calibrate_posterior_threshold {ppseq}

Calibrate the posterior probability threshold

Description

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)
  )

# 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)
  )