VNM (version 7.1)

S.Weight: Identify optimal weights for given dose levels.

Description

Find optimal proportions of subjectives at the given dose levels to estimate the model parameters, the ED50 and the MED simultaneously under the 4-parameter logistiv model. This also can be used to find the optimal weights at the given dose under the 2 or 3-parameter logistic models by setting the parameter values differently.

Usage

S.Weight(X,P,lambda,delta,epsilon_w)

Arguments

X

A numeric vector. Given dose levels to search the optimal weights.

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 logistiv 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).

lambda

A numeric vector. User-selected weights for the first two objectives. 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 <= 1.

delta

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

epsilon_w

Numeric. Stopping criterion for the Newton Raphson method to search the optimal weights for the given dose levels. Default is 10^-6.

Value

An object of class SW.

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 dose levels
	dose=c(-6.91,-4.89,-4.18,6.91)
	
	##Model parameter values for the 4PL
	par.4PL=c(0.137,1.563,.00895,-1.790)
	
	##Find the optimal weights for the given dose levels
	Res.W=S.Weight(dose, par.4PL, lambda=c(1/3,1/3), delta=-1)
	
	##Print the obtained optimal weights, and its verification
    summary(Res.W)
# }