optbound {seqdesphII} | R Documentation

## Find optimal boundaries

### Description

This function takes as an input argument the results of a forward simulation as returned by "read.forwsim" and finds the optimal boundaries. It is possible to constrain the optimization to rules satisfying type I and II error rates, and to obtain an smoothed estimate of the expected utility before optimizing.

### Usage

    optbound(forwsim, errImax, errIImax, util = "u", max = TRUE, avedraws = TRUE, smooth = FALSE, span = 0.75)

### Arguments

`forwsim` | List containing forward simulation results as returned by "read.forwsim".
`errImax` | Upper bound of type I error probability. Only boundaries satisfying it will be included in the optimization
`errIImax` | Same as "errImax" but for type II error.
`util` | Name of the element in "forwsim" containing the expected utility that is to be optimized.
`max` | If TRUE the goal is to maximize the utility, otherwise it is to minimize it.
`avedraws` | When set to TRUE, multiple optimal solutions will be averaged to give a single solution.
`smooth` | Should the utility surface be loess smoothed previous to optimization?
`span` | The parameter alpha which controls the degree of smoothing as defined in 'loess'.

### Details

When performing constrained optimization it is possible that no rules satisfy the constraints. If no rules satisfy the type II error constraint, the rule with the lowest type II error rate is selected amongst those that satisfy the type I error constraint. If no rules satisfy the type I II error constraint either, the rule with the lowest type I error is selected.

### Value

List with the following components:

`b` | Values of b0,b1,b2 maximizing the expected utility.
`u` | Estimated expected utility at the optimum.
`err` | Matrix with estimated type I & II error probabilities at the optimum in 1st and 2nd columns, respectively.
`dt` | Mean number of patients tested with each treatment at the optimum.
`mse` | Estimated mean square error in parameter estimation at the optimum.
`span` | If smooth set to TRUE, value of the smoothing parameter.

### Author(s)

David Rossell

### References

Rossell D, Mueller P, Rosner G. Screening Designs for Drug Development.

### See Also

read.forwsim

### Examples

    dir <- 'C:/R/R-2.2.1/library/forwsim/data'                                                 #read forward simulation output
    sim1 <- read.forwsim(dir)

    opt1 <- optbound(sim1,errImax=1,errIImax=1,util='u',smooth=FALSE)                          #unconstrained optimization
    opt2 <- optbound(sim1,errImax=.05,errIImax=.2,util='u',smooth=FALSE)                       #constrained optimization

    opt3 <- optbound(sim1,errImax=1,errIImax=1,util='u',smooth=TRUE,span=seq(.02,.15,.01))     #optimize smooth surface
    opt4 <- optbound(sim1,errImax=.1,errIImax=.2,util='u',smooth=TRUE,span=seq(.02,.15,.01))   #constrained optimization of smooth surface

    opt5 <- optbound(sim1,errImax=.05,errIImax=.15,util='dt',max=FALSE,smooth=FALSE)           #minimize E(sample size) s.t. type I&II error constraints

[Package seqdesphII version 0.0 Index]