Bayesian and frequentist operating characteristics for a fixed-sample single-arm BF design

Computes operating characteristics for a genuine fixed-sample single-arm binomial design with final efficacy decision based on BF01 <= k.

Usage

powerbinbf01_fixed(
  n,
  k,
  p0,
  a0 = 1,
  b0 = 1,
  a1 = 1,
  b1 = 1,
  da0 = 1,
  db0 = 1,
  da1 = 1,
  db1 = 1,
  dp = NA_real_,
  type = c("point", "direction"),
  k_ce = NULL,
  grid_size = 801L
)

Arguments

n

Integer scalar. Total sample size.

k

Numeric scalar. Efficacy threshold on the BF01 scale.

p0

Numeric scalar in (0, 1). Null response probability.

a0, b0

Numeric scalars. Beta analysis-prior parameters under H0.

a1, b1

Numeric scalars. Beta analysis-prior parameters under H1.

da0, db0

Numeric scalars. Beta design-prior parameters under H0.

da1, db1

Numeric scalars. Beta design-prior parameters under H1.

dp

Optional numeric scalar in (0,1). If supplied, frequentist power under H1 is computed at p = dp.

type

Character string. One of \"point\" or \"direction\".

k_ce

Optional numeric scalar greater than 1. Threshold for compelling evidence in favour of H0 on the BF01 scale.

grid_size

Integer number of grid points used for numerical averaging.

Value

A list with Bayesian and frequentist operating characteristics for the fixed-sample design.

Details

Bayesian operating characteristics are computed under separate design priors:

• for type = "direction", Bayesian power averages over p > p0 under the H1 design prior truncated to (p0, 1], Bayesian type-I error averages over p <= p0 under the H0 design prior truncated to [0, p0], and CE(H0) is averaged over the same truncated H0 design prior;

• for type = "point", Bayesian power averages under the H1 design prior on (0, 1), Bayesian type-I error is evaluated at the point null p = p0, and CE(H0) is also evaluated at p = p0.