simulate_funmediation_example {funmediation}

simulate_funmediation_example function

Description

Simulates a dataset for demonstrating the funmediation function.

Usage

simulate_funmediation_example(
  nsub = 500,
  nlevels = 2,
  ntimes = 100,
  observe_rate = 0.4,
  alpha_int = function(t) {
     return(t^0.5)
 },
  alpha_X = function(t) {
     return(-(t/2)^0.5)
 },
  beta_M = function(t) {
     (1/2) * (exp(t) - 1)
 },
  beta_int = 0,
  beta_X = 0.2,
  sigma_Y = 1,
  sigma_M_error = 2,
  rho_M_error = 0.8,
  simulate_binary_Y = FALSE,
  make_covariate_S = FALSE
)

Arguments

nsub

Number of subjects

nlevels

Number of treatment groups or levels on the treatment variable X. Subjects are assumed to be randomly assigned to each level with equal probability (i.e., the probability per level is 1/nlevel). Default is 2 for a randomized controlled trial with a control group X=0 and an experimental group X=1. There should not be less than 2 or more than 5 groups for purposes of this function.

ntimes

Number of potential times that could be observed on each subject

observe_rate

Proportion of potential times on which there are actually observations. Not all times are observed; this is assumed to be completely random and to be done by design to reduce participant burden.

alpha_int

Function representing the time-varying mean of mediator variable for the level of treatment with all treatment dummy codes X set to 0 (e.g., the control group).

alpha_X

Function representing the time-varying effect of X on the mediator (if there are two treatment levels) or a list of nlevels-1 functions representing the effect of receiving each nonzero level of X rather than control (if there are more than two treatment levels).

beta_M

Function representing the functional coefficient for cumulative (scalar-on-function) effect of the mediator M on the treatment Y adjusting for the treatment X

beta_int

Mean of Y if the X is zero and M is the 0 function

beta_X

Numeric value representing the direct effect of X on Y after adjusting for M (if there are two treatment levels) or a vector of nlevels-1 numeric values (if there are more than two treatment levels)

sigma_Y

Error standard deviation of the outcome Y (conditional on treatment and mediator trajectory)

sigma_M_error

Error standard deviation of the mediator M (conditional on treatment and time)

rho_M_error

Autoregressive correlation coefficient of the error in the mediator M, from one observation to the next

simulate_binary_Y

Whether Y should be generated from a binary logistic (TRUE) or Gaussian (FALSE) model

make_covariate_S

Whether to generate a random binary covariate S at the subject (i.e., time-invariant) level. It will be generated to have zero population-level relationship to the outcome.

Value

A list with the following components:

time_grid

The time grid for interpreting functional coefficients.

true_alpha_int

True value of the time-varying alpha_int parameter, representing the time-specific mean of the mediator M when the treatment value X is 0.

true_alpha_X

True value of the time-varying alpha_X parameter, representing the effect of X on M. This is a single number if nlevels=2, or a vector of effects if nlevels>2.

true_beta_int

True value of the beta_M parameter, representing the mean of the outcome Y when X=0 and M=0.

true_beta_M

True value of the beta_M parameter, representing the functional effect of treatment on the outcome Y.

true_beta_X

True value of the beta_X parameter, representing the effect of treatment on the outcome Y adjusting for the mediator. This is a single function if nlevels=2, or a vector of functions if nlevels>2.

true_indirect

True value of the indirect parameter, representing the indirect (mediated) effect of treatment on the outcome Y. This is a single number if nlevels=2, or a vector of effects if nlevels>2.

dataset

The simulated longitudinal dataset in long form.

Examples

set.seed(123)
# Simplest way to call the function:
simulation_all_defaults <- simulate_funmediation_example()
summary(simulation_all_defaults)
head(simulation_all_defaults)
# Changing the sample size to be larger:
simulation_larger <- simulate_funmediation_example(nsub=10000)
summary(simulation_larger)
# Changing the effect of the mediator to be null:
simulation_null <- simulate_funmediation_example(beta_M=function(t) {return(0*t)})
summary(simulation_null)
# Simulating a exposure variable with three levels (two dichotomous dummy codes)
simulation_three_group <- simulate_funmediation_example(nlevels=3,
                              alpha_X = list(function(t) {return(.1*t)},
                                             function(t) {return(-(t/2)^.5)}),
                              beta_X = c(-.2,.2))
print(summary(simulation_three_group));