure) + const(M1) + const(M2) + const(M3), data = data5, robust=T)
multi.media=multimediate(lmodel.m,correlated=TRUE,model.y,treat='Exposure',treat.value=1,control.value=0,J=1000,conf.level=0.95,data=data5)
multi.media=multimediate(lmodel.m,correlated=TRUE,model.y,treat='Exposure',treat.value=1,control.value=0,J=1000,conf.level=0.95,data=data5)
summary(multi.media, opt='avg')
AllanJe/multimediate documentation built on July 25, 2024, 12:14 p.m.
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Multiple mediation analysis
knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
library(multimediate)
This function is based on the work presented in Jerolon et al 2020 and the R package mediation presented in Tingley et al 2014. Models supported by our R function are shown in the following table.
| Models supported by multimediate. | |||||
|---|---|---|---|---|---|
| Outcome | |||||
| Mediators | Linear | Binary | Ordered categorical | Non-ordered categorical | |
| Linear | Ok | Ok | Ok | Not yet | |
| Binary (Probit) | Ok | Ok | Ok | Not yet | |
| Ordered categorical | Ok | Ok | Ok | Not yet | |
| Non-ordered categorical | Not yet | Not yet | Not yet | Not yet | |
Example 1
We will do a mediation analysis with the following model.
- Binary treatment : $T$
- Linear Outcome : $Y$
- Linear mediators : $M_1,M_2,M_3$
- Binary covariables : $C_1,C_2,C_3$
In this first example the covariable $C_1$ is affecting all three mediators and the outcome $Y$; the covariable $C_2$ is affecting $M_1$ and the outcome $Y$; and the covariable $C_3$ is affecting $M_2$ and the outcome $Y$ as described in the diagramm.
data(data1) data1$Treatment=as.factor(data1$Treatment) data1$C1=as.factor(data1$C1) data1$C2=as.factor(data1$C2) data1$C3=as.factor(data1$C3) data1$M1=as.numeric(data1$M1) data1$M2=as.numeric(data1$M2) data1$M3=as.numeric(data1$M3) data1$Outcome=as.numeric(data1$Outcome) summary(data1)
The regression models are then as follows.
M1reg=lm(M1~ Treatment + C1 + C2, data=data1) M2reg=lm(M2~ Treatment + C1 + C3, data=data1) M3reg=lm(M3~ Treatment + C1 , data=data1) Yreg=lm(Outcome~ Treatment + M1 + M2 + M3 + C1 + C2 + C3, data=data1)
Once the regressions are done, we can then proceed to the multiple mediation analysis using the multimediate function. Then display the results with the summary function.
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
| True values of causal effects in data 1. | |||||
|---|---|---|---|---|---|
| Total Effect | Direct Effect | Joint Indirect Effect | Indirect Effect by M1 | Indirect Effect by M2 | Indirect Effect by M3 |
| 92 | 10 | 82 | 10 | 18 | 54 |
summary(med.analysis,opt="avg") #plot(med.analysis)
Example 2
- Binary treatment : $T$
- Binary Outcome : $Y$
- Linear mediators : $M_1,M_2,M_3$
- Binary covariables : $C_1,C_2,C_3$
data(data2) data2$Treatment=as.factor(data2$Treatment) data2$C1=as.factor(data2$C1) data2$C2=as.factor(data2$C2) data2$C3=as.factor(data2$C3) data2$M1=as.numeric(data2$M1) data2$M2=as.numeric(data2$M2) data2$M3=as.numeric(data2$M3) data2$Outcome=as.factor(data2$Outcome) summary(data2)
M1reg=lm(M1~ Treatment + C1, data=data2) M2reg=lm(M2~ Treatment + C2, data=data2) M3reg=lm(M3~ Treatment + C3, data=data2) Yreg=glm(Outcome~ Treatment + M1 + M2 + M3 + C1 + C2 + C3, data=data2, family = binomial("logit"))
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95,fun=median)
| True values of causal effects in data 2 on log OR scale. | |||||
|---|---|---|---|---|---|
| Total Effect | Direct Effect | Joint Indirect Effect | Indirect Effect by M1 | Indirect Effect by M2 | Indirect Effect by M3 |
| 1.311 | 0.71 | 0.601 | 0.195 | 0.19 | 0.216 |
summary(med.analysis,opt="avg",logit="all") # summary(med.analysis,opt="avg",logit="effects") # plot(med.analysis) # summary(med.analysis,opt="avg",logit="OR") #plot(med.analysis,logit = "OR") #summary(med.analysis,opt="avg",logit="logOR") #plot(med.analysis,logit = "logOR")
Example 3
- Binary treatment $T$
- Polytomic Outcome $Y$
- Linear mediators $M_1,M_2,M_3$
- Binary covariables $C_1,C_2,C_3$
data(data3) data3$Treatment=as.factor(data3$Treatment) data3$C1=as.factor(data3$C1) data3$C2=as.factor(data3$C2) data3$C3=as.factor(data3$C3) data3$M1=as.numeric(data3$M1) data3$M2=as.numeric(data3$M2) data3$M3=as.numeric(data3$M3) data3$Outcome=as.factor(data3$Outcome) summary(data3)
M1reg=lm(M1~ Treatment + C1 + C3, data=data3) M2reg=lm(M2~ Treatment + C1 + C2, data=data3) M3reg=lm(M3~ Treatment + C2 + C3, data=data3) library(MASS) Yreg=polr(Outcome ~ Treatment + M1 + M2 + M3 + C1 + C2 + C3 , data = data3, method = "probit")
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=100,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=100,conf.level=0.95) summary(med.analysis,opt="avg")
| Values of causal effects in data 3. | |||||
|---|---|---|---|---|---|
| Total Effect | Direct Effect | Joint Indirect Effect | Indirect Effect by M1 | Indirect Effect by M2 | Indirect Effect by M3 |
| 2.21 | 0.5 | 1.71 | 0.32 | 0.44 | 0.60 |
summary(med.analysis,opt="avg")
Example 4
- Binary treatment $T$
- Linear Outcome $Y$
- Linear mediator $M_1$
- Binary mediator $,M_2$
- Polytomic mediator $M_3$
- Binary covariables $C_1,C_2,C_3$
data(data4) data4$Treatment=as.factor(data4$Treatment) data4$C1=as.factor(data4$C1) data4$C2=as.factor(data4$C2) data4$C3=as.factor(data4$C3) data4$M1=as.numeric(data4$M1) data4$M3=as.factor(data4$M3) data4$M2=as.factor(data4$M2) data4$Outcome=as.numeric(data4$Outcome) summary(data4)
M1reg=lm(M1~ Treatment + C1 + C2 + C3, data = data4) M2reg=glm(M2~ Treatment + C1 + C3, data = data4, family = binomial("probit")) M3reg=polr(M3~Treatment + C2 + C3 , data = data4, method = "probit") Yreg=lm(Outcome~ Treatment + M1 + M2 + M3 + C1 + C2 + C3, data=data4)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
med.analysis=multimediate(lmodel.m=list(M1reg,M2reg,M3reg),correlated=TRUE,model.y=Yreg, treat="Treatment",treat.value=1,control.value=0,J=1000,conf.level=0.95)
| Values of causal effects in data 4. | |||||
|---|---|---|---|---|---|
| Total Effect | Direct Effect | Joint Indirect Effect | Indirect Effect by M1 | Indirect Effect by M2 | Indirect Effect by M3 |
| 57.68 | 10 | 47.48 | 34.2 | 0 | 13.48 |
summary(med.analysis,opt="avg")
Example 5
- Binary treatment $T$
- Survival Outcome $Y$
- Linear mediators $M_1,M_2,M_3$
data(data5) # data5$Exposure=as.factor(data5$Exposure) # data5$M1=as.numeric(data5$M1) # data5$M3=as.numeric(data5$M3) # data5$M2=as.numeric(data5$M2) # data5$Outcome=as.numeric(data5$Outcome) summary(data5)
modM1=lm(M1 ~ Exposure, data = data5) modM2=lm(M2 ~ Exposure, data = data5) modM3=lm(M3 ~ Exposure, data = data5) lmodel.m=list(modM1,modM2, modM3) library(timereg) model.y=aalen(Surv(surv_time, event) ~ const(Exposure) + const(M1) + const(M2) + const(M3), data = data5, robust=T)
multi.media=multimediate(lmodel.m,correlated=TRUE,model.y,treat='Exposure',treat.value=1,control.value=0,J=1000,conf.level=0.95,data=data5)
multi.media=multimediate(lmodel.m,correlated=TRUE,model.y,treat='Exposure',treat.value=1,control.value=0,J=1000,conf.level=0.95,data=data5)
summary(multi.media, opt='avg')
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