R: Compute the expected parameter relative standard errors

get_rse {PopED}

R Documentation

Compute the expected parameter relative standard errors

Description

This function computes the expected relative standard errors of a model given a design and a previously computed FIM.

Usage

get_rse(
  fim,
  poped.db,
  bpop = poped.db$parameters$bpop[, 2],
  d = poped.db$parameters$d[, 2],
  docc = poped.db$parameters$docc,
  sigma = poped.db$parameters$sigma,
  use_percent = TRUE,
  fim.calc.type = poped.db$settings$iFIMCalculationType,
  prior_fim = poped.db$settings$prior_fim,
  ...
)

Arguments

`fim`	A Fisher Information Matrix (FIM).
`poped.db`	A PopED database.
`bpop`	A vector containing the values of the fixed effects used to compute the `fim`.
`d`	A vector containing the values of the diagonals of the between subject variability matrix.
`docc`	Matrix defining the IOV, the IOV variances and the IOV distribution as for d and bpop.
`sigma`	Matrix defining the variances can covariances of the residual variability terms of the model. can also just supply the diagonal parameter values (variances) as a `c()`.
`use_percent`	Should RSE be reported as percent?
`fim.calc.type`	The method used for calculating the FIM. Potential values: 0 = Full FIM. No assumption that fixed and random effects are uncorrelated. 1 = Reduced FIM. Assume that there is no correlation in the FIM between the fixed and random effects, and set these elements in the FIM to zero. 2 = weighted models (placeholder). 3 = Not currently used. 4 = Reduced FIM and computing all derivatives with respect to the standard deviation of the residual unexplained variation (sqrt(SIGMA) in NONMEM). This matches what is done in PFIM, and assumes that the standard deviation of the residual unexplained variation is the estimated parameter (NOTE: NONMEM estimates the variance of the residual unexplained variation by default). 5 = Full FIM parameterized with A,B,C matrices & derivative of variance. 6 = Calculate one model switch at a time, good for large matrices. 7 = Reduced FIM parameterized with A,B,C matrices & derivative of variance.
`prior_fim`	A prior FIM to be added to the `fim`. Should be the same size as the `fim`.
`...`	Additional arguments passed to `inv`.

Value

A named list of RSE values. If the estimated parameter is assumed to be zero then for that parameter the standard error is returned.

Examples

## 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. 

library(PopED)

## find the parameters that are needed to define from the structural model
ff.PK.1.comp.oral.md.CL

## -- 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.prop,
                                  bpop=c(CL=0.15, V=8, KA=1.0, Favail=1), 
                                  # notfixed_bpop=c(1,1,1,0),
                                  notfixed_bpop=c(CL=1,V=1,KA=1,Favail=0),
                                  d=c(CL=0.07, V=0.02, KA=0.6), 
                                  sigma=0.01,
                                  groupsize=32,
                                  xt=c( 0.5,1,2,6,24,36,72,120),
                                  minxt=0,
                                  maxxt=120,
                                  a=70)


## evaluate initial design with the reduced FIM
FIM.1 <- evaluate.fim(poped.db) 
FIM.1
det(FIM.1)
det(FIM.1)^(1/7)
get_rse(FIM.1,poped.db)

## evaluate initial design with the full FIM
FIM.0 <- evaluate.fim(poped.db,fim.calc.type=0) 
FIM.0
det(FIM.0)
det(FIM.0)^(1/7)
get_rse(FIM.0,poped.db)

## evaluate initial design with the reduced FIM 
## computing all derivatives with respect to the 
## standard deviation of the residual unexplained variation 
FIM.4 <- evaluate.fim(poped.db,fim.calc.type=4) 
FIM.4
det(FIM.4)
get_rse(FIM.4,poped.db,fim.calc.type=4)

## evaluate initial design with the full FIM with A,B,C matricies
## should give same answer as fim.calc.type=0
FIM.5 <- evaluate.fim(poped.db,fim.calc.type=5) 
FIM.5
det(FIM.5)
get_rse(FIM.5,poped.db,fim.calc.type=5)

## evaluate initial design with the reduced FIM with 
## A,B,C matricies and derivative of variance
## should give same answer as fim.calc.type=1 (default)
FIM.7 <- evaluate.fim(poped.db,fim.calc.type=7) 
FIM.7
det(FIM.7)
get_rse(FIM.7,poped.db,fim.calc.type=7)

## evaluate FIM and rse with prior FIM.1
poped.db.prior = create.poped.database(poped.db, prior_fim = FIM.1)
FIM.1.prior <- evaluate.fim(poped.db.prior)
all.equal(FIM.1.prior,FIM.1) # the FIM is only computed from the design in the poped.db
get_rse(FIM.1.prior,poped.db.prior) # the RSE is computed with the prior information