Simulate from the longitudinal pooled model.

hbl_sim_pool(
  n_study = 5,
  n_group = 3,
  n_patient = 100,
  n_rep = 4,
  n_continuous = 0,
  n_binary = 0,
  constraint = FALSE,
  s_alpha = 1,
  s_delta = 1,
  s_beta = 1,
  s_sigma = 1,
  s_lambda = 1,
  covariance_current = "unstructured",
  covariance_historical = "unstructured",
  alpha = stats::rnorm(n = n_rep, mean = 0, sd = s_alpha),
  delta = stats::rnorm(n = (n_group - 1) * (n_rep - as.integer(constraint)), mean = 0, sd
    = s_delta),
  beta = stats::rnorm(n = n_study * (n_continuous + n_binary), mean = 0, sd = s_delta),
  sigma = stats::runif(n = n_study * n_rep, min = 0, max = s_sigma),
  rho_current = stats::runif(n = 1, min = -1, max = 1),
  rho_historical = stats::runif(n = n_study - 1, min = -1, max = 1)
)

Arguments

n_study

Number of studies to simulate.

n_group

Number of groups (e.g. study arms) to simulate per study.

n_patient

Number of patients to simulate per study per group.

n_rep

Number of repeated measures (time points) per patient.

n_continuous

Number of continuous covariates to simulate (all from independent standard normal distributions).

n_binary

Number of binary covariates to simulate (all from independent Bernoulli distributions with p = 0.5).

constraint

Logical of length 1, whether to pool all study arms at baseline (first rep). Appropriate when the response is the raw response (as opposed to change from baseline) and the first rep (i.e. time point) is prior to treatment.

s_alpha

Numeric of length 1, prior standard deviation of the study-specific control group mean parameters alpha.

s_delta

Numeric of length 1, prior standard deviation of the study-by-group effect parameters delta.

s_beta

Numeric of length 1, prior standard deviation of the fixed effects beta.

s_sigma

Numeric of length 1, prior upper bound of the residual standard deviations.

s_lambda

shape parameter of the LKJ priors on the unstructured correlation matrices.

covariance_current

Character of length 1, covariance structure of the current study. Possible values are "unstructured" for fully parameterized covariance matrices, "ar1" for AR(1) covariance matrices, and "diagonal" for residuals independent across time within each patient. In MCMC (e.g. hbl_mcmc_hierarchical()), the covariance structure affects computational speed. Unstructured covariance is slower than AR(1), and AR(1) is slower than diagonal. This is particularly true for covariance_historical if there are many historical studies in the data.

covariance_historical

Same as covariance_current, but for the covariance structure of each separate historical study. Each historical study has its own separate covariance matrix.

alpha

Numeric vector of length n_rep for the pooled and model and length n_study * n_rep for the independent and hierarchical models. alpha is the vector of control group mean parameters. alpha enters the model by multiplying with $matrices$x_alpha (see the return value). The control group in the data is the one with the group column equal to 1.

delta

Numeric vector of length (n_group - 1) * (n_rep - as.integer(constraint)) of treatment effect parameters. delta enters the model by multiplying with $matrices$x_delta (see the return value). The control (non-treatment) group in the data is the one with the group column equal to 1.

beta

Numeric vector of n_study * (n_continuous + n_binary) fixed effect parameters. Within each study, the first n_continuous betas are for the continuous covariates, and the rest are for the binary covariates. All the betas for one study appear before all the betas for the next study, and studies are arranged in increasing order of the sorted unique values in $data$study in the output. betas enters the model by multiplying with $matrices$x_alpha (see the return value).

sigma

Numeric vector of n_study * n_rep residual standard deviation parameters for each study and rep. The elements are sorted with all the standard deviations of study 1 first (all the reps), then all the reps of study 2, etc.

rho_current

Numeric of length 1 between -1 and 1, AR(1) residual correlation parameter for the current study.

rho_historical

Numeric of length n_study - 1 between -1 and 1, AR(1) residual correlation parameters for the historical studies.

Value

A list with the following elements:

  • data: tidy long-form dataset with the patient-level data. one row per patient per rep and indicator columns for the study, group (e.g. treatment arm), patient ID, and rep. The response columns is the patient response. The other columns are baseline covariates. The control group is the one with the group column equal to 1, and the current study (non-historical) is the one with the maximum value of the study column. Only the current study has any non-control-group patients, the historical studies have only the control group.

  • parameters: named list of model parameter values. See the model specification vignette for details.

  • matrices: A named list of model matrices. See the model specification vignette for details.

See also

Examples

hbl_sim_pool(n_continuous = 1)$data
#> # A tibble: 2,800 × 10
#>    study group patient   rep covariate_study1_continuous1 covariate_study2_con…¹
#>    <int> <int>   <int> <int>                        <dbl>                  <dbl>
#>  1     1     1       1     1                       0.0212                      0
#>  2     1     1       1     2                       0.0212                      0
#>  3     1     1       1     3                       0.0212                      0
#>  4     1     1       1     4                       0.0212                      0
#>  5     1     1       2     1                      -0.103                       0
#>  6     1     1       2     2                      -0.103                       0
#>  7     1     1       2     3                      -0.103                       0
#>  8     1     1       2     4                      -0.103                       0
#>  9     1     1       3     1                      -0.195                       0
#> 10     1     1       3     2                      -0.195                       0
#> # ℹ 2,790 more rows
#> # ℹ abbreviated name: ¹​covariate_study2_continuous1
#> # ℹ 4 more variables: covariate_study3_continuous1 <dbl>,
#> #   covariate_study4_continuous1 <dbl>, covariate_study5_continuous1 <dbl>,
#> #   response <dbl>