VNM (version 7.1)

Deff: Checking D-efficiency for estimating model parameters.

Description

Obtaining D-efficiency for estimating model parameters for a given design under the 4-parameter logistic model. This also can be used to compute the D-efficiency under the 2 or 3-parameter logistic models by setting the parameter values differently.

Usage

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

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.

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 (\(\theta_4\)), p2 is Emax (\(\theta_1\)), p3 is the ED50 (exp(-\(\frac{\theta_3}{\theta_2}\))) and p4 is the slope at the ED50 (-\(\theta_2\)). 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. 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 select the initial design to search D-optimal design for estimating model parameters. 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.

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

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.)

Hyun, S. W., Wong, W.K. Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels. (International Journal of Biostatistics, 11, 253-271, 2015)

Examples

# NOT RUN {
	##The given design
	dose=c(-6.91,-4.89,-4.18,6.91)
	weight=c(.344,.323,.162,.171)
	
	##Model parameter values for the 4PL
	par.4PL=c(0.137,1.563,.00895,-1.790)
	
	##Check D-efficiency of the given design and its verification plot
	Res.D=Deff(weight, P=par.4PL, dose, LB=log(.001), UB=log(1000))
	summary(Res.D)
	plot(Res.D)
# }