Simulate individual-level DiD data for a collection of studies

Generates individual-level pre/post observations for both arms of a set of difference-in-differences studies under a hierarchical model. This is the gold-standard view of the data; the as_* family of functions then produce the data as it would appear under different levels of access.

Usage

simulate_meta_did(
  n_studies = 20L,
  n_control = 100L,
  n_treatment = 100L,
  true_effect = -0.15,
  sigma_effect = 0.03,
  true_trend = -0.02,
  sigma_trend = 0,
  baseline_mean = 0.45,
  baseline_sd = 0,
  within_sd = 0.12,
  rho = 0.5,
  seed = NULL,
  covariates = NULL,
  beta_cov = NULL
)

Arguments

n_studies: Number of studies. Default 20.
n_control: Number of individuals per study in the control arm. Default 100L.
n_treatment: Number of individuals per study in the treatment arm. Default 100L.
true_effect: Population mean treatment effect. Default -0.15.
sigma_effect: Between-study SD of treatment effects. Default 0.03.
true_trend: Population mean time trend. Default -0.02.
sigma_trend: Between-study SD of time trends. Default 0.
baseline_mean: Population mean of study baselines. Default 0.45.
baseline_sd: Between-study SD of baselines. Default 0.
within_sd: Individual-level SD (the same for pre and post and for both groups). Default 0.12.
rho: Pre-post correlation within individuals. Directly parameterises the off-diagonal of the bivariate normal covariance matrix. Default 0.5.
seed: Integer random seed for reproducibility. Default NULL.
covariates: An optional data frame with n_studies rows containing study-level covariate values. Column names are used as covariate names. Default NULL (no covariates).
beta_cov: A numeric vector of true covariate regression coefficients, with length equal to ncol(covariates). Required when covariates is provided. Each coefficient represents the change in treatment effect per unit increase in the corresponding covariate. Default NULL.

Value

A data frame with columns study_id, subject_id, group ("control" or "treatment"), time ("pre" or "post"), value, plus any covariate columns (repeated for each observation within a study). The true study-level parameters are attached as attribute "true_params".

Data-generating model

Study-level parameters are drawn hierarchically: $$\theta_i \sim \text{Normal}(\texttt{true\_effect},\, \texttt{sigma\_effect}^2)$$ $$\gamma_i \sim \text{Normal}(\texttt{true\_trend},\, \texttt{sigma\_trend}^2)$$ $$b_i \sim \text{Normal}(\texttt{baseline\_mean},\, \texttt{baseline\_sd}^2)$$

Within each study, individual (pre, post) pairs are drawn from a bivariate normal distribution with covariance matrix $$\Sigma = \sigma^2 \begin{pmatrix} 1 & \rho \\ \rho & 1 \end{pmatrix}$$ making the role of $\rho$ as the pre-post correlation explicit. The mean vector for the control group is $(b_i,\, b_i + \gamma_i)$ and for the treatment group $(b_i,\, b_i + \gamma_i + \theta_i)$.

Examples

dat <- simulate_meta_did(n_studies = 10, true_effect = -0.15, seed = 42)
head(dat)
#> # A tibble: 6 × 5
#>   study_id subject_id group   time  value
#>   <chr>         <int> <chr>   <chr> <dbl>
#> 1 study_1           1 control pre   0.607
#> 2 study_1           1 control post  0.506
#> 3 study_1           2 control pre   0.724
#> 4 study_1           2 control post  0.578
#> 5 study_1           3 control pre   0.283
#> 6 study_1           3 control post  0.296
attr(dat, "true_params")
#> # A tibble: 10 × 4
#>    study_id   theta  beta baseline
#>    <chr>      <dbl> <dbl>    <dbl>
#>  1 study_1  -0.109  -0.02     0.45
#>  2 study_2  -0.167  -0.02     0.45
#>  3 study_3  -0.139  -0.02     0.45
#>  4 study_4  -0.131  -0.02     0.45
#>  5 study_5  -0.138  -0.02     0.45
#>  6 study_6  -0.153  -0.02     0.45
#>  7 study_7  -0.105  -0.02     0.45
#>  8 study_8  -0.153  -0.02     0.45
#>  9 study_9  -0.0894 -0.02     0.45
#> 10 study_10 -0.152  -0.02     0.45