Skip to contents

Simulate a small trial with rare-disease features

Source: R/simulate_rare.R
simulate_rare_trial.Rd

Draws a two-arm longitudinal trial with the features that make small trials in rare disease hard to read: few participants, heterogeneous progression (a mixture of fast and slow progressors with a random slope), an effect that varies with progression, sites, dropout, and optionally one planted defect. It is the data generator of the simulation studies in the methods paper and complements simulate_trial(), which it leaves unchanged.

Usage

simulate_rare_trial(
  n_per_arm = 25,
  delta = 0,
  n_visits = 4,
  sigma = 10,
  rho = 0.6,
  dropout = 0.03,
  baseline_beta = 0.5,
  population = c("homogeneous", "mixture", "heavy"),
  fast_frac = 0.35,
  fast_decline = 8,
  slope_sd = 4,
  fast_effect = 1.6,
  t_df = 3,
  n_sites = 8,
  site_sd = 2.5,
  defect = c("none", "outlier", "site", "mnar", "allocation"),
  n_outliers = 1,
  outlier_size = 10,
  mnar_strength = 1.5,
  mnar_dropout = 3 * dropout,
  fast_to_active = 0.25,
  seed = NULL
)

Arguments

n_per_arm

Participants per arm (exactly balanced).

delta

Average treatment effect at the last visit (higher is better).

n_visits, sigma, rho

Visits, residual SD and AR(1) correlation.

dropout

Missing-at-random dropout probability per visit.

baseline_beta

Slope of the response on the baseline.

population

"homogeneous", "mixture" or "heavy".

fast_frac, fast_decline, slope_sd, fast_effect

Mixture settings.

t_df

Degrees of freedom of the heavy-tailed errors.

n_sites, site_sd

Number of sites and SD of the site effect on progression.

defect

"none", "outlier", "site", "mnar" or "allocation".

n_outliers, outlier_size

Outlier settings (size in units of sigma).

mnar_strength, mnar_dropout

Informative-dropout settings.

fast_to_active

Allocation-defect setting: the weight with which a fast progressor is drawn into the active arm (slow progressors get 1 - fast_to_active); 0.5 is fair allocation.

seed

Random seed; the caller's random-number state is restored. The draws use R's default generators whatever the caller's RNGkind(), so a seed gives the same trial in a plain session and on parallel workers.

Value

A data frame in long format with one row per observed visit: id, arm ("REF" or "ACT"), site, base, fast (0/1), visit ("V1", ...) and y.

Details

The response is a change score at visits 1 to n_visits. For participant i at visit v, with \(t_v = v / V\), $$y_{iv} = \beta (b_i - 50) + (d_i + s_i + u_{site(i)}) t_v + T_i e_i t_v + \epsilon_{iv},$$ where \(b_i\) is the baseline, \(d_i\) the extra decline of a fast progressor, \(s_i\) a random slope, \(u\) a site effect, \(T_i\) the active-arm indicator, \(e_i\) the participant's treatment effect and \(\epsilon\) AR(1) errors with standard deviation sigma.

Populations:

  • "homogeneous": no progression heterogeneity; fast is recorded but is not prognostic, so models with and without it target the same effect.

  • "mixture": a fraction fast_frac of fast progressors lose a further fast_decline points by the last visit; random slope with SD slope_sd; the effect is fast_effect times larger in fast progressors, scaled so that the average effect is delta.

  • "heavy": as homogeneous with Student-t errors on t_df degrees of freedom, scaled to the same standard deviation.

Defects (each makes a significant result one that should not be trusted):

  • "outlier": n_outliers active-arm participants shifted up by outlier_size standard deviations at every visit (a data error).

  • "site": the treatment effect delta applies at site 1 only.

  • "mnar": active-arm dropout also depends on the unobserved next value, so participants about to decline leave (informative dropout), with a baseline dropout rate of mnar_dropout per visit.

  • "allocation": allocation is not independent of prognosis (for example a stratification error or selection at enrolment). Participants are drawn into the active arm with weight fast_to_active for fast progressors and 1 - fast_to_active for slow ones, so with fast_to_active < 0.5 fast progressors (who decline more in the "mixture" population) gather in the reference arm. An analysis that omits fast is then biased in favour of the active arm; one that adjusts for it is not.

See also

simulate_trial() for the simpler generator.

Examples

d <- simulate_rare_trial(n_per_arm = 20, delta = 5, population = "mixture", seed = 1)
head(d)
#>      id arm  site     base fast visit         y
#> 1 S0001 REF site7 39.34409    0    V1 18.126327
#> 2 S0001 REF site7 39.34409    0    V2  2.774974
#> 3 S0001 REF site7 39.34409    0    V3 11.429294
#> 4 S0001 REF site7 39.34409    0    V4 -5.396804
#> 5 S0002 ACT site6 34.36218    0    V1  1.571670
#> 6 S0002 ACT site6 34.36218    0    V2  6.179818
spec <- stress_spec(d, "y", "id", "visit", "arm", "REF", covariates = ~ base + fast)
stress_fit(spec)[, c("estimate", "stderr", "p")]
#>   estimate   stderr         p
#> 1 5.239965 4.102245 0.2110184