This function is meant to be used in the context of a clinical trial with a binary endpoint. For a vector of possible posterior decision thresholds, the function simulates many trials and then calculates the average number of times the posterior probability exceeds a given threshold. In a null case, this will result in the type I error at a given threshold. In an alternative case, this will result in the power at a given threshold.

## Usage

calibrate_posterior_threshold(
p,
N,
p0,
direction = "greater",
delta = NULL,
prior = c(0.5, 0.5),
S = 5000,
theta
)

## Arguments

p

vector of length two containing the probability of event in the standard of care and experimental arm c(p0, p1) for the two-sample case; integer of event probability for one-sample case

N

vector of length two containing the total sample size c(N0, N1) for two-sample case; integer of sample size so far N for one-sample case

p0

The target value to compare to in the one-sample case. Set to NULL for the two-sample case.

direction

"greater" (default) if interest is in p(p1 > p0) and "less" if interest is in p(p1 < p0) for two-sample case. For one-sample case, "greater" if interest is in p(p > p0) and "less" if interest is in p(p < p0).

delta

clinically meaningful difference between groups. Typically 0 for the two-sample case. NULL for the one-sample case (default).

prior

hyperparameters of prior beta distribution. Beta(0.5, 0.5) is default

S

number of samples drawn from the posterior, and number of simulated trials. Default is 5000

theta

The target posterior probability thresholds to consider. Integer or vector.

## Value

Returns a tibble with the posterior probability threshold(s) and associated proportion of positive trials.

## Examples

set.seed(123)

# Setting S = 100 for speed, in practice you would want a much larger sample

# One-sample case
calibrate_posterior_threshold(
p = 0.1,
N = 50,
p0 = 0.1,
S = 100,
theta = c(0.9, 0.95)
)
#> # A tibble: 2 × 2
#>   pp_threshold prop_pos
#>          <dbl>    <dbl>
#> 1         0.9      0.14
#> 2         0.95     0.02

# Two-sample case
calibrate_posterior_threshold(
p = c(0.1, 0.1),
N = c(50, 50),
p0 = NULL,
delta = 0,
S = 100,
theta = c(0.9, 0.95)
)
#> # A tibble: 2 × 2
#>   pp_threshold prop_pos
#>          <dbl>    <dbl>
#> 1         0.9      0.1
#> 2         0.95     0.04