utility_bias_normal: Utility function for bias adjustment programs with normally...

In Sterniii3/drugdevelopR: Utility-Based Optimal Phase II/III Drug Development Planning

Utility function for bias adjustment programs with normally distributed outcomes.

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_bias_normal() function.

Usage

utility_normal_L(
  n2,
  kappa,
  Adj,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K,
  N,
  S,
  steps1,
  stepm1,
  stepl1,
  b1,
  b2,
  b3,
  fixed
)

utility_normal_L2(
  n2,
  kappa,
  Adj,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K,
  N,
  S,
  steps1,
  stepm1,
  stepl1,
  b1,
  b2,
  b3,
  fixed
)

utility_normal_R(
  n2,
  kappa,
  Adj,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K,
  N,
  S,
  steps1,
  stepm1,
  stepl1,
  b1,
  b2,
  b3,
  fixed
)

utility_normal_R2(
  n2,
  kappa,
  Adj,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K,
  N,
  S,
  steps1,
  stepm1,
  stepl1,
  b1,
  b2,
  b3,
  fixed
)

Arguments

n2	total sample size for phase II; must be even number
kappa	threshold value for the go/no-go decision rule
Adj	adjustment parameter
w	weight for mixture prior distribution
Delta1	assumed true treatment effect for standardized difference in means
Delta2	assumed true treatment effect for standardized difference in means
in1	amount of information for Delta1 in terms of sample size
in2	amount of information for Delta2 in terms of sample size
a	lower boundary for the truncation
b	upper boundary for the truncation
alpha	significance level
beta	1-beta power for calculation of sample size for phase III
c2	variable per-patient cost for phase II
c3	variable per-patient cost for phase III
c02	fixed cost for phase II
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", default: 0
stepm1	lower boundary for effect size category "medium" = upper boundary for effect size category "small" default: 0.5
stepl1	lower boundary for effect size category "large" = upper boundary for effect size category "medium", default: 0.8
b1	expected gain for effect size category "small"
b2	expected gain for effect size category "medium"
b3	expected gain for effect size category "large"
fixed	choose if true treatment effects are fixed or random, if TRUE Delta1 is used as fixed effect

Value

The output of the functions utility_normal_L(), utility_normal_L2(), utility_normal_R() and utility_normal_R2() is the expected utility of the program.

Examples

res <- utility_normal_L(kappa = 0.1, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,
                                 K = Inf, N = Inf, S = -Inf, 
                                 steps1 = 0, stepm1 = 0.5, stepl1 = 0.8,
                                 b1 = 3000, b2 = 8000, b3 = 10000, 
                                 fixed = TRUE)
          res <- utility_normal_L2(kappa = 0.1, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,
                                 K = Inf, N = Inf, S = -Inf, 
                                 steps1 = 0, stepm1 = 0.5, stepl1 = 0.8,
                                 b1 = 3000, b2 = 8000, b3 = 10000, 
                                 fixed = TRUE)
          res <- utility_normal_R(kappa = 0.1, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,
                                 K = Inf, N = Inf, S = -Inf, 
                                 steps1 = 0, stepm1 = 0.5, stepl1 = 0.8,
                                 b1 = 3000, b2 = 8000, b3 = 10000, 
                                 fixed = TRUE)
          res <- utility_normal_R2(kappa = 0.1, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,
                                 K = Inf, N = Inf, S = -Inf, 
                                 steps1 = 0, stepm1 = 0.5, stepl1 = 0.8,
                                 b1 = 3000, b2 = 8000, b3 = 10000, 
                                 fixed = TRUE)

Sterniii3/drugdevelopR documentation built on Jan. 26, 2024, 6:17 a.m.