Conditioned MICE imputation / with restrictions

Question

I have a dataset like this:

d <- data.frame(X1 = c(1, 1, NA, NA, 0, NA, NA, 1, 0),
                X2 = c(NA, 0, NA, NA, 0, NA, NA, 1, 0))

  X1 X2
1  1 NA
2  1  0
3 NA NA
4 NA NA
5  0  0
6 NA NA
7 NA NA
8  1  1
9  0  0

I want to perform mice imputation with the following condition based on the future imputed values of X1:

• If X1 = 0 --> X2 = 0
• If X1 = 1 --> X2 = 0 or 1

How can I write this condition? The base code for my imputation is:

library(mice)
imp <- mice(d, seed=123, m=5, maxit=10)

I am having troubles in understand. Thank you

Answer 1

We can use a passive imputation approach as described by Heymans and Eekhout (2019) by specifying the imputation method. If X1 is 0, X2 will always be 0, but if X1 is 1, then the usual pmm method (or whatever method you specify) applies.

library(mice)
set.seed(123)

d <- data.frame(X1 = c(1, 1, NA, NA, 0, NA, NA, 1, 0),
                X2 = c(NA, 0, NA, NA, 0, NA, NA, 1, 0))

fakeimp <- mice(d, seed = 123, maxit = 0, printFlag = FALSE)
meth <- fakeimp$method
meth["X2"] <- "~I((ifelse(X1 == 0, 0, X2)))"

imp <- mice(d, seed = 123, m = 5, maxit = 10, method = meth, printFlag = FALSE)

full <- complete(imp, action = "long", include = FALSE)
head(full)
#>   .imp .id X1 X2
#> 1    1   1  1  1
#> 2    1   2  1  0
#> 3    1   3  1  0
#> 4    1   4  0  0
#> 5    1   5  0  0
#> 6    1   6  0  0