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Calibration of the decision thresholds

Source: R/qdm_calibrate.R
qdm_calibrate.Rd

Chooses the thresholds \(\gamma_{go}\) and \(\gamma_{nogo}\) of the criterion of a design so that the probabilities of a false Go decision and a false NoGo decision are controlled.

Usage

qdm_calibrate(
  design,
  scenario_go,
  scenario_nogo,
  target_go,
  target_nogo,
  grid = seq(0.01, 0.99, by = 0.01),
  nsim = 10000L,
  seed = NULL
)

Arguments

design

A design created by design_binary, design_continuous, design_binary2, design_continuous2 or design_tte. Its thresholds are replaced by the calibrated ones. For two endpoints with a marginal rule (rule = "and" or "or"), the same threshold is used for both endpoints.

scenario_go, scenario_nogo

Data frames with one row each, giving the scenarios used to calibrate \(\gamma_{go}\) and \(\gamma_{nogo}\) (see qdm_oc for the columns). For two binary endpoints, the correlations must be feasible.

target_go, target_nogo

Upper bounds for the probabilities that the Go criterion is met under scenario_go and that the NoGo criterion is met under scenario_nogo, strictly between 0 and 1.

grid

Candidate thresholds, strictly between 0 and 1.

nsim, seed

As in qdm_oc. The probabilities for all values of grid are computed from the same outcomes (simulated studies or enumerated outcomes) and the same Monte Carlo draws.

Value

An object of class "qdm_calibration": a list with elements

gamma_go, gamma_nogo

The chosen thresholds (NA if no value in grid meets the target).

prob_go, prob_nogo

The probabilities that the Go criterion is met under scenario_go and that the NoGo criterion is met under scenario_nogo, at the chosen thresholds.

target_go, target_nogo

The targets.

curve

A data frame with the columns gamma (the grid), prob_go and prob_nogo (the two probabilities at each threshold).

oc

A data frame of the decision probabilities with the chosen thresholds under the two scenarios (NULL if a threshold was not found).

design

The design with the chosen thresholds (NULL if a threshold was not found).

scenario_go, scenario_nogo, method

The scenarios and the method of computation.

Details

The threshold \(\gamma_{go}\) is the smallest value in grid for which the probability that the Go criterion is met under scenario_go (typically a scenario with no or a small treatment effect) is at most target_go. The threshold \(\gamma_{nogo}\) is the smallest value in grid for which the probability that the NoGo criterion is met under scenario_nogo (typically a scenario with the expected treatment effect) is at most target_nogo. Both probabilities decrease as the threshold increases, so the chosen thresholds are the least strict ones that meet the targets.

The decision probabilities of the design with the chosen thresholds are computed under both scenarios. If \(\gamma_{go} + \gamma_{nogo} \le 1\) (and, for two endpoints with the marginal rule "or", for any thresholds), Miss decisions (both criteria met) can occur, and a warning is given when they have positive probability.

See also

Other operations: qdm_boundary(), qdm_decide(), qdm_oc()

Examples

des <- design_binary(
  n_t = 12, n_c = 12,
  prior_t = prior_beta(0.5, 0.5), prior_c = prior_beta(0.5, 0.5),
  criterion = criterion_posterior(theta_tv = 0.2, theta_mav = 0.1,
                                  gamma_go = 0.5, gamma_nogo = 0.8)
)
cal <- qdm_calibrate(des,
                     scenario_go = data.frame(pi_t = 0.4, pi_c = 0.4),
                     scenario_nogo = data.frame(pi_t = 0.7, pi_c = 0.4),
                     target_go = 0.05, target_nogo = 0.2)
cal
#> Calibration of the decision thresholds (exact enumeration of the outcomes)
#>   gamma_go   = 0.74: P(Go criterion met | scenario_go) = 0.03368 (target 0.05)
#>   gamma_nogo = 0.39: P(NoGo criterion met | scenario_nogo) = 0.182 (target 0.2)
#> Decision probabilities with the chosen thresholds
#>       scenario pi_t pi_c      Go   NoGo   Gray Miss
#>    scenario_go  0.4  0.4 0.03368 0.7338 0.2326    0
#>  scenario_nogo  0.7  0.4 0.36483 0.1820 0.4531    0
plot(cal)

cal$design
#> Design: one binary endpoint
#>   Treatment: n = 12, prior Beta(a = 0.5, b = 0.5)
#>   Control: concurrent, n = 12, prior Beta(a = 0.5, b = 0.5)
#> Posterior probability criterion
#>   Go:   P(theta > 0.2 | data) >= 0.74
#>   NoGo: P(theta <= 0.1 | data) >= 0.39