Description Usage Arguments Details Value Note References See Also Examples
This function uses general equivalence theorem to verify the optimality of a multiple objective optimal design found for the 4-Parameter Hill model and the 4-parameter logistic model. For more details, See Hyun and Wong (2015).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | sensmultiple(
dose,
w,
minDose,
maxDose,
inipars,
lambda,
delta,
Hill_par = TRUE,
sens.control = list(),
calculate_criterion = TRUE,
plot_sens = TRUE,
tol = sqrt(.Machine$double.xmin),
silent = FALSE
)
|
dose |
A vector of design points. It is either dose values or logarithm of dose values when |
w |
A vector of design weights. |
minDose |
Minimum dose D. For the 4-parameter logistic model, i.e. when |
maxDose |
Maximum dose D. For the 4-parameter logistic model, i.e. when |
inipars |
A vector of initial estimates for the vector of parameters (a, b, c, d).
For the 4-parameter logistic model, i.e. when |
lambda |
A vector of relative importance of each of the three criteria, i.e. λ = (λ_1, λ_2, λ_3). Here 0 < λ_i < 1 and s ∑ λ_i = 1. |
delta |
Predetermined meaningful value of the minimum effective dose MED. When δ < 0 , then θ_2 > 0 or when δ > 0, then θ_2 < 0. |
Hill_par |
Hill model parameterization? Defaults to |
sens.control |
Control Parameters for Calculating the ELB. For details, see |
calculate_criterion |
Calculate the criterion? Defaults to |
plot_sens |
Plot the sensitivity (derivative) function? Defaults to |
tol |
Tolerance for finding the general inverse of the Fisher information matrix. Defaults to |
silent |
Do not print anything? Defaults to |
ELB is a measure of proximity of a design to the optimal design without knowing the latter. Given a design, let ε be the global maximum of the sensitivity (derivative) function over x belong to χ. ELB is given by
ELB = p/(p + ε),
where p is the number of model parameters. Obviously,
calculating ELB requires finding ε and
another optimization problem to be solved.
The tuning parameters of this optimization can be regulated via the argument sens.minimax.control
.
See, for more details, Masoudi et al. (2017).
an object of class sensminimax
that is a list with the following elements:
type
Argument type
that is required for print methods.
optima
A matrix
that stores all the local optima over the parameter space.
The cost (criterion) values are stored in a column named Criterion_Value
.
The last column (Answering_Set
)
shows if the optimum belongs to the answering set (1) or not (0). See 'Details' of sens.minimax.control
.
Only applicable for minimax or standardized maximin designs.
mu
Probability measure on the answering set.
Corresponds to the rows of optima
for which the associated row in column Answering_Set
is equal to 1.
Only applicable for minimax or standardized maximin designs.
max_deriv
Global maximum of the sensitivity (derivative) function (ε in 'Details').
ELB
D-efficiency lower bound. Can not be larger than 1. If negative, see 'Note' in sensminimax
or sens.minimax.control
.
merge_tol
Merging tolerance to create the answering set from the set of all local optima. See 'Details' in sens.minimax.control
.
Only applicable for minimax or standardized maximin designs.
crtval
Criterion value. Compare it with the column Crtiterion_Value
in optima
for minimax and standardized maximin designs.
time
Used CPU time (rough approximation).
DO NOT use this function to verify c-optimal designs for estimating 'MED' or 'ED50' (verifying single objective optimal designs) because the results may be unstable.
The reason is that for the c-optimal criterion the generalized inverse of the Fisher information matrix is not stable and depends
on the tolerance value (tol
).
Theoretically, ELB can not be larger than 1. But if so, it may have one of the following reasons:
max_deriv
is not a GLOBAL maximum. Please increase the value of the parameter maxeval
in sens.minimax.control
to find the global maximum.
The sensitivity function is shifted below the y-axis because
the number of model parameters has not been specified correctly (less value given).
Please specify the correct number of model parameters via argument npar
.
Hyun, S. W., and Wong, W. K. (2015). Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels. The international journal of biostatistics, 11(2), 253-271.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | #################################################################
# Verifying optimality of a design for the 4-parameter Hill model
#################################################################
## initial estiamtes for the parameters of the Hill model
a <- 0.008949 # ED50
b <- -1.79 # Hill constant
c <- 0.137 # lower limit
d <- 1.7 # upper limit
# D belongs to c(.001, 1000) ## dose in mg
## Hill parameters are c(a, b, c, d)
# dose, minDose and maxDose vector in mg scale
sensmultiple (dose = c(0.001, 0.009426562, 0.01973041, 999.9974),
w = c(0.4806477, 0.40815, 0.06114173, 0.05006055),
minDose = .001, maxDose = 1000,
Hill_par = TRUE,
inipars = c(a, b, c, d),
lambda = c(0.05, 0.05, .90),
delta = -1)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.