OneSampleNormal2 {BayesDIP}

One sample Normal model with two-parameter unknown - both mean and variance unknown

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

OneSampleNormal2(
  prior,
  N = 100,
  mu0,
  mu1,
  var0,
  var,
  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. Normal(mu0,var/k) and var ~ Inverse-Gamma(v/2, v*var0/2)

   where mu0 = prior mean, k = sample size of prior observations (Normal prior),

   v = sample size of prior observations (Gamma prior), var0 = prior sample variance

The second and third elements of the list are the parameters k and v, respectively.

N

The planned sample size.

mu0

The null mean value, which could be taken as the standard or current mean.

mu1

The mean value of the new treatment.

var0

The prior sample variance

var

The variance

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)
OneSampleNormal2(list(2,2,1), N = 100, mu0 = 100, mu1 = 95, var0=225, var=225, d = 0,
                        ps = 0.95, pf = 0.05, alternative = "less",
                        seed = 202210, sim = 10)
# with DIP
OneSampleNormal2(list(1,0,0), N = 100, mu0 = 100, mu1 = 95, var0=225, var=225, d = 0,
                        ps = 0.95, pf = 0.05, alternative = "less",
                        seed = 202210, sim = 10)