# VNM-package: Tools for constructing 3-objective optimal designs In VNM: Finding Multiple-Objective Optimal Designs for the 4-Parameter Logistic Model

## Description

The package contains several functions useful for finding 3-objective optimal designs to estimate the shape of dose-response, the ED50 and the MED for the 4PL model. The package also can be used for the 2PL or the 3PL models.

Below is the 4PL model used in this package:

4-parameter logistic(4PL) model

Y=\frac{θ_1}{1+e^{θ_2{x}+θ_3}}+θ_4+\varepsilon, \varepsilon \sim N(0,σ^{2})

Here x is the dose in log scale, θ_1 is the Emax, θ_2 is the negative of the Hill's coefficient in the Hill's model that controls the rate of change in the response, θ_3 is -θ_2 log(ED50) and θ_4 is the lower limit of the response when θ_1 >0, θ_2 \neq 0, and -∞ < ED50 < ∞. The 4PL model becomes the 2PL model when θ_1 = 1 and θ_4 = 0 or the 3PL model when θ_4 = 0.

## Details

 Package: VNM Type: Package Version: 1.0 Date: 2014-05-15 License: GPL-2

The main functions are:

MOPT: Finds and verifies that the generated design is the multiple-objective optimal design.

Deff: Computes D-efficiency of the generated design for estimating the model parameters.

ceff1: Computes c-efficiency of the generated design for estimating the ED50.

ceff2: Computes c-efficiency of the generated design for estimating the MED.

S.Weight: Computes the optimal weights for the fixed design points.

## Author(s)

Seung Won Hyun, Weng Kee Wong, and Yarong Yang

## References

Hyun, S.W., Wong, W.K, Yang, Y. VNM: An R Package for Finding Multiple-Objective Optimal Designs for the 4-Parameter Logistic Model. (Conditionally accepted for publication, Journal of Statistical Software)

Hyun, S. W., Wong, W.K. Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels. (International Journal of Biostatistics, 11, 253-271, 2015)

## Examples

 1 2 3 4 5 6 7 8 9 ##Find the 3-objective optimal design for the 4PL model result=MOPT(LB=log(.001), UB=log(1000), P=c(0.137,1.563,.00895,-1.790),lambda=c(1/3,1/3), delta=-1) ##Generated the 3-objective optimal design Res.D=summary(result) ##Verification plot of the generated design plot(result) 

### Example output

Computing maximum value of the sensitvity function...
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Obtained multiple-objective optimal design:
X-selected dose levels; W-corresponding proportions of subjects
[,1]      [,2]       [,3]       [,4]        [,5]      [,6]
X -6.9100000 -4.920000 -4.8400000 -4.2200000 -4.12000000 6.9000000
W  0.3446819  0.201239  0.1172388  0.1364176  0.02912984 0.1712929


VNM documentation built on July 4, 2017, 9:24 a.m.