calcCrit: Calculate design criterion for a specified design.

Description

This function calculates the design criterion for a specified design under a specified candidate set of models. For type = MED this is the weighted average of log-variances for the MED under the different models, note that these are only the variances up to a constant which is irrelevant in the optimization. For type = Dopt this is the weighted average of log-determinants of the inverse of the Fisher information. For type = MED&Dopt this an equally weighted mixture of the criterions type = Dopt and type = MED.

Usage

calcCrit(design, fullModels, weights, doses, clinRel, 
         nold = rep(0, length(doses)), n2 = NULL, 
         scal=1.2*max(doses), off=0.1*max(doses),
         type = c("MED", "Dopt", "MED&Dopt"), standDopt = FALSE)

Arguments

design

Numeric vector of allocation weights or matrix for the different doses. The rows of the matrices need to sum to 1. Alternatively also an object of class "design" can be used. Note that there should be at least as many design points availabl

fullModels

List containing all model parameters for the models (can for example be a fullMod object, see the fullMod function for details). When an MED optimal design should be calculated the MED needs to

weights

Vector of model probabilities for the models specified in fullModels.

doses

Doses available

clinRel

Clinical relevance

nold

Vector of sample sizes already allocated to the different doses.

Sample size for next cohort.

scal

Scal parameter for beta model

off

Offset parameter for linlog model

type

Determines which type of design criterion to calculate. "MED&Dopt" uses both optimality criteria with equal weight.

standDopt

Logical determining, whether the D-optimality criterion (specifically the log-determinant) should be standardized by the number of parameters in the model or not (only of interest if type = "Dopt" or type = "MED&Dopt"). This is of interest, when

Value

Value of design criterion

References

Atkinson, A.C., Donev, A.N. and Tobias, R.D. (2007). Optimum Experimental Designs, with SAS, Oxford University Press Dette, H., Bretz, F., Pepelyshev, A. and Pinheiro, J. C. (2008). Optimal Designs for Dose Finding Studies, Journal of the American Statisical Association, 103, 1225--1237

Examples

Run this code

## Example (i) Dette et al. (2008), p. 1228, Table 2, line 5
## calculate optimal design for Emax model
mods <- list(emax = 25)
doses <- c(0, 18.75, 150)
fMod <- fullMod(mods, doses, base=0, maxEff=0.4)
fMod$emax[2] <- 0.6666667
weights <- 1 # just one model
des <- calcOptDesign(fMod, weights, doses, clinRel=0.2) 

## now compare this design to equal allocations on
## 0, 10, 25, 50, 100, 150
doses2 <- c(0, 10, 25, 50, 100, 150)
design2 <- c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6)
crit2 <- calcCrit(design2, fMod, weights, doses2, clinRel=0.2)
## ratio of asymptotic variances (constant cancels)
exp(des$crit-crit2)
## slightly modified design
design3 <- c(0.3, 0.3, 0.2, 0, 0, 0.2)
crit3 <- calcCrit(design3, fMod, weights, doses2, clinRel=0.2)
## ratio of asymptotic variances
exp(des$crit-crit3)


## Example (ii) Dette et al. (2008), p. 1230, Table 5, line 5
## calculate optimal design for beta model
fmods <- list(betaMod = c(0.33, 2.31))
doses <- c(0, 0.49, 25.2, 108.07, 150)
fMod <- fullMod(fmods, doses, base=0, maxEff=0.4, scal=200)
weights <- 1
deswgts <- calcOptDesign(fMod, weights, doses, clinRel=0.1,
                scal=200, control=list(maxit=1000))

## now compare this design to equal allocations on
## 0, 10, 25, 50, 100, 150
doses2 <- c(0, 10, 25, 50, 100, 150)
design2 <- c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6)
crit2 <- calcCrit(design2, fMod, weights, doses2, clinRel=0.1, scal=200)
## ratio of asymptotic variances
exp(deswgts$crit-crit2)

## example with matrix
designs <- rbind(c(0.25,0.5,0.25), c(0.5,0.25,0.25), c(0.34,0.33,0.33))
mods <- list(emax = 25)
doses <- c(0, 18.75, 150)
fMod <- fullMod(mods, doses, base=0, maxEff=1)
weights <- 1
calcCrit(designs, fMod, weights, doses, clinRel = 0.2)