minimize: Find optimal two-stage design by constraint minimization

In adoptr: Adaptive Optimal Two-Stage Designs

Find optimal two-stage design by constraint minimization

Description

minimize takes an unconditional score and a constraint set (or no constraint) and solves the corresponding minimization problem using nloptr (using COBYLA by default). An initial design has to be defined. It is also possible to define lower- and upper-boundary designs. If this is not done, the boundaries are determined automatically heuristically.

Usage

minimize(
  objective,
  subject_to,
  initial_design,
  lower_boundary_design = get_lower_boundary_design(initial_design),
  upper_boundary_design = get_upper_boundary_design(initial_design),
  c2_decreasing = FALSE,
  check_constraints = TRUE,
  opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-05, maxeval = 10000),
  ...
)

Arguments

objective	objective function
subject_to	constraint collection
initial_design	initial guess (x0 for nloptr)
lower_boundary_design	design specifying the lower boundary.
upper_boundary_design	design specifying the upper boundary
c2_decreasing	if TRUE, the c2_pivots are forced to be monotonically decreasing
check_constraints	if TRUE, it is checked if constrains are fulfilled
opts	options list passed to nloptr
...	further optional arguments passed to nloptr

Value

a list with elements:

design	The resulting optimal design
nloptr_return	Output of the corresponding nloptr call
call_args	The arguments given to the optimization call

Examples

# Define Type one error rate
toer <- Power(Normal(), PointMassPrior(0.0, 1))

# Define Power at delta = 0.4
pow <- Power(Normal(), PointMassPrior(0.4, 1))

# Define expected sample size at delta = 0.4
ess <- ExpectedSampleSize(Normal(), PointMassPrior(0.4, 1))

# Compute design minimizing ess subject to power and toer constraints

minimize(

   ess,

   subject_to(
      toer <= 0.025,
      pow  >= 0.9
   ),

   initial_design = TwoStageDesign(50, .0, 2.0, 60.0, 2.0, 5L)

)

adoptr documentation built on Oct. 3, 2024, 1:08 a.m.