drugdevelopR (version 1.0.2)

EPsProg_bias_binary: Expected probability of a successful program for bias adjustment programs with binary 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_binary_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_binary_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_binary_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_binary_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_binary_L(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)
EPsProg_binary_L2(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)
EPsProg_binary_R(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)
EPsProg_binary_R2(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)

Value

The output of the functions EPsProg_binary_L(), EPsProg_binary_L2(), EPsProg_binary_R() and EPsProg_binary_R2() is the expected probability of a successful program.

Arguments

RRgo

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

p0

assumed true rate of control group

w

weight for mixture prior distribution

p11

assumed true rate of treatment group

p12

assumed true rate of treatment group

in1

amount of information for p11 in terms of sample size

in2

amount of information for p12 in terms of sample size

fixed

choose if true treatment effects are fixed or random, if TRUE p11 is used as fixed effect

Examples

res <- EPsProg_binary_L(RRgo = 0.8, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)
          res <- EPsProg_binary_L2(RRgo = 0.8, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)
          res <- EPsProg_binary_R(RRgo = 0.8, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)
          res <- EPsProg_binary_R2(RRgo = 0.8, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)