In LindaValeri/CMAverse: Causal Mediation Analysis

This example demonstrates how to estimate causal effects with multiple imputations by using cmest when the dataset contains missing values. For this purpose, we simulate some data containing a continuous baseline confounder $C_1$, a binary baseline confounder $C_2$, a binary exposure $A$, a binary mediator $M$ and a binary outcome $Y$. The true regression models for $A$, $M$ and $Y$ are: $$logit(E(A|C_1,C_2))=0.2+0.5C_1+0.1C_2$$ $$logit(E(M|A,C_1,C_2))=1+2A+1.5C_1+0.8C_2$$ $$logit(E(Y|A,M,C_1,C_2)))=-3-0.4A-1.2M+0.5AM+0.3C_1-0.6C_2$$

To create the dataset with missing values, we randomly delete 10% of values in the dataset.

set.seed(1)
expit <- function(x) exp(x)/(1+exp(x))
n <- 10000
C1 <- rnorm(n, mean = 1, sd = 0.1)
C2 <- rbinom(n, 1, 0.6)
A <- rbinom(n, 1, expit(0.2 + 0.5*C1 + 0.1*C2))
M <- rbinom(n, 1, expit(1 + 2*A + 1.5*C1 + 0.8*C2))
Y <- rbinom(n, 1, expit(-3 - 0.4*A - 1.2*M + 0.5*A*M + 0.3*C1 - 0.6*C2))
data_noNA <- data.frame(A, M, Y, C1, C2)
missing <- sample(1:(5*n), n*0.1, replace = FALSE)
C1[missing[which(missing <= n)]] <- NA
C2[missing[which((missing > n)*(missing <= 2*n) == 1)] - n] <- NA
A[missing[which((missing > 2*n)*(missing <= 3*n) == 1)] - 2*n] <- NA
M[missing[which((missing > 3*n)*(missing <= 4*n) == 1)] - 3*n] <- NA
Y[missing[which((missing > 4*n)*(missing <= 5*n) == 1)] - 4*n] <- NA
data <- data.frame(A, M, Y, C1, C2)

The DAG for this scientific setting is:

library(CMAverse)
cmdag(outcome = "Y", exposure = "A", mediator = "M",
      basec = c("C1", "C2"), postc = NULL, node = TRUE, text_col = "white")

To conduct multiple imputations, we set the multimp argument to be TRUE. The regression-based approach is used for illustration. The multiple imputation results:

res_multimp <- cmest(data = data, model = "rb", outcome = "Y", exposure = "A",
                     mediator = "M", basec = c("C1", "C2"), EMint = TRUE,
                     mreg = list("logistic"), yreg = "logistic",
                     astar = 0, a = 1, mval = list(1), 
                     estimation = "paramfunc", inference = "delta", 
                     multimp = TRUE, args_mice = list(m = 10))

summary(res_multimp)

Compare the multiple imputation results with true results:

res_noNA <- cmest(data = data_noNA, model = "rb", outcome = "Y", exposure = "A",
                  mediator = "M", basec = c("C1", "C2"), EMint = TRUE,
                  mreg = list("logistic"), yreg = "logistic",
                  astar = 0, a = 1, mval = list(1), 
                  estimation = "paramfunc", inference = "delta")