VNM (version 4.1)

Deff: D-efficiency for 4-parameter logistic model.

Description

Obtaining D-efficiency for estimating model parameters for a given design under the 4-parameter logistic model.

Usage

Deff(weight,P,dose,LB,UB,r,grid,epsilon,epsilon_w)

Arguments

weight

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

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. For the 4-parameter logistic model, a user needs to specify all 4 nominal values in P: P=(p1, p2, p3, p4). For the 3-parameter logistic model, a user needs to specify only the 3 nominal values, Emax, the ED50, and the slope: P=(p2 ,p3, p4). For the 2-parameter logistic model, a user needs to specify only the 2 nominal values, the ED50 and the slope: P=(p3, p4).

dose

A vector. K dose levels for a given design.

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.

r

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

grid

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

epsilon

Numeric. Stopping criterion for the algorithm to search D-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

An object of class OPT.

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 (2015), Multiple Objective Optimal Designs to Study the Interesting Features in a Dose-Response Relationship, accepted by the International Journal of Biostatistics.

Examples

  Deff(weight=c(0.314,0.275,0.307,0.104),P=c(60,340,107.14,1),
dose=c(-6.91,2.99,4.96,6.21),LB=log(.001),UB=log(500),r=30)