Dropout Missing Data Example

# Simulate longitudinal data
fixed <- ~1 + time + diff + act + time:act
random <- ~1 + time + diff
fixed_param <- c(4, 2, 6, 2.3, 7)
random_param <- list(random_var = c(7, 4, 2), rand_gen = "rnorm")
cov_param <- list(dist_fun = c('rnorm', 'rnorm'),
                  var_type = c("level1", "level2"),
                  opts = list(list(mean = 0, sd = 1.5),
                              list(mean = 0, sd = 4)))
n <- 150
p <- 30
error_var <- 4
with_err_gen <- 'rnorm'
data_str <- "long"
temp_long <- sim_reg(fixed, random, random3 = NULL, fixed_param,
                     random_param, random_param3 = NULL,
                     cov_param, k = NULL, n, p, error_var, 
                     with_err_gen, data_str = data_str)

# simulate missing data
temp_long_miss <- missing_data(temp_long, miss_prop = .25, 
                               type = 'dropout', 
                               clust_var = 'clustID', 
                               within_id = 'withinID')
head(temp_long_miss)

From the example above, first two level longitudinal data are simulated. Then the missing_data function is used to generate the missing data. The function call includes the data frame to generate missing data, the proportion of values that are missing (in this case approximately 25% of the data will be identified as missing), the type is dropout, and the cluster ID variable is named as ‘clustID’. The output shows that two additional variables are added, a dichotomous variable reflecting whether the outcome is missing (a value of 1) or not (0) and a new outcome variable (labeled as sim_data2) to reflect the new outcome with missing data. To verify that indeed about 25% of the data are now missing:

prop.table(table(temp_long_miss$missing))

## 
##         0         1 
## 0.7488889 0.2511111

prop.table(table(is.na(temp_long_miss$sim_data2)))

## 
##     FALSE      TRUE 
## 0.7488889 0.2511111

MAR Missing Data Example

The mar missing data is similar to that of dropout missing data, but instead of being conditional on time, a third variable can be added to base the missing data on. For example, in a study, perhaps those individuals with lower income are less likely to report the outcome of the study. As such, the mar missing data implementation in simglm allows you to simulate missing data in a similar framework as the example above. Below is an example from a single level regression (assuming that the covariates are grand mean centered).

# simulate data
fixed <- ~1 + age + income
fixed_param <- c(2, 0.3, 1.3)
cov_param <- list(dist_fun = c('rnorm', 'rnorm'), 
                  var_type = c("single", "single"),
                  opts = list(list(mean = 0, sd = 4),
                              list(mean = 0, sd = 3)))
n <- 150
error_var <- 3
with_err_gen <- 'rnorm'
temp_single <- sim_reg(fixed = fixed, fixed_param = fixed_param,
                       cov_param = cov_param,
                       n = n, error_var = error_var, with_err_gen = with_err_gen,
                       data_str = "single")

# generate missing data
miss_prop <- c(0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05)
miss_prop <- rep(miss_prop, each = 15)
tmp_single_miss <- missing_data(temp_single, miss_prop = miss_prop, 
                                type = 'mar', miss_cov = 'income')
head(tmp_single_miss)

First single level data are simulated for 150 individuals. Missing proportions are then generated. In this example, 10 different proportions are created in decreasing order. This is important as the data generation arranges the covariate from smallest to largest. Then the missing proportions are repeated so that the miss_prop vector is the same length as the number of individuals. The second new addition is the argument miss_cov, this is the covariate that is used to generate the missing data. In this example, the covariate income is used.

Three additional variables are added in this function, miss_prop, miss_prob, and sim_data2 which reflect the missing proportion, the missing probability, and the new simulated data with missing data included. The missing data are generated if the miss_prob variable is greater than miss_prop, then the value is NA, otherwise it is not. The percentages can be summarized with the following table to show the structure of missing data depends on the variable income.

table(tmp_single_miss$miss_prop,is.na(tmp_single_miss$sim_data2))

##       
##        FALSE TRUE
##   0.05    15    0
##   0.1     15    0
##   0.15    13    2
##   0.2     15    0
##   0.25    11    4
##   0.3     12    3
##   0.35    11    4
##   0.4      9    6
##   0.45     8    7
##   0.5      6    9