drugdevelopR (version 1.0.2)

En3_bias_normal: Expected sample size for phase III for bias adjustment programs and 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 functions En3_normal_L(), En3_normal_L2(), En3_normal_R() and En3_normal_R2(). Each function describes a specific case:

• En3_normal_L(): calculates the optimal sample size 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

• En3_normal_L2(): calculates the optimal sample size 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

• En3_normal_R(): calculates the optimal sample size for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• En3_normal_R2(): calculates the optimal sample size 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

En3_normal_L(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)
En3_normal_L2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)
En3_normal_R(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)
En3_normal_R2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

Value

The output of the functions En3_normal_L, En3_normal_L2, En3_normal_R and En3_normal_R2 is the expected number of participants in phase III.

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 is the power for calculation of sample size for phase III

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

Examples

res <- En3_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, fixed = FALSE)
          res <- En3_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, fixed = TRUE)
          res <- En3_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, fixed = FALSE)
          res <- En3_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, fixed = FALSE)