The function performs a linearization of the model with respect to the residual variability. Derivative of model w.r.t. eps evaluated at eps=0 and b=b_ind.

gradf_eps(model_switch, xt_ind, x, a, bpop, b_ind, bocc_ind, num_eps, poped.db)

Arguments

model_switch

A matrix that is the same size as xt, specifying which model each sample belongs to.

xt_ind

A vector of the individual/group sample times

x

A matrix for the discrete design variables. Each row is a group.

a

A matrix of covariates. Each row is a group.

bpop

The fixed effects parameter values. Supplied as a vector.

b_ind

vector of individual realization of the BSV terms b

bocc_ind

Vector of individual realizations of the BOV terms bocc

num_eps

The number of eps() in the model.

poped.db

A PopED database.

Value

A matrix of size (samples per individual x number of epsilons)

See also

Examples

library(PopED) ############# START ################# ## Create PopED database ## (warfarin model for optimization) ##################################### ## Warfarin example from software comparison in: ## Nyberg et al., "Methods and software tools for design evaluation ## for population pharmacokinetics-pharmacodynamics studies", ## Br. J. Clin. Pharm., 2014. ## Optimization using an additive + proportional reidual error ## to avoid sample times at very low concentrations (time 0 or very late samples). ## find the parameters that are needed to define from the structural model ff.PK.1.comp.oral.sd.CL
#> function (model_switch, xt, parameters, poped.db) #> { #> with(as.list(parameters), { #> y = xt #> y = (DOSE * Favail * KA/(V * (KA - CL/V))) * (exp(-CL/V * #> xt) - exp(-KA * xt)) #> return(list(y = y, poped.db = poped.db)) #> }) #> } #> <bytecode: 0x7fe20a979808> #> <environment: namespace:PopED>
## -- parameter definition function ## -- names match parameters in function ff sfg <- function(x,a,bpop,b,bocc){ parameters=c(CL=bpop[1]*exp(b[1]), V=bpop[2]*exp(b[2]), KA=bpop[3]*exp(b[3]), Favail=bpop[4], DOSE=a[1]) return(parameters) } ## -- Define initial design and design space poped.db <- create.poped.database(ff_fun=ff.PK.1.comp.oral.sd.CL, fg_fun=sfg, fError_fun=feps.add.prop, bpop=c(CL=0.15, V=8, KA=1.0, Favail=1), notfixed_bpop=c(1,1,1,0), d=c(CL=0.07, V=0.02, KA=0.6), sigma=c(prop=0.01,add=0.25), groupsize=32, xt=c( 0.5,1,2,6,24,36,72,120), minxt=0.01, maxxt=120, a=c(DOSE=70), mina=c(DOSE=0.01), maxa=c(DOSE=100)) ############# END ################### ## Create PopED database ## (warfarin model for optimization) ##################################### #for the FO approximation ind=1 gradf_eps(model_switch=t(poped.db$design$model_switch[ind,,drop=FALSE]), xt_ind=t(poped.db$design$xt[ind,,drop=FALSE]), x=zeros(0,1), a=t(poped.db$design$a[ind,,drop=FALSE]), bpop=poped.db$parameters$bpop[,2,drop=FALSE], b_ind=zeros(poped.db$parameters$NumRanEff,1), bocc_ind=zeros(poped.db$parameters$NumDocc,1), num_eps=size(poped.db$parameters$sigma,1), poped.db)["dfeps_de0"]
#> $dfeps_de0 #> [,1] [,2] #> [1,] 3.4254357 1 #> [2,] 5.4711041 1 #> [3,] 7.3821834 1 #> [4,] 7.9462805 1 #> [5,] 5.6858561 1 #> [6,] 4.5402483 1 #> [7,] 2.3116966 1 #> [8,] 0.9398657 1 #>