VNM (version 2.0)

MOPT: Identify multiple-objective optimal designs for estimating model parameters, ED50, 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.

Usage

MOPT(LB, UB, P, lambda, delta, r, grid, epsilon, epsilon_w)

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.

P

A Numeric vector. Solicited information on nominal values for the vector. p=(p1, p2, p3, p4), where p1 is the lower limit of the response, p2 is Emax, p3 is the ED50 and p4 is the slope at the ED50.

lambda

A numeric vector. User select weights. lambda=c(q1, q2), where q1, q2 represent weights for estimating model parameter and estimating the ED50 respectively. They are non-negative and q1+q2

delta

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

r

Numeric. The number fo iteritions to set an initial design to search the multiple-objective optimal design. Default is 10 and needed to be increased (for example, r=30 or 50) if the searched multiple-objective optimal design is not a true optimal. It can

grid

Numeric. The grid density to discretize the predetermined dose interval. Default is 0.01.

epsilon

Numeric. Stopping criterion for the algorithm to search the multiple-objective optimal design. Default is 0.001.

epsilon_w

Numeric. Stopping criterion for the Newton Raphson method inside of the algorithm. Default is 10^-6.

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 (2014), VNM: An R Package for Finding Multiple-Objective Optimal Designs for the 4-Parameter Logistic Model, submitted to Journal of Statistical Software. Seung Won Hyun and Weng Kee Wong (2014), Multiple Objective Optimal Designs to Study the Interesting Features in a Dose-Response Relationship, submitted to the International Journal of Biostatistics.

Examples

MOPT(LB=-3, UB=0, P=c(0.137,1.563,0.453,-0.825), lambda=c(1/2,1/3), delta=-1)