Ess_multiple_normal: Expected sample size for phase III for multiple endpoints with normally distributed outcomes

Description

Given phase II results are promising enough to get the "go"-decision to go to phase III this function now calculates the expected sample size for phase III. The results of this function are necessary for calculating the utility of the program, which is then in a further step maximized by the optimal_multiple_normal() function

Usage

Ess_multiple_normal(
  kappa,
  n2,
  alpha,
  beta,
  Delta1,
  Delta2,
  in1,
  in2,
  sigma1,
  sigma2,
  fixed,
  rho,
  rsamp
)

Value

the output of the function Ess_multiple_normal is the expected number of participants in phase III

Arguments

kappa: threshold value for the go/no-go decision rule; vector for both endpoints
n2: total sample size for phase II; must be even number
alpha: significance level
beta: 1-beta power for calculation of sample size for phase III
Delta1: assumed true treatment effect given as difference in means for endpoint 1
Delta2: assumed true treatment effect given as difference in means for endpoint 2
in1: amount of information for Delta1 in terms of sample size
in2: amount of information for Delta2 in terms of sample size
sigma1: standard deviation of first endpoint
sigma2: standard deviation of second endpoint
fixed: choose if true treatment effects are fixed or random, if TRUE Delta1 is used as fixed effect
rho: correlation between the two endpoints
rsamp: sample data set for Monte Carlo integration