EDpeff {Opt5PL}

Obtaining c-efficiency for estimating the EDp under the 5-parameter logistic model.

Description

Obtaining c-efficiency for estimating the EDp for a given design under the 5-parameter logistic models. For the output, the function shows three things: 1. the obtained c-optimal design for the given parameter values; 2. the c-efficiency of the given design; and 3. the number of subjects required for the given design in order to provide the same performance as the c-optimal design does.

Usage

EDpeff(weight,dose,P,EDp,LB,UB,r,epsilon,grid,N_dose)

Arguments

weight

A numeric vector. The first K-1 weights for a given design with K design points(K dose levels). The weights represent the proportional allocations of subjects to the dose levels in a given design.

dose

A numeric vector. K dose levels for a given design.

P

A numeric vector. Solicited information on nominal values for the vector for the 5PL model. P=(p1, p2, p3, p4, p5), where p1 is the upper limit of the response, p2 is the slope that control the stiffness of the response curve, p3 is the position of the transition region in dose, p4 is the lower limit of the response, and p5 is the asymmetric factor.

EDp

Numeric. An user select value to define the EDp. For example, EDp=.05 to define the ED50.

LB

Numeric. Predetermined lower bound of the dose range for the original dose level.

UB

Numeric. Predetermined lower bound of the dose range for the original dose level.

r

Numeric. The number of iterations to set an initial design to search the c-optimal design for the EDp in order to compute the efficiency. Default is 30 and needed to be increased (for example, r=50) if the searched the c-optimal design is not a true optimal. It can be verified by the verification plot.

epsilon

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

grid

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

N_dose

Set to TRUE if the original dose levels take negative values. Set to FALSE if the original dose levels take positive values. Default is FALSE

Author(s)

Seung Won Hyun, Weng Kee Wong, and Yarong Yang

References

Hyun, S. W., Wong, W.K., Yang, Y. Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays. (submitted to Statistical Methods in Medical Research)

Hyun, S.W., Wong, W.K, Yang, Y. VNM: An R Package for Finding Multiple-Objective Optimal Designs for the 4-Parameter Logistic Model. (Journal of Statistical Software, 83, 1-19, 2018, doi:10.18637/jss.v083.i05.)

Examples

##Under the 5PL model with the parameter values
##T5=(30000,0.5,800,0.5,2) and the dose range [1.95,32000],
##find the c-efficiency of the broad range design.

##The broad range design
dose=c(1.95,7.8,31.25,125,500,2000,8000,32000)
dlength=length(dose)
weight=rep(1/dlength,dlength-1)

##Parameter values for the 5PL model
T5=c(30000,0.5,800,0.5,2)

##Compute the c-efficiency of the broad range design
EDpeff(weight,dose,P=T5,EDp=.5,LB=1.95,UB=32000,grid=.01)