Posterior Distribution of Minimum X% Effective Dose

post_medx(
  x,
  ed,
  probs,
  time,
  lower,
  upper,
  greater,
  small_bound,
  return_samples,
  ...
)

# S3 method for dreamer_bma
post_medx(
  x,
  ed,
  probs = c(0.025, 0.975),
  time = NULL,
  lower = min(x$doses),
  upper = max(x$doses),
  greater = TRUE,
  small_bound = 0,
  return_samples = FALSE,
  ...
)

# S3 method for dreamer_mcmc
post_medx(
  x,
  ed,
  probs = c(0.025, 0.975),
  time = NULL,
  lower = min(attr(x, "doses")),
  upper = max(attr(x, "doses")),
  greater = TRUE,
  small_bound = 0,
  return_samples = FALSE,
  index = 1:(nrow(x[[1]]) * length(x)),
  ...
)

Arguments

x: output from dreamer_mcmc().
ed: a number between 0 and 100 indicating the ed% dose that is being sought.
probs: a vector of quantiles to calculate on the posterior.
time: the slice of time for which to calculate the posterior EDX dose. Applies to longitudinal models only.
lower: the lower bound of the doses for calculating EDX.
upper: the upper bound of the doses for calculating EDX.
greater: if TRUE, higher values indicate better efficacy. If FALSE, lower responses indicate better efficacy.
small_bound: the minimum (greater = TRUE) or maximum (greater = FALSE) bound of the response.
return_samples: logical indicating if the posterior samples should be returned.
...: additional arguments for specific methods.
index: a vector indicating which MCMC samples to use in the calculation. If NULL (default), all MCMC samples are used.

Value

Posterior quantities and samples (if applicable), generally in the form of a list. The pr_edx_exists column gives the posterior probability that an EDX% effect exists.

Details

The minimum X% effective dose is the dose that has X% of the largest effect for doses between lower and upper. When greater is TRUE, larger positive responses are considered more effective and vice versa. The X% response is calculated as small_bound + ed / 100 * (max_effect - small_bound) where "max_effect" is the maximum response for doses between lower and upper. The X% effective dose is the smallest dose which has X% response within the dose range. It is possible that for some MCMC samples, an X% effective dose may not exist, so probabilities are not guaranteed to sum to one.

Examples

set.seed(888)
data <- dreamer_data_linear(
  n_cohorts = c(20, 20, 20),
  dose = c(0, 3, 10),
  b1 = 1,
  b2 = 3,
  sigma = 5
)

# Bayesian model averaging
output <- dreamer_mcmc(
 data = data,
 n_adapt = 1e3,
 n_burn = 1e3,
 n_iter = 1e3,
 n_chains = 2,
 silent = FALSE,
 mod_linear = model_linear(
   mu_b1 = 0,
   sigma_b1 = 1,
   mu_b2 = 0,
   sigma_b2 = 1,
   shape = 1,
   rate = .001,
   w_prior = 1 / 2
 ),
 mod_quad = model_quad(
   mu_b1 = 0,
   sigma_b1 = 1,
   mu_b2 = 0,
   sigma_b2 = 1,
   mu_b3 = 0,
   sigma_b3 = 1,
   shape = 1,
   rate = .001,
   w_prior = 1 / 2
 )
)
#> mod_linear
#> start : 2024-04-01 17:24:43.340
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 6
#>    Unobserved stochastic nodes: 3
#>    Total graph size: 50
#> 
#> Initializing model
#> 
#> finish: 2024-04-01 17:24:43.362
#> total : 0.02 secs
#> mod_quad
#> start : 2024-04-01 17:24:43.362
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 6
#>    Unobserved stochastic nodes: 4
#>    Total graph size: 59
#> 
#> Initializing model
#> 
#> finish: 2024-04-01 17:24:43.391
#> total : 0.03 secs

post_medx(output, ed = c(50, 90))
#> $stats
#>   ed pr_edx_exists     mean     2.5%    97.5%
#> 1 50             1 4.934277 4.449656 5.568752
#> 2 90             1 8.986711 8.785120 9.183197
#> 

# from a single model
post_medx(output$mod_linear, ed = c(50, 90))
#> $stats
#>   ed pr_edx_exists     mean     2.5%    97.5%
#> 1 50             1 4.900778 4.660334 5.120568
#> 2 90             1 8.980156 8.932067 9.024114
#>