How to simulate MAR missing data in R? - r

Question

I would like to simulate some missing data in R but am having trouble. I have created two variables ('pre' and 'post') that represent a measurement for the same individual pre- and post-treatment (i.e. paired data). I have been able to do it for data that is Missing Completely at Random (MCAR) - see below, but am unable to figure out how to code it for Missing at Random (MAR). For the MAR missing data, I would like to create 3 categories based on the pre-treatment observations that will determine how many of the post-treatment observations are missing. i.e.
For pre > 25, 40% post missing
For pre > 21 and ≤ 25, 30% post missing
For pre ≤ 21, 20% post missing
Can anyone help out? (I'd be really grateful!)
Thanks
set.seed(80122)
n <- 1000
# Simulate 1000 people with high pre-treatment (mean 28, sd 3) and normal (mean 18, sd 3) post-treatment. Correlation between paired data = 0.7.
data <- rmvnorm(n,mean=c(28,18),sigma=matrix(c(9,0.7*sqrt(81),0.7*sqrt(81),9),2,2)) # Covariance matrix
# Split into pre and post treatment and check correlation is what was specified
pre <- data[, 1]
post <- data[, 2]
cor.test(pre,post)
# Simulate MCAR
mcar <- 1 - rbinom(n, 1, 0.2) # Will create ~ 20% zero's which we'll convert to NA's
post_mcar <- post
post_mcar[mcar == 0] <- mcar[mcar==0] # Replace post data with random zero's from mcar vector
post_mcar[mcar == 0] <- NA # Change zero's to NAs

Answer 1

This is an old question, but I thought I'd take a crack at it.
Simulate fake data as in the OP:
library(tidyverse)
library(mvtnorm)
# Number of data values
n <- 1000
# Simulate 1000 people with high pre-treatment (mean 28, sd 3) and normal (mean 18, sd 3) post-treatment. Correlation between paired data = 0.7.
set.seed(80122)
data <- rmvnorm(n, mean=c(28,18),
sigma=matrix(c(9,0.7*sqrt(81),0.7*sqrt(81),9),2,2)) # Covariance matrix
Convert to data frame:
data = as.data.frame(data)
names(data) = c("pre", "post")
Simulate missing completely at random (MCAR) data:
data$post_mcar <- data$post
set.seed(2)
data$post_mcar[sample(1:nrow(data), 0.2*nrow(data))] = NA
Simulate missing at random (MAR) data: First, we'll create a grouping variable, frac, whose value is the fraction of the group that we want to set to missing. We'll use the cut function to create these groups and set the label values, then we'll convert the labels to numeric for later use:
data = data %>%
mutate(post_mar = post,
frac = as.numeric(as.character(cut(pre, breaks=c(-Inf, 21, 25, Inf),
labels=c(0.2,0.3,0.4)))))
Now, group by frac and set a randomly selected fraction of the values to NA, using frac to determine the fraction of values set to NA.
set.seed(3)
data = data %>%
group_by(frac) %>%
mutate(post_mar=replace(post_mar, row_number(post_mar) %in% sample(1:n(), round(unique(frac)*n())), NA)) %>%
ungroup
Here are the last 6 rows of the resulting data frame:
pre post post_mcar post_mar frac
995 28.63476 19.35081 19.35081 19.35081 0.4
996 32.86278 24.16119 NA NA 0.4
997 28.25965 16.64538 16.64538 16.64538 0.4
998 24.35255 17.80365 17.80365 17.80365 0.3
999 28.12426 18.25222 18.25222 NA 0.4
1000 27.55075 14.47757 14.47757 14.47757 0.4
Here's a check on the fraction of values missing in each group. Note that the actual percentage of values set to missing can differ from frac if the requested percentage doesn't result in an integer number of rows. Here, for example, there's no way to select 20% of 8 values. It can be 12.5% (1 value) or 25% (2 values).
data %>% group_by(frac) %>%
summarise(N=n(),
N_missing=sum(is.na(post_mar)),
Frac_missing=N_missing/N)
frac N N_missing Frac_missing
1 0.2 8 2 0.2500000
2 0.3 138 41 0.2971014
3 0.4 854 342 0.4004684