There are multiple ways to simulate MMRM datasets using
brms and brms.mmrm.
Simple
brm_simulate_simple() simulates a dataset from the prior
predictive distribution of a simple special case of an MMRM.1
library(brms.mmrm)
set.seed(0)
sim <- brm_simulate_simple(
n_group = 3,
n_patient = 100,
n_time = 4
)The data element has a classed tibble you
can directly supply to brm_formula() and
brm_model().
sim$data
#> # A tibble: 1,200 × 4
#> patient time response group
#> <chr> <chr> <dbl> <chr>
#> 1 patient_001 time_1 1.11 group_1
#> 2 patient_001 time_2 2.15 group_1
#> 3 patient_001 time_3 2.54 group_1
#> 4 patient_001 time_4 -1.73 group_1
#> 5 patient_002 time_1 1.11 group_1
#> 6 patient_002 time_2 2.64 group_1
#> 7 patient_002 time_3 1.69 group_1
#> 8 patient_002 time_4 0.783 group_1
#> 9 patient_003 time_1 0.118 group_1
#> 10 patient_003 time_2 2.48 group_1
#> # ℹ 1,190 more rowsThe parameters element has the corresponding parameter
values simulated from the joint prior. Arguments to
brm_simulate_simple() control hyperparameters.
str(sim$parameters)
#> List of 5
#> $ beta : num [1:6] 1.263 -0.326 1.33 1.272 0.415 ...
#> $ tau : num [1:4] -0.092857 -0.029472 -0.000577 0.240465
#> $ sigma : num [1:4] 0.911 0.971 0.999 1.272
#> $ lambda : num [1:4, 1:4] 1 0.415 -0.818 -0.282 0.415 ...
#> $ covariance: num [1:4, 1:4] 0.831 0.368 -0.745 -0.326 0.368 ...And the model_matrix element has the regression model
matrix of fixed effect parameters.
head(sim$model_matrix)
#> groupgroup_1 groupgroup_2 groupgroup_3 timetime_2 timetime_3 timetime_4
#> 1 1 0 0 0 0 0
#> 2 1 0 0 1 0 0
#> 3 1 0 0 0 1 0
#> 4 1 0 0 0 0 1
#> 5 1 0 0 0 0 0
#> 6 1 0 0 1 0 0Change from baseline
brm_data_change() can convert the outcome variable from
raw response to change from baseline. This applies to real datasets
passed through [brm_data()] as well as simulated ones from
e.g. [brm_simulate_simple()]. The dataset above uses raw response with a
baseline time point of "time_1"
sim$data
#> # A tibble: 1,200 × 4
#> patient time response group
#> <chr> <chr> <dbl> <chr>
#> 1 patient_001 time_1 1.11 group_1
#> 2 patient_001 time_2 2.15 group_1
#> 3 patient_001 time_3 2.54 group_1
#> 4 patient_001 time_4 -1.73 group_1
#> 5 patient_002 time_1 1.11 group_1
#> 6 patient_002 time_2 2.64 group_1
#> 7 patient_002 time_3 1.69 group_1
#> 8 patient_002 time_4 0.783 group_1
#> 9 patient_003 time_1 0.118 group_1
#> 10 patient_003 time_2 2.48 group_1
#> # ℹ 1,190 more rowsbrm_data_change() subtracts baseline, replaces the raw
response column with a new change from baseline column, adds a new
column for the original baseline raw response, and adjusts the internal
attributes of the classed object accordingly.
brm_data_change(
data = sim$data,
name_change = "new_change",
name_baseline = "new_baseline"
)
#> # A tibble: 900 × 5
#> patient time group new_change new_baseline
#> <chr> <chr> <chr> <dbl> <dbl>
#> 1 patient_001 time_2 group_1 1.04 1.11
#> 2 patient_001 time_3 group_1 1.43 1.11
#> 3 patient_001 time_4 group_1 -2.84 1.11
#> 4 patient_002 time_2 group_1 1.53 1.11
#> 5 patient_002 time_3 group_1 0.576 1.11
#> 6 patient_002 time_4 group_1 -0.328 1.11
#> 7 patient_003 time_2 group_1 2.37 0.118
#> 8 patient_003 time_3 group_1 3.07 0.118
#> 9 patient_003 time_4 group_1 -1.14 0.118
#> 10 patient_004 time_2 group_1 1.57 1.29
#> # ℹ 890 more rowsAdvanced
For a more nuanced simulation, build up the dataset layer by layer.
Begin with brm_simulate_outline() to create an initial
structure and a random missingness pattern. In
brm_simulate_outline(), missing responses can come from
either transitory intercurrent events or from dropouts. The
missing column indicates which outcome values will be
missing (NA_real_) in a later step. The
response column is entirely missing for now and will be
simulated later.
data <- brm_simulate_outline(
n_group = 2,
n_patient = 100,
n_time = 4,
rate_dropout = 0.3
)
data
#> # A tibble: 800 × 5
#> patient time group missing response
#> <chr> <chr> <chr> <lgl> <dbl>
#> 1 patient_001 time_1 group_1 FALSE NA
#> 2 patient_001 time_2 group_1 TRUE NA
#> 3 patient_001 time_3 group_1 TRUE NA
#> 4 patient_001 time_4 group_1 TRUE NA
#> 5 patient_002 time_1 group_1 FALSE NA
#> 6 patient_002 time_2 group_1 FALSE NA
#> 7 patient_002 time_3 group_1 TRUE NA
#> 8 patient_002 time_4 group_1 TRUE NA
#> 9 patient_003 time_1 group_1 FALSE NA
#> 10 patient_003 time_2 group_1 FALSE NA
#> # ℹ 790 more rowsOptionally add random continuous covariates
brm_simulate_continuous() and random categorical covariates
using brm_simulate_categorical(). In each case, the
covariates are non-time-varying, which means each patient gets only one
unique value.
data <- data |>
brm_simulate_continuous(names = c("biomarker1", "biomarker2")) |>
brm_simulate_categorical(
names = c("status1", "status2"),
levels = c("present", "absent")
)
data
#> # A tibble: 800 × 9
#> patient time group missing response biomarker1 biomarker2 status1 status2
#> <chr> <chr> <chr> <lgl> <dbl> <dbl> <dbl> <chr> <chr>
#> 1 patient_0… time… grou… FALSE NA 0.328 -0.655 present absent
#> 2 patient_0… time… grou… TRUE NA 0.328 -0.655 present absent
#> 3 patient_0… time… grou… TRUE NA 0.328 -0.655 present absent
#> 4 patient_0… time… grou… TRUE NA 0.328 -0.655 present absent
#> 5 patient_0… time… grou… FALSE NA 1.04 -0.779 absent absent
#> 6 patient_0… time… grou… FALSE NA 1.04 -0.779 absent absent
#> 7 patient_0… time… grou… TRUE NA 1.04 -0.779 absent absent
#> 8 patient_0… time… grou… TRUE NA 1.04 -0.779 absent absent
#> 9 patient_0… time… grou… FALSE NA 0.717 -0.954 present absent
#> 10 patient_0… time… grou… FALSE NA 0.717 -0.954 present absent
#> # ℹ 790 more rowsAs described in the next section, brms.mmrm has a
convenient function brm_simulate_prior() to simulate the
outcome variable response using the data skeleton above and
the prior predictive distribution. However, if you prefer a full custom
approach, you may need granular details about the parameterization,
which requires the model matrix. Fortunately, brms supports
a make_standata() function to provide this, given a dataset
and a formula. You may need to temporarily set the response variable to
something non-missing, and you may wish to specify a custom prior.
library(brms)
formula <- brm_formula(data = mutate(data, response = 0))
formula
#> response ~ group + group:time + time + biomarker1 + biomarker2 + status1 + status2 + unstr(time = time, gr = patient)
#> sigma ~ 0 + time
stan_data <- make_standata(
formula = formula,
data = mutate(data, response = 0)
)
model_matrix <- stan_data$X
head(model_matrix)
#> Intercept groupgroup_2 timetime_2 timetime_3 timetime_4 biomarker1 biomarker2
#> 1 1 0 0 0 0 0.3283275 -0.6547971
#> 2 1 0 1 0 0 0.3283275 -0.6547971
#> 3 1 0 0 1 0 0.3283275 -0.6547971
#> 4 1 0 0 0 1 0.3283275 -0.6547971
#> 5 1 0 0 0 0 1.0385746 -0.7793828
#> 6 1 0 1 0 0 1.0385746 -0.7793828
#> status1present status2present groupgroup_2:timetime_2 groupgroup_2:timetime_3
#> 1 1 0 0 0
#> 2 1 0 0 0
#> 3 1 0 0 0
#> 4 1 0 0 0
#> 5 0 0 0 0
#> 6 0 0 0 0
#> groupgroup_2:timetime_4
#> 1 0
#> 2 0
#> 3 0
#> 4 0
#> 5 0
#> 6 0Prior
Function brm_simulate_prior() simulates from the prior
predictive distribution. It requires a dataset and a formula, and it
accepts a custom prior constructed with
brms::set_prior().
formula <- brm_formula(data = data)
library(brms)
prior <- set_prior("student_t(3, 0, 1.3)", class = "Intercept") +
set_prior("student_t(3, 0, 1.2)", class = "b") +
set_prior("student_t(3, 0, 1.1)", class = "b", dpar = "sigma") +
set_prior("lkj(1)", class = "cortime")
prior
#> prior class coef group resp dpar nlpar lb ub source
#> student_t(3, 0, 1.3) Intercept <NA> <NA> user
#> student_t(3, 0, 1.2) b <NA> <NA> user
#> student_t(3, 0, 1.1) b sigma <NA> <NA> user
#> lkj(1) cortime <NA> <NA> user
sim <- brm_simulate_prior(
data = data,
formula = formula,
prior = prior,
refresh = 0
)The output object sim has multiple draws from the prior
predictive distribution. sim$outcome has outcome draws, and
sim$parameters has parameter draws.
sim$model_matrix has the model matrix, and
sim$model has the full brms model fit object.
You can pass sim$model to functions from brms
and bayesplot such as pp_check().
names(sim)
#> [1] "data" "model" "model_matrix" "outcome" "parameters"In addition, sim$data has a copy of the original
dataset, but with the outcome variable taken from the final draw from
the prior predictive distribution. In addition, the missingness pattern
is automatically applied so that sim$data$response is
NA_real_ whenever sim$data$missing equals
TRUE.
sim$data
#> # A tibble: 800 × 9
#> patient time group missing response biomarker1 biomarker2 status1 status2
#> <chr> <chr> <chr> <lgl> <dbl> <dbl> <dbl> <chr> <chr>
#> 1 patient_0… time… grou… FALSE 3.90 0.328 -0.655 present absent
#> 2 patient_0… time… grou… TRUE NA 0.328 -0.655 present absent
#> 3 patient_0… time… grou… TRUE NA 0.328 -0.655 present absent
#> 4 patient_0… time… grou… TRUE NA 0.328 -0.655 present absent
#> 5 patient_0… time… grou… FALSE 3.46 1.04 -0.779 absent absent
#> 6 patient_0… time… grou… FALSE 2.66 1.04 -0.779 absent absent
#> 7 patient_0… time… grou… TRUE NA 1.04 -0.779 absent absent
#> 8 patient_0… time… grou… TRUE NA 1.04 -0.779 absent absent
#> 9 patient_0… time… grou… FALSE 5.28 0.717 -0.954 present absent
#> 10 patient_0… time… grou… FALSE 0.120 0.717 -0.954 present absent
#> # ℹ 790 more rowsPosterior
brms supports posterior predictive simulations and
checks through functions posteiror_predict(),
posterior_epred(), and pp_check(). These can
be used with a brms model fit object either from
brm_model() or from brm_simulate_prior().
data <- sim$data
formula <- brm_formula(data = data)
model <- brm_model(data = data, formula = formula, refresh = 0)
outcome_draws <- posterior_predict(object = model)The returned outcome_draws object is a numeric array of
posterior predictive draws, with one row per draw and one column per
non-missing observation (row) in the original data.