alpha.split {DesignCTPB}

The optimal design given one set of proportion for each sub-population

Description

First, the function fits a smooth surface given grid values of alpha(that's sig.lv for each sub-population) and the corresponding power values, and we suggest thin plate splines here. Second, we apply a L-BFGS-B optimization method to estimate the optimal power values and the corresponding alpha value on the estimated thin plate spline surface.

Usage

alpha.split(
  r = c(1, 0.5, 0.3),
  N1 = 20480,
  N2 = 10240,
  N3 = 2000,
  E = NULL,
  sig = NULL,
  sd_full = 1/base::sqrt(20),
  delta = NULL,
  delta_linear_bd = c(0.2, 0.8),
  seed = NULL
)

Arguments

r

vector for the proportion for each sub-population, r_1 is 1, r_i>r_i+1

N1

integer, which is fixed as 10240 in our package

N2

integer, which is fixed as 20480 in our package

N3

integer, the number of grid point for the sig.lv, which should be the multiples of 5, because we apply 5 stream parallel

E

integer, the total number of events for the Phase 3 clinical trail, if not specified by user, then an estimation will apply

sig

the vector of standard deviation of each sub-population

sd_full

a numeric number, which denotes the prior information of standard deviation for the harzard reduction if sig is not specified, then sd_full must has an input value to define the standard deviation of the full population

delta

vector,the point estimation of harzard reduction in prior information, if not specified we apply a linear scheme by giving bound to the linear harzard reduction

delta_linear_bd

vector of length 2, specifying the upper bound and lower bound for the harzard reduction; if the delta is not specified for each sub-population, then the linear scheme will apply and the input is a must.

seed

integer, seed for random number generation

Value

list of the optimal results given specific r: optimal alpha split and the corresponding optimal power value

Examples

## Not run: 
#In the example, we apply a linear scheme for the harzard reduction 
alpha.split(r=c(1,0.4,0.1), N3=2000, sd_full=1/sqrt(20),delta_linear_bd = c(0.2,0.8))

## End(Not run)