VNM (version 1.0)

MOPT: Identify multiple-objective optimal designs for estimating 3 objectives (model parameters, the ED50, the MED).

Description

Identify multiple-objective optimal design (i.e., optimal dose levels and corresponding optimal weights) that maximizes the efficiencies for estimating model parameters, the ED50, and the MED 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

MOPT(LB, UB, nit, T, q1, q2, dt)

Arguments

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.

nit

Numeric. The number of iterations to set an initial design to search multiple-objective optimal designs for estimating the 3 objectives. Default is 1 and needed to be increased (for example, nit=10 or 30 or 50) if the searched multiple-objective optimal d

T

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

q1

Numeric. A weight for estimating model parameters. The weight represents relative importance of estimating the model parameters compared to the other two objectives.

q2

Numeric. A weight for estimating the ED50. The weight represents relative importance of estimating the ED50 compared to the other two objectives.

dt

Numeric. Predetermined clinically significant effect to define the MED. The MED is the dose producing the mean response of dt units better than the minimum dose.

Value

• 1. A matrix showing the multiple-objective optimal design for estimating model parameters, the ED50, and the MED. The first row of the matrix represents optimal dose levels to be used and the second row of the matrix represents the optimal weights for the corresponding dose levels. The weight represents the proportional allocation of subjects to the corresponding dose level; 2. A verification plot of the multiple-objective optimal design by the General Equivalence Theorem.

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

LB1=-3
   UB1=0
   nit1<-10
   T1<-c(-1.563,-0.825,-0.653,1.700)
   q11<-1/2
   q22<-1/3
   dt1<--1
   MOPT(LB=LB1, UB=UB1, nit=nit1, T=T1, q1=q11, q2=q22, dt=dt1)