Simulate power for planning a SAD validation study

Simulates paired studies (each rater assesses the same images without and with a SAD) and compares the power of the conventional two-stage approach, a paired t test on \(\rho_c\), with the likelihood ratio test of the one-stage model for any effect of the SAD on mean or dispersion (4 df).

Usage

sad_simulate(
  n_rater = c(10, 20, 40),
  n_image = c(20, 40),
  nsim = 200,
  shift = -3,
  slope_change = 0,
  precision = 1,
  bias0 = 3,
  slope0 = 1.1,
  sd_rater = 5,
  sd_slope = 0.18,
  sd_image = 3.5,
  sigma0 = 8,
  rho_rater = 0.5,
  severity = function(n) stats::runif(n, 0.5, 80),
  cores = 1,
  seed = 1
)

Arguments

n_rater, n_image

Vectors with the numbers of raters and images; all combinations are simulated.

nsim

Number of simulated studies per scenario.

shift

Change in bias at 10% severity caused by the SAD (percentage points).

slope_change

Change in slope caused by the SAD.

precision

Multiplier of the rater and residual standard deviations with the SAD (< 1 means the SAD makes estimates more precise).

bias0, slope0

Bias at 10% severity and slope without the SAD.

sd_rater, sd_slope

Standard deviations of rater intercepts and slopes.

sd_image

Standard deviation of image difficulty.

sigma0

Residual standard deviation at 10% severity without the SAD.

rho_rater

Correlation of a rater's effects with and without the SAD.

severity

Function of n that draws the actual severities.

cores

Number of cores (parallel::mclapply(); ignored on Windows).

seed

Random seed; the user's random number stream is restored.

Value

A tibble with one row per scenario and the rejection rates at 5% (power_two_stage, power_one_stage) and the number of converged fits.

Details

Default parameters are typical values estimated from ten published SAD validation studies. Estimates are truncated to 0-100%. The one-stage model uses the "sep" structure. With fewer than about 20 raters the likelihood ratio test can be liberal; a parametric bootstrap is then safer.

Examples

# \donttest{
if (requireNamespace("glmmTMB", quietly = TRUE)) {
  sad_simulate(n_rater = 10, n_image = 20, nsim = 5)
}
#> # A tibble: 1 × 5
#>   n_rater n_image power_two_stage power_one_stage  n_ok
#>     <dbl>   <dbl>           <dbl>           <dbl> <int>
#> 1      10      20               0               0     5
# }