EPsProg_bias_normal: Expected probability of a successful program for bias...

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

Expected probability of a successful program for bias adjustment programs with normally distributed outcomes

Description

To discount for overoptimistic results in phase II when calculating the optimal sample size in phase III, it is necessary to use the following functions, which each describe a specific case:

• EPsProg_normal_L(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval), however the go-decision is not affected by the bias adjustment

• EPsProg_normal_L2(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval) when the go-decision is also affected by the bias adjustment

• EPsProg_normal_R(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• EPsProg_normal_R2(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor) when the go-decision is also affected by the bias adjustment

Usage

EPsProg_normal_L(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

EPsProg_normal_L2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

EPsProg_normal_R(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

EPsProg_normal_R2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

Arguments

kappa	threshold value for the go/no-go decision rule
n2	total sample size for phase II; must be even number
Adj	adjustment parameter
alpha	significance level
beta	1-beta power for calculation of sample size for phase III
step1	lower boundary for effect size
step2	upper boundary for effect size
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
fixed	choose if true treatment effects are fixed or random, if TRUE Delta1 is used as fixed effect

Value

The output of the functions EPsProg_normal_L(), EPsProg_normal_L2(), EPsProg_normal_R() and EPsProg_normal_R2() is the expected probability of a successful program.

Examples

res <- EPsProg_normal_L(kappa = 0.1, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)
          res <- EPsProg_normal_L2(kappa = 0.1, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)
          res <- EPsProg_normal_R(kappa = 0.1, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)
          res <- EPsProg_normal_R2(kappa = 0.1, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)

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