ceff2: Checking c-efficiency for estimating the MED.

In VNM: Finding Multiple-Objective Optimal Designs for the 4-Parameter Logistic Model

Description

Obtaining c-efficiency for estimating the minimum effective dose MED for a given design under the 4-parameter logistic model. MED is the dose that produces a mean response of δ unites better than the minimum dose. This also can be used to compute the c-efficiency for MED under the 2 or 3-parameter logistic models by setting the parameter values differently.

Usage

ceff2(weight,P,dose,LB,UB,delta,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 (θ_4), p2 is Emax (θ_1), p3 is the ED50 (exp(-\frac{θ_3}{θ_2})) and p4 is the slope at the ED50 (-θ_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.
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 of iteritions to select the initial design to search c-optimal design for estimating the MED. Default is 10 and needed to be increased (for example, r = 30 or 50) if the searched c-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 c-optimal design for the MED. 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.

Author(s)

Seung Won Hyun, Weng Kee Wong, and Yarong Yang

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

	##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)
	
	##delta to define MED
	delta=-1
	
	##Check c-efficiency of the given design for estimating the MED and its verification plot 
	Res.c2=ceff2(weight, P=par.4PL, dose, LB=log(.001), UB=log(1000), delta, r=30)
	summary(Res.c2)
	plot(Res.c2)

Example output

c-optimal design for MED: 
        [,1]       [,2]       [,3]       [,4]
X -6.9100000 -4.6300000 -4.6000000 1.81000000
W  0.4999989  0.1098072  0.3438358 0.04635802
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 
c-efficiency for MED: 0.7536244 

VNM documentation built on May 1, 2019, 9:13 p.m.