Design or evaluate a single-arm two-stage Bayes factor trial

Calibrates or evaluates a single-arm two-stage Bayes factor design for a binary endpoint with one interim analysis for futility.

Usage

design_singlearm_bf(
  n1_min,
  n2_max,
  k,
  k_f,
  p0,
  a0 = 1,
  b0 = 1,
  a1 = 1,
  b1 = 1,
  dp = NA_real_,
  da0 = 1,
  db0 = 1,
  da1 = 1,
  db1 = 1,
  type = c("point", "direction"),
  calibration = c("Bayesian", "frequentist", "hybrid", "full"),
  target_power = 0.8,
  target_type1 = 0.05,
  target_ce_h0 = 0,
  target_freq_power = 0.8,
  target_freq_type1 = 0.05,
  algorithm = c("optimal", "manual"),
  interim = NULL,
  final = NULL,
  power_cushion = 0,
  ...
)

Arguments

n1_min

Integer. Minimum admissible interim sample size.

n2_max

Integer. Maximum admissible final sample size.

k

Numeric scalar greater than 0. Efficacy threshold on the \(BF_{01}\) scale.

k_f

Numeric scalar greater than 1. Futility threshold on the \(BF_{01}\) scale.

p0

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

a0, b0

Positive numeric scalars. Beta analysis-prior parameters under \(H_0\).

a1, b1

Positive numeric scalars. Beta analysis-prior parameters under \(H_1\).

dp

Optional numeric scalar in \((0,1)\). Fixed point alternative used for frequentist power calculations under \(H_1\).

da0, db0

Positive numeric scalars. Beta design-prior parameters under \(H_0\).

da1, db1

Positive numeric scalars. Beta design-prior parameters under \(H_1\).

type

Character string specifying the Bayes-factor test. One of "point" or "direction".

calibration

Character string specifying the calibration mode. One of "Bayesian", "frequentist", "hybrid", or "full".

target_power

Numeric scalar in \((0,1)\). Target corrected Bayesian power.

target_type1

Numeric scalar in \((0,1)\). Target corrected Bayesian type-I error.

target_ce_h0

Numeric scalar in \([0,1)\). Optional lower bound on the corrected Bayesian probability of compelling evidence in favour of \(H_0\).

target_freq_power

Numeric scalar in \((0,1)\). Target corrected frequentist power at dp.

target_freq_type1

Numeric scalar in \((0,1)\). Target corrected frequentist type-I error at \(p = p_0\).

algorithm

Character string specifying whether the design should be optimized or only evaluated.

interim

Optional integer interim sample size used when algorithm = "manual".

final

Optional integer final sample size used when algorithm = "manual".

power_cushion

Optional additive cushion applied only in the fixed-sample anchor search of the first optimization step. This can be useful because introducing an interim futility analysis typically reduces corrected power relative to the fixed-sample anchor.

...

Reserved for future extensions.

Value

An object of class "singlearm_bf_design".

Details

The design uses the Bayes factor \(BF_{01}\). Small values of \(BF_{01}\) indicate evidence against \(H_0\), so final efficacy is concluded when \(BF_{01} \\le k\). Large values indicate evidence in favour of \(H_0\), so interim futility is concluded when \(BF_{01} \\ge k_f\).

Analysis priors are specified separately under \(H_0\) and \(H_1\) via a0, b0, a1, b1. Design priors are specified separately under \(H_0\) and \(H_1\) via da0, db0, da1, db1.