VNM (version 1.0)

Deff: D-efficiency for estimating model parameters.

Description

Obtaining D-efficiency for estimating model parameters for a given design under the 4-parameter logistic model. The 4-parameter logistic model is used to describe the dose-response curve: Y=t1/(1+exp(t2*X+t3))+t4+e, where e~N(0,sigma^2); X=log(dose); t1=the minimum effect-the maximum effect; t2=the slope; t3=log(ED50)^(-t2); and t4=the maximum effect.

Usage

Deff(weight,T,dose,nit,LB,UB)

Arguments

weight

A numeric vector. Weights for a given design. The weights represent the proportional allocations of subjects to the dose levels in a given design.

T

A numeric vector. Predetermined parameter values for the 4-parameter logistic model. T=c(t1,t2,t3,t4).

dose

A vector. K dose levels for a given design.

nit

Numeric. The number of iterations to set an initial design to search D-optimal design for estimating model parameters. Default is 1 and needed to be increased (for example, nit=10 or 30 or 50) if the searched D-optimal design is not a true optimal. It can

LB

Numeric. Predetermined lower bound of the dose range for the log dose.

UB

Numeric. Predetermined upper bound of the dose range for the log dose.

Value

• 1. D-optimal design for estimating model parameters; 2. A verification plot of the D-optimal design by the General Equivalence Theorem; 3. D-efficiency for estimating model parameters for a given design.

References

Seung Won Hyun, Weng Kee Wong, and Yarong Yang (2013), Multiple Objective Optimal Designs to Study the Interesting Features in a Dose-Response Relationship, forthcoming.

Examples

T1<-c(-1.563,-1.790,-8.442,1.700)
  dose1<-c(-4,-2.23,-1.14,1.00)
  weight1<-c(0.309,0.254,0.290)
  weight1<-c(weight1,1-sum(weight1))
  Deff(weight=weight1,T=T1,dose=dose1,nit=10,LB=-4,UB=1)