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Bayesian and frequentist operating characteristics for a single-arm two-stage BF design

Source: R/powerbinbf01seq.R
powerbinbf01seq.Rd

Computes naive fixed-sample and corrected two-stage operating characteristics for a single-arm binomial design with one interim analysis for futility. The Bayes factor is oriented as BF01, so efficacy corresponds to small values (BF01 <= k) and futility corresponds to large values (BF01 >= kf).

Usage

powerbinbf01seq(
  n1,
  n2,
  k,
  kf,
  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

n1

Integer scalar. Interim sample size.

n2

Integer scalar. Final sample size, with n1 < n2.

k

Numeric scalar. Efficacy threshold on the BF01 scale.

kf

Numeric scalar. Futility 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.

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], and Bayesian type-I error averages over p <= p0 under the H0 design prior truncated to [0, p0];

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

If dp is supplied, additional frequentist power under H1 is computed at the fixed point alternative p = dp. Frequentist type-I error is computed at p = p0.