Simulate proportional decline model.

Simulate a dataset from the proportional decline model.

Usage

pmrm_simulate_decline_proportional(
  patients = 300,
  visit_times = seq(from = 0, to = 4, by = 1),
  spline_knots = visit_times,
  spline_method = c("natural", "fmm"),
  tau = 0,
  alpha = log(spline_knots + 1),
  beta = c(0, 0.1, 0.2),
  gamma = numeric(0L),
  sigma = rep(1, length(visit_times)),
  rho = rep(0, length(visit_times) * (length(visit_times) - 1L)/2L)
)

Arguments

patients: Positive integer scalar, total number of patients in the output dataset. Patients are allocated (roughly) uniformly across the study arms.
visit_times: Numeric vector, the continuous scheduled time after randomization of each study visit.
spline_knots: Numeric vector of spline knots on the continuous scale, including boundary knots.
spline_method: Character string, spline method to use for the base model. Must be "natural" or "fmm". See stats::splinefun() for details.
tau: Positive numeric scalar, standard deviation for jittering the simulated time points. Defaults to 0 so that the observed continuous times are just the scheduled visit times.
alpha: Numeric vector of spline coefficients for simulating the mean function f(t_{ij} | spline_knots, alpha). Must have length(spline_knots) elements.
beta: Numeric vector with one element per study arm (including the control arm). See vignette("models", package = "pmrm") for details on this parameter.
gamma: Numeric vector of model coefficients for covariate adjustment. The simulation functions in pmrm simulate length(gamma) columns for the covariate adjustment model matrix W. Set to numeric(0) to omit covariates.
sigma: A positive numeric vector of visit-level standard deviation parameters.
rho: A finite numeric vector of correlation parameters. Must have length J * (J - 1) / 2, where J is length(visit_times). The full covariance matrix Sigma is given by diag(sigma) %*% RTMB::unstructured(length(sigma))$corr(rho) %*% diag(sigma).

Value

A tibble of clinical data simulated from the model. See the "Simulated data" section of this help file for details.

Details

See vignette("models", package = "pmrm") for details.

Simulated data

The datasets returned from the simulation functions have one row per patient visit and the following columns which conform to the notation from vignette("models", package = "pmrm"):

patient: Character vector of patient ID labels.
visit: Ordered factor of clinical visits with labels included. min(visit) indicates the baseline visit.
arm: Ordered factor of study arms with visits included. min(arm) indicates the control arm.
i: integer ID of each patient.
j: integer ID of each clinical visit. j == 1 at baseline.
k: integer ID of the study arm of patient i. k == 1 for the control arm.
y: clinical outcomes.
t: observed continuous time since baseline.
beta: the scalar component of the treatment effect parameter beta defined for patient i.
mu: expected clinical outcome at the given patient visit.
w_*: columns of the covariate adjustment model matrix W.
e: residuals.

Examples

  pmrm_simulate_decline_proportional()
#> # A tibble: 1,500 × 11
#>    patient   visit   arm       i     j     k      y     t  beta    mu      e
#>    <chr>     <ord>   <ord> <int> <int> <int>  <dbl> <dbl> <dbl> <dbl>  <dbl>
#>  1 patient_1 visit_1 arm_1     1     1     1  0.839     0   0   0      0.839
#>  2 patient_1 visit_2 arm_1     1     2     1  1.23      1   0   0.693  0.540
#>  3 patient_1 visit_3 arm_1     1     3     1  2.97      2   0   1.10   1.87 
#>  4 patient_1 visit_4 arm_1     1     4     1  1.83      3   0   1.39   0.445
#>  5 patient_1 visit_5 arm_1     1     5     1  1.94      4   0   1.61   0.332
#>  6 patient_2 visit_1 arm_2     2     1     2 -1.91      0   0.1 0     -1.91 
#>  7 patient_2 visit_2 arm_2     2     2     2  1.98      1   0.1 0.624  1.36 
#>  8 patient_2 visit_3 arm_2     2     3     2  1.72      2   0.1 0.989  0.733
#>  9 patient_2 visit_4 arm_2     2     4     2  2.63      3   0.1 1.25   1.38 
#> 10 patient_2 visit_5 arm_2     2     5     2  1.59      4   0.1 1.45   0.141
#> # ℹ 1,490 more rows