OneSampleBernoulli {BayesDIP}

One sample Bernoulli model

Description

For a given planned sample size, the efficacy and futility boundaries, return the power, the type I error, the expected sample size and its standard deviation, the probability of reaching the efficacy and futility boundaries.

Usage

OneSampleBernoulli(
  prior,
  N = 100,
  p0,
  p1,
  d = 0,
  ps = 0.95,
  pf = 0.05,
  alternative = c("less", "greater"),
  seed = 202209,
  sim = 5000
)

Arguments

prior

A list of length 3 containing the distributional information of the prior. The first element is a number specifying the type of prior. Options are

1. DIP ;

2. Beta(a,b), where a = shape, b = scale

The second and third elements of the list are the parameters a and b, respectively.

N

The planned sample size.

p0

The null response rate, which could be taken as the standard or historical rate.

p1

The response rate of the new treatment.

d

The target improvement (minimal clinically meaningful difference).

ps

The efficacy boundary (upper boundary).

pf

The futility boundary (lower boundary).

alternative

less (lower values imply greater efficacy) or greater (larger values imply greater efficacy).

seed

The seed for simulations.

sim

The number of simulations.

Value

A list of the arguments with method and computed elements

Examples

# with traditional Bayesian prior Beta(1,1)
OneSampleBernoulli(list(2,1,1), N = 100, p0 = 0.3, p1 = 0.5, d = 0.05,
                   ps = 0.98, pf = 0.05, alternative = "greater",
                   seed = 202210, sim = 10)
# with DIP
OneSampleBernoulli(list(1,0,0), N = 100, p0 = 0.3, p1 = 0.5, d = 0.05,
                   ps = 0.98, pf = 0.05, alternative = "greater",
                   seed = 202210, sim = 10)