Obtaining c-efficiency for estimating the ED50 for a given design under the 4-parameter logistic model. Here the ED50 is the dose producing a 50 percent response between the estimates of the minimum and maximum of the response. The 4-parameter logistic model is used to describe the dose-response curve: Y=t1/(1+exp(t2*X+t3))+t4+e, where e~N(0,sigma^2); X=log(dose); t1=the minimum effect-the maximum effect; t2=the slope; t3=log(ED50)^(-t2); and t4=the maximum effect.
ceff1(weight,P,dose,LB,UB,r,grid,epsilon,epsilon_w)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.
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).
A vector. K dose levels for a given design.
Numeric. Predetermined lower bound of the dose range for the log dose.
Numeric. Predetermined upper bound of the dose range for the log dose.
Numeric. The number fo iterations to set an initial design to search c-optimal design for estimating the ED50. 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. It can be verified by the verification plot.
Numeric. The grid density to discretize the predetermined dose interval. Default is 0.01.
Numeric. Stopping criterion for the algorithm to search c-optimal design for the ED50. Default is 0.001.
Numeric. Stopping criterion for the Newton Raphson method inside of the algorithm. Default is 10^-6.
An object of class OPT.
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.
ceff1(weight = c(0.330, 0.302, 0.270, 0.098), P = c(22, 16.8, 70, 1),
dose = c(-6.91, 2.22, 3.75, 4.60), LB = log(.001), UB = log(100),r = 30)
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