utility_multiple_tte: Utility function for multiple endpoints in a time-to-event-setting

Description

The utility function calculates the expected utility of our drug development program and is given as gains minus costs and depends on the parameters and the expected probability of a successful program. The utility is in a further step maximized by the optimal_multiple_tte() function. Note, that for calculating the utility of the program, two different benefit triples are necessary:

one triple for the case that the more important endpoint overall survival (OS) shows a significant positive treatment effect
one triple when only the endpoint progression-free survival (PFS) shows a significant positive treatment effect

Usage

utility_multiple_tte(
  n2,
  HRgo,
  alpha,
  beta,
  hr1,
  hr2,
  id1,
  id2,
  c2,
  c02,
  c3,
  c03,
  K,
  N,
  S,
  steps1,
  stepm1,
  stepl1,
  b11,
  b21,
  b31,
  b12,
  b22,
  b32,
  fixed,
  rho,
  rsamp
)

Value

The output of the function utility_multiple_tte() is the expected utility of the program.

Arguments

n2: total sample size for phase II; must be even number
HRgo: threshold value for the go/no-go decision rule;
alpha: significance level
beta: 1-beta power for calculation of sample size for phase III
hr1: assumed true treatment effect on HR scale for endpoint OS
hr2: assumed true treatment effect on HR scale for endpoint PFS
id1: amount of information for hr1 in terms of sample size
id2: amount of information for hr2 in terms of sample size
c2: variable per-patient cost for phase II
c02: fixed cost for phase II
c3: variable per-patient cost for phase III
c03: fixed cost for phase III
K: constraint on the costs of the program, default: Inf, e.g. no constraint
N: constraint on the total expected sample size of the program, default: Inf, e.g. no constraint
S: constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint
steps1: lower boundary for effect size category "small" in HR scale, default: 1
stepm1: lower boundary for effect size category "medium" in HR scale = upper boundary for effect size category "small" in HR scale, default: 0.95
stepl1: lower boundary for effect size category "large" in HR scale = upper boundary for effect size category "medium" in HR scale, default: 0.85
b11: expected gain for effect size category "small" if endpoint OS is significant
b21: expected gain for effect size category "medium"if endpoint OS is significant
b31: expected gain for effect size category "large" if endpoint OS is significant
b12: expected gain for effect size category "small" if endpoint OS is not significant
b22: expected gain for effect size category "medium"if endpoint OS is not significant
b32: expected gain for effect size category "large" if endpoint OS is not significant
fixed: choose if true treatment effects are fixed or random, if TRUE hr1 is used as fixed effect
rho: correlation between the two endpoints
rsamp: sample data set for Monte Carlo integration