Nothing
R/func_methods.R
In npde: Normalised prediction distribution errors for nonlinear mixed-effect models
########### Compute Probability of being under the LOQ, for all observations
#' Compute P(y_ij<LOQ) for all observations
#'
#' For each observation in the dataset, computes the probability to be below LOQ
#' using the simulations under the model. This is generally performed automatically.
#'
#'
#' @usage compute.ploq(npdeObject)
#' @param npdeObject an object returned by a call to \code{\link{npde}} or \code{\link{autonpde}}
#' @return an object of class NpdeObject with a component ploq in the ["results"] slot
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @keywords internal
compute.ploq<-function(npdeObject) {
# For each observation, computes the probability of being LOQ under the model
### when the data has different LOQ values, the LOQ is taken to be the smallest LOQ
### p_LOQ is computed as the % of simulated values under the LOQ
if(length(npdeObject["data"]["icens"])==0)
return(npdeObject)
ploq<-c()
ploqfull<-rep(NA,dim(npdeObject["data"]["data"])[1])
tab<-npdeObject["data"]["data"][npdeObject["data"]["not.miss"],] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][npdeObject["data"]["not.miss"],] # corresponding simulated data
yobs<-tab[, npdeObject["data"]["name.response"]]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
if(length(npdeObject["data"]["loq"])>0) {
loq<-npdeObject["data"]["loq"]
if(npdeObject@options$verbose) cat("Computing p(y<LOQ) using LOQ=",loq,"\n")
} else {
yloq<-npdeObject["data"]["data"][npdeObject["data"]["icens"], npdeObject["data"]["name.response"]]
if(length(unique(yloq))==1) {
if(npdeObject@options$verbose) cat("Same LOQ for all missing data, loq=",loq,"\n")
loq<-unique(yloq)
} else {
loq<-min(unique(yloq))
if(npdeObject@options$verbose) cat("Computing p(y<LOQ) for the lowest LOQ, loq=",loq,"\n")
}
npdeObject["data"]["loq"]<-loq
}
for(isuj in unique(npdeObject["data"]["data"][,"index"])) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
tcomp<-apply(matsim,2,"<",loq)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
ploq<-c(ploq,ycal)
}
ploqfull[npdeObject["data"]["not.miss"]]<-ploq
npdeObject["results"]["ploq"]<-ploqfull
#saving pd
invisible(npdeObject)
}
########### Compute pd
#' Internal functions used to compute prediction discrepancies
#'
#' Functions used by \code{npde} and \code{autonpde} to compute prediction
#' discrepancies (not intended for the end-user).
#'
#' These functions are normally not called by the end-user.
#'
#' @usage computepd(npdeObject,...)
#' @param npdeObject an object of class NpdeObject
#' @param \ldots additional options to modify
#' @return an object of class NpdeObject; the results slot will now include prediction discrepancies (pd) as well as model predictions (ypred) obtained as the mean of the simulated data for each observation
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @keywords internal
computepd<-function(npdeObject,...) {
npdeObject@options<-replace.control.options(npdeObject@options,...)
if(npdeObject["options"]$cens.method=="omit" | length(npdeObject["data"]["icens"])==0)
object<-computepd.omit(npdeObject) else {
if(npdeObject["options"]$cens.method=="cdf") {
if(length(npdeObject["results"]["ploq"])==0)
npdeObject<-compute.ploq(npdeObject)
object<-computepd.cdf(npdeObject)
}
if(npdeObject["options"]$cens.method %in% c("ipred","ypred"))
object<-computepd.replace(npdeObject)
if(npdeObject["options"]$cens.method=="fix")
object<-computepd.replace(npdeObject,...)
if(npdeObject["options"]$cens.method=="loq") {
if(length(npdeObject["data"]["loq"])==0)
npdeObject<-compute.ploq(npdeObject)
object<-computepd.replace(npdeObject)
}
}
return(object)
}
# Functions to sort the lines/columns of a matrix
linesort<-function(mat) {
for(i in 1:dim(mat)[1])
mat[i,]<-sort(mat[i,])
return(mat)
}
colsort<-function(mat) {
for(i in 1:dim(mat)[2])
mat[,i]<-sort(mat[,i])
return(mat)
}
computepd.omit<-function(npdeObject) {
# Preparing vectors for the different results
ypredfull<-pdfull<-rep(NaN,dim(npdeObject["data"]["data"])[1])
ycomp<-npdeObject["data"]["data"][,npdeObject["data"]["name.response"]]
# Extracting only non-missing and non-censored data
if(length(npdeObject["data"]["icens"])==0) keep<-npdeObject["data"]["not.miss"] else keep<-(npdeObject["data"]["not.miss"] & npdeObject["data"]["data"][,npdeObject["data"]["name.cens"]]==0)
# missing and censored data = NaN in complete data
ycomp[!keep]<-NaN
tab<-npdeObject["data"]["data"][keep,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][keep,] # corresponding simulated data
yobs<-tab[,npdeObject["data"]["name.response"]]
idobs<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
ysuj<-yobs[idobs==isuj]
# Compute ypred
ypred<-rowMeans(matsim)
ypredall<-c(ypredall,ypred)
# compute pd_ij
tcomp<-apply(matsim,2,"<",ysuj)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
if(npdeObject["options"]$ties) {
ycal[!is.na(ycal) & ycal==0]<-1/(2*nrep)
ycal[!is.na(ycal) & ycal==1]<-1-1/(2*nrep)
} else {
idx<-which(!is.na(ycal) & ycal>0 & ycal<1)
ycal[!is.na(ycal) & ycal==0]<-runif(sum(ycal==0),0,1/nrep)
ycal[!is.na(ycal) & ycal==1]<-runif(sum(ycal==0),1-1/nrep,1)
ycal[idx]<-ycal[idx]+runif(length(idx),0,1/nrep)
}
pd<-c(pd,ycal)
}
pdfull[keep]<-pd
ypredfull[keep]<-ypredall
# Saving results
if(length(npdeObject["results"]["res"])==0) { # create data.frame res
res<-data.frame(ypred=ypredfull,ycomp=ycomp,pd=pdfull)
npdeObject["results"]["res"]<-res
} else { # append to data.frame res
npdeObject["results"]["res"]$ypred<-ypredfull
npdeObject["results"]["res"]$ycomp<-ycomp
npdeObject["results"]["res"]$pd<-pdfull
}
return(npdeObject)
}
computepd.replace<-function(npdeObject,fix=NULL) {
# Preparing vectors for the different results
ypredfull<-pdfull<-rep(NaN,dim(npdeObject["data"]["data"])[1])
ycomp<-npdeObject["data"]["data"][,npdeObject["data"]["name.response"]]
# Extracting only non-missing data
keep<-npdeObject["data"]["not.miss"]
# missing data = NaN in complete data
ycomp[!keep]<-NaN
tab<-npdeObject["data"]["data"][keep,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][keep,] # corresponding simulated data
yobs<-tab[,npdeObject["data"]["name.response"]]
icens<-tab[,npdeObject["data"]["name.cens"]]
idobs<-tab[,npdeObject["data"]["name.group"]]
if(npdeObject["options"]$cens.method=="fix" & !is.null(fix))
yobs[icens==1]<-fix
if(npdeObject["options"]$cens.method=="ipred")
yobs[icens==1]<-tab[icens==1,npdeObject["data"]["name.ipred"]]
if(npdeObject["options"]$cens.method=="loq")
yobs[icens==1]<-npdeObject["data"]["loq"]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
ysuj<-yobs[idobs==isuj]
# Compute ypred
ypred<-rowMeans(matsim)
ypredall<-c(ypredall,ypred)
if(npdeObject["options"]$cens.method=="ypred") ysuj[icens[idobs==isuj]==1]<-ypred[icens[idobs==isuj]==1]
# compute pd_ij
tcomp<-apply(matsim,2,"<",ysuj)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
if(npdeObject["options"]$ties) {
ycal[!is.na(ycal) & ycal==0]<-1/(2*nrep)
ycal[!is.na(ycal) & ycal==1]<-1-1/(2*nrep)
} else {
idx<-which(!is.na(ycal) & ycal>0 & ycal<1)
ycal[!is.na(ycal) & ycal==0]<-runif(sum(ycal==0),0,1/nrep)
ycal[!is.na(ycal) & ycal==1]<-runif(sum(ycal==0),1-1/nrep,1)
ycal[idx]<-ycal[idx]+runif(length(idx),0,1/nrep)
}
pd<-c(pd,ycal)
}
pdfull[keep]<-pd
ypredfull[keep]<-ypredall
if(npdeObject["options"]$cens.method=="ypred")
ycomp[npdeObject["data"]["icens"]]<-ypredfull[npdeObject["data"]["icens"]]
if(npdeObject["options"]$cens.method %in% c("ipred","fix","loq")) {
ycomp[npdeObject["data"]["icens"]]<-yobs[icens==1]
}
# Saving results
if(length(npdeObject["results"]["res"])==0) { # create data.frame res
res<-data.frame(ypred=ypredfull,ycomp=ycomp,pd=pdfull)
npdeObject["results"]["res"]<-res
} else { # append to data.frame res
npdeObject["results"]["res"]$ypred<-ypredfull
npdeObject["results"]["res"]$ycomp<-ycomp
npdeObject["results"]["res"]$pd<-pdfull
}
return(npdeObject)
}
computepd.cdf<-function(npdeObject) {
# Censored observation
### cdf: replace pd_ij with random sample from a uniform distribution [0-p_LOQ_ij], where p_LOQ_ij is the probability of being under the LOQ (==previous computation of pd_ij because y_ij=censoring value)
# Preparing vectors for the different results
ypredfull<-pdfull<-rep(NaN,dim(npdeObject["data"]["data"])[1])
ycomp<-npdeObject["data"]["data"][,npdeObject["data"]["name.response"]]
# Indicators for censored data to be imputed
not.miss<-npdeObject["data"]["not.miss"]
# missing data = NaN in complete data
ycomp[!not.miss]<-NaN
tab<-npdeObject["data"]["data"][not.miss,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][not.miss,] # corresponding simulated data
yobs<-tab[,npdeObject["data"]["name.response"]]
ycens<-tab[,npdeObject["data"]["name.cens"]]
ploq<-npdeObject["results"]["ploq"][not.miss]
loq<-npdeObject["data"]["loq"]
has.cens<-(length(loq)>0)
idobs<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
# ECO ici comment gerer les indices proprement ?
# Compute prediction discrepancies
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
# compute pd_ij
tcomp<-apply(matsim,2,"<",yobs[idobs==isuj])
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
pdsuj<-ycal<-rowMeans(tcomp)
ploq.suj<-ploq[idobs==isuj]
# impute pd_ij for censored data
iobs.loq<-which(ycens[idobs==isuj]==1)
if(length(iobs.loq)>0)
pdsuj[iobs.loq]<-runif(length(iobs.loq),0,ploq.suj[iobs.loq])
# Compute ypred
ypred<-rowMeans(matsim)
ypredall<-c(ypredall,ypred)
# If we plan to compute npde afterwards, we need to impute observed & simulated data under the LOQ; for simulated data, we first need to impute pd in the same way
isim.loq<-which(matsim<loq,arr.ind=TRUE)
if(npdeObject["options"]$calc.npde & (dim(isim.loq)[1]+length(iobs.loq))>0) {
# when pd=k/K, jitter by imputing an observation to a value between ysim(k) (kth simulated value) and ysim(k+1)
matsort<-linesort(matsim)
if(!npdeObject["options"]$ties) {
# Pb of jittering when the imputed pd is 1 (k=K) because no ysim(K+1)
ncol<-dim(matsort)[2]
matsort<-cbind(matsort,matsort[,ncol]*2-matsort[,(ncol-1)])
}
if(length(iobs.loq)>0){
ids1<-trunc(pdsuj[iobs.loq]*nrep)+1
if(!npdeObject["options"]$ties) {
yobs.imp<-yobs[idobs==isuj]
for(j in 1:length(iobs.loq)) yobs.imp[iobs.loq[j]]<-runif(1, matsort[iobs.loq[j],ids1[j]],matsort[iobs.loq[j],(ids1[j]+1)])
yobs[idobs==isuj]<-yobs.imp
} else {
yobs.imp<-yobs[idobs==isuj]
yobs.imp[iobs.loq]<-diag(matsort[iobs.loq,ids1,drop=F])
yobs[idobs==isuj]<-yobs.imp
}
}
# saving the imputed data for simulations in the simulated dataset
if(dim(isim.loq)[1]>0) {
pdsim.imp<-runif(dim(isim.loq)[1],0,ploq.suj[isim.loq[,1]])
ids2<-trunc(pdsim.imp*nrep)+1
isim.repl<-isim.loq
if(!npdeObject["options"]$ties) {
ids2[ids2>=nrep]<-nrep-1
isim.repl[,2]<-ids2
isim.repl2<-isim.repl
isim.repl2[,2]<-isim.repl2[,2]+1
matsim[isim.loq]<-runif(dim(isim.loq)[1], matsort[isim.repl], matsort[isim.repl2])
} else {
isim.repl[,2]<-ids2
matsim[isim.loq]<-matsort[isim.repl]
}
ysim[idsim==isuj & ysim<loq]<-matsim[isim.loq]
}
}
pd<-c(pd,pdsuj)
}
# Dealing with extreme values of pd & smoothing if !(npdeObject["options"]$ties)
if(npdeObject["options"]$ties) {
pd[pd==0]<-1/(2*nrep)
pd[pd==1]<-1-1/(2*nrep)
} else {
idx<-which(pd>0 & pd<1)
pd[pd==0]<-runif(sum(pd==0),0,1/nrep)
pd[pd==1]<-runif(sum(pd==1),1-1/nrep,1)
pd[idx]<-pd[idx]+runif(length(idx),0,1/nrep)
}
if(npdeObject["options"]$calc.npde) {
ycomp[not.miss]<-yobs
npdeObject["sim.data"]["datsim"][not.miss,"ysim.imp"]<-ysim
}
ypredfull[not.miss]<-ypredall
pdfull[not.miss]<-pd
# Saving results
if(length(npdeObject["results"]["res"])==0) { # create data.frame res
res<-data.frame(ypred=ypredfull,ycomp=ycomp,pd=pdfull)
npdeObject["results"]["res"]<-res
} else { # append to data.frame res
npdeObject["results"]["res"]$ypred<-ypredfull
npdeObject["results"]["res"]$ycomp<-ycomp
npdeObject["results"]["res"]$pd<-pdfull
}
return(npdeObject)
}
########### Compute npde
#' Internal functions used to compute normalised prediction distribution errors (npde)
#'
#' Functions used by \code{npde} and \code{autonpde} to compute prediction
#' discrepancies (not intended for the end-user).
#'
#' These functions are normally not called by the end-user.
#'
#' @usage computenpde(npdeObject,...)
#' @param npdeObject an object of class NpdeObject
#' @param \ldots additional options to modify
#' @return an object of class NpdeObject; the results slot will now include prediction discrepancies (npde) as well as decorrelated observed data, while the sim.data slot will now include decorrelated simulated data
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @keywords internal
computenpde<-function(npdeObject,...) {
npdeObject@options<-replace.control.options(npdeObject@options,...)
if(npdeObject["options"]$cens.method=="cdf" & length(npdeObject["data"]["icens"])>0 & length(npdeObject["results"]["res"]$ycomp)==0) {
cat("With method",npdeObject["options"]$cens.method,"prediction discrepancies need to be computed first \n")
npdeObject<-computepd(npdeObject)
}
if(npdeObject["options"]$cens.method=="omit" | length(npdeObject["data"]["icens"])==0)
object<-computenpde.omit(npdeObject) else
object<-computenpde.loq(npdeObject)
return(object)
}
computenpde.omit<-function(npdeObject) {
# Compute (normalised) prediction distribution errors omitting BQL
# Preparing vectors for the different results
# Indicators for censored data to be imputed
if(npdeObject["options"]$cens.method=="omit" & length(npdeObject["data"]["icens"])>0) {
tab<-npdeObject["data"]["data"]
not.miss<-(tab[,npdeObject["data"]["name.miss"]]==0 & tab[,npdeObject["data"]["name.cens"]]==0)
} else not.miss<-npdeObject["data"]["not.miss"]
tab<-npdeObject["data"]["data"][not.miss,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][not.miss,] # corresponding simulated data
ypred<-pde<-rep(NA,dim(tab)[1])
yobs.all<-ydobs<-tab[,npdeObject["data"]["name.response"]]
npdefull<-ydobsfull<-rep(NA,dim(npdeObject["data"]["data"])[1])
ydsimfull<-rep(NA,dim(npdeObject["sim.data"]["datsim"])[1])
id<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
xerr<-0
ysim<-ydsim<-tabsim$ysim
idsim<-tabsim$idsim
# computing pde
for(isuj in unique(id)) {
yobs<-yobs.all[id==isuj]
matsim<-matrix(ydsim[idsim==isuj],ncol=nrep)
x<-calcnpde(isuj,yobs,matsim,nrep,npdeObject["options"]$method, npdeObject["options"]$verbose)
if(x$xerr>0) {
xerr<-x$xerr
break
}
pde[id==isuj]<-x$pde
ydsim[idsim==isuj]<-x$ydsim
ydobs[id==isuj]<-x$ydobs
ypred[id==isuj]<-x$ypred
}
if(xerr>0) {
cat("The computation of the pde has failed for subject",isuj,"because \n")
if(xerr==1) {
if(npdeObject["options"]$method=="cholesky") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
if(npdeObject["options"]$method=="inverse") cat("the covariance matrix of the simulated data could not be diagonalised through eigen().\n")
if(npdeObject["options"]$method=="polar") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
}
if(xerr==2) cat("the covariance matrix of the simulated data could not be inverted.\n")
cat("This usually means that the covariance matrix is not positive-definite, or that is is poorly conditioned.\n")
cat("This can be caused by simulations widely different from observations (in \n")
cat("other words, a poor model).\n")
cat("We suggest to plot a prediction interval from the simulated data to check\n")
cat("whether the simulations are reasonable, and to consider prediction\n")
cat("discrepancies.\n")
cat("Prediction discrepancies will now be computed.\n")
break
}
# saving pde
if(xerr==0) {
if(npdeObject["options"]$ties) {
pde[pde==0]<-1/(2*nrep)
pde[pde==1]<-1-1/(2*nrep)
} else {
idx<-which(pde>0 & pde<1)
pde[pde==0]<-runif(sum(pde==0),0,1/nrep)
pde[pde==1]<-runif(sum(pde==1),1-1/nrep,1)
pde[idx]<-pde[idx]+runif(length(idx),0,1/nrep)
}
npde<-qnorm(pde)
npdeObject["results"]["xerr"]<-xerr
npdefull[not.miss]<-npde
ydobsfull[not.miss]<-ydobs
ydsimfull[not.miss]<-ydsim
if(length(npdeObject["results"]["res"])==0) {
res<-data.frame(npde=npdefull,ydobs=ydobsfull)
npdeObject["results"]["res"]<-res
} else {
npdeObject["results"]["res"]$ydobs<-ydobsfull
npdeObject["results"]["res"]$npde<-npdefull
}
npdeObject["sim.data"]["datsim"]$ydsim<-ydsimfull
if(!npdeObject["options"]$calc.pd) {
ypredfull<-npdefull
ypredfull[not.miss]<-ypred
npdeObject["results"]["res"]$ypred<-ypredfull
}
} else {
npde<-rep(NA,length(pde))
npdeObject["options"]$calc.pd<-TRUE
}
return(npdeObject)
}
computenpde.loq<-function(npdeObject) {
# Compute (normalised) prediction distribution errors in the presence of BQL data
# ECO TODO: securiser ici, faire test
if(length(npdeObject["data"]["icens"])>0 & length(npdeObject["results"]["res"]$pd)==0) {
cat("Please compute prediction discrepancies first \n")
return(npdeObject)
}
# Preparing vectors for the different results
# Indicators for censored data to be imputed
not.miss<-npdeObject["data"]["not.miss"]
tab<-npdeObject["data"]["data"][not.miss,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][not.miss,] # corresponding simulated data
ycens<-tab[,npdeObject["data"]["name.cens"]]
ypred<-pde<-rep(NA,dim(tab)[1])
if(npdeObject["options"]$cens.method%in% c("ipred","ypred","cdf"))
yobs.all<-ydobs<-npdeObject["results"]["res"][not.miss,"ycomp"] else
yobs.all<-ydobs<-tab[,npdeObject["data"]["name.response"]]
npdefull<-ydobsfull<-rep(NA,dim(npdeObject["data"]["data"])[1])
ydsimfull<-rep(NA,dim(npdeObject["sim.data"]["datsim"])[1])
loq<-npdeObject["data"]["loq"]
has.cens<-(length(loq)>0)
id<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
xerr<-0
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
if(npdeObject["options"]$cens.method=="cdf") ydsim<-tabsim$ysim.imp else ydsim<-ysim
# computing pde
for(isuj in unique(id)) {
yobs<-yobs.all[id==isuj]
matsim<-matrix(ydsim[idsim==isuj],ncol=nrep)
x<-calcnpde(isuj,yobs,matsim,nrep,npdeObject["options"]$method, npdeObject["options"]$verbose)
if(x$xerr>0) {
xerr<-x$xerr
break
}
pde[id==isuj]<-x$pde
ydsim[idsim==isuj]<-x$ydsim
ydobs[id==isuj]<-x$ydobs
ypred[id==isuj]<-x$ypred
}
if(xerr>0) {
cat("The computation of the pde has failed for subject",isuj,"because \n")
if(xerr==1) {
if(npdeObject["options"]$method=="cholesky") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
if(npdeObject["options"]$method=="inverse") cat("the covariance matrix of the simulated data could not be diagonalised through eigen().\n")
if(npdeObject["options"]$method=="polar") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
}
if(xerr==2) cat("the covariance matrix of the simulated data could not be inverted.\n")
cat("This usually means that the covariance matrix is not positive-definite, or that is is poorly conditioned.\n")
cat("This can be caused by simulations widely different from observations (in \n")
cat("other words, a poor model).\n")
cat("We suggest to plot a prediction interval from the simulated data to check\n")
cat("whether the simulations are reasonable, and to consider prediction\n")
cat("discrepancies.\n")
cat("Prediction discrepancies will now be computed.\n")
break
}
# saving pde
if(xerr==0) {
# Dealing with extreme values of npde & smoothing if !(npdeObject["options"]$ties)
if(npdeObject["options"]$ties) {
pde[pde==0]<-1/(2*nrep)
pde[pde==1]<-1-1/(2*nrep)
} else {
idx<-which(pde>0 & pde<1)
pde[pde==0]<-runif(sum(pde==0),0,1/nrep)
pde[pde==1]<-runif(sum(pde==1),1-1/nrep,1)
pde[idx]<-pde[idx]+runif(length(idx),0,1/nrep)
}
npde<-qnorm(pde)
npdeObject["results"]["xerr"]<-xerr
npdefull[not.miss]<-npde
npdeObject["results"]["res"]$npde<-npdefull
ydobsfull[not.miss]<-ydobs
ydsimfull[not.miss]<-ydsim
npdeObject["results"]["res"]$ydobs<-ydobsfull
npdeObject["sim.data"]["datsim"]$ydsim<-ydsimfull
} else {
npde<-rep(NA,length(pde))
npdeObject["options"]$calc.pd<-TRUE
}
return(npdeObject)
}
########### Compute npde - decorrelation methods
calcnpde<-function(isuj,yobs,matsim,nrep,decorr.method,verbose) {
# matsim: simulated data, with BQL data replaced (depending on method)
# matsim: simulated data, raw
if (verbose) cat("Computing the npde for subject ",isuj,"\n")
#Computing decorrelated ysim* and yobs* for subject isuj
#variance-covariance matrix computed using the cov function
#Computing ypred
varsim<-cov(t(matsim))
moysim<-rowMeans(matsim)
#computing V-1/2 with Cholesky
xerr<-0
if(length(moysim)>1) {
y<-switch(decorr.method,
cholesky=decorr.chol(varsim),
polar=decorr.polar(varsim),
inverse=decorr.inverse(varsim))
if(y$xerr==0) ymat<-y$y else xerr<-y$xerr
} else ymat<-1/sqrt(varsim)
if(xerr==0) {
#decorrelation of the simulations
decsim<-t(ymat)%*%(matsim-moysim)
decobs<-t(ymat)%*%(yobs-moysim)
ydsim<-c(decsim)
#decorrelation of the observations
ydobs<-decobs
#Computing the pde
tcomp<-apply(decsim,2,"<",decobs)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
pde<-ycal
}
return(list(xerr=xerr,pde=pde,ydsim=ydsim,ydobs=ydobs,ypred=moysim))
}
decorr.chol<-function(x) {
xerr<-0
xmat<-try(chol(x))
if(is.numeric(xmat)) {
ymat<-try(solve(xmat))
if(!is.numeric(ymat))
xerr<-2
} else
xerr<-1
return(list(y=ymat,xerr=xerr))
}
decorr.inverse<-function(x) {
xerr<-0
var.eig<-eigen(x)
xmat<-try(var.eig$vectors %*% diag(sqrt(var.eig$values)) %*% solve(var.eig$vectors))
if(is.numeric(xmat)) {
ymat<-try(solve(xmat))
if(!is.numeric(ymat))
xerr<-2
} else
xerr<-1
return(list(y=ymat,xerr=xerr))
}
decorr.polar<-function(x) {
xerr<-0
xmat<-try(chol(x))
if(is.numeric(xmat)) {
svdec<-svd(xmat)
umat<-svdec$u %*% t(svdec$v)
vmat<-t(umat) %*% xmat
ymat<-try(solve(vmat))
if(!is.numeric(ymat))
xerr<-2
} else
xerr<-1
return(list(y=ymat,xerr=xerr))
}
########### Compute distribution of pd/npde under the model, using simulations
#' Compute distribution of pd/npde using simulations
#'
#' This function is used to built the distribution of pd/npde using the simulations under the model. The default is to build only the distribution of pd, and to sample from N(0,1) when building the distribution of npde under the null hypothesis.
#'
#' @aliases dist.pred.sim calcnpde.sim
#' @usage dist.pred.sim(npdeObject,nsamp, ...)
#' @param npdeObject an object returned by a call to \code{\link{npde}} or \code{\link{autonpde}}
#' @param nsamp number of datasets (defaults to 100 or to the number of replications if it is smaller)
#' @param \dots additional arguments. Currently only the value of calc.pd and calc.npde may be passed on, and will override their corresponding value in the "options" slot of npdeObject
#' @return an object of class NpdeObject; the ["results"] slot will contain pd and/or npde for a sample of the simulated datasets (depending on whether calc.pd/calc.npde are ), stored in pd.sim and/or npde.sim
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @export
#' @examples
#'
#' data(theopp)
#' data(simtheopp)
#' x<-autonpde(theopp,simtheopp,1,3,4,boolsave=FALSE)
#' # Use random samples from N(0,1) to obtain a prediction interval on the empirical cdf of the npde
#' plot(x,plot.type="ecdf",bands=TRUE,approx.pi=TRUE)
#' # defaults to computing the pd and npde for 100 simulated datasets (here, all the simulated datasets)
#' x<-dist.pred.sim(x)
#' # Use the npde from the simulated datasets to obtain a prediction interval on the empirical cdf
#' plot(x,plot.type="ecdf",bands=TRUE,approx.pi=FALSE)
dist.pred.sim<-function(npdeObject,nsamp, ...) {
args1<-match.call(expand.dots=TRUE)
i1<-match("calc.pd",names(args1))
calc.pd<-NA
if(!is.na(i1)) calc.pd<-as.logical(as.character(args1[[i1]]))
if(is.na(calc.pd)) calc.pd<- npdeObject["options"]$calc.pd
i1<-match("calc.npde",names(args1))
calc.npde<-NA
if(!is.na(i1)) calc.npde<-as.logical(as.character(args1[[i1]]))
if(is.na(calc.npde)) calc.npde<- npdeObject["options"]$calc.npde
if(!calc.pd & !calc.npde) {
cat("At least one of calc.pd or calc.npde must be TRUE.\n")
return(npdeObject)
}
# ECO not necessary since we're not using the imputed data... why not ??? maybe should ?
# if(npdeObject["options"]$cens.method=="cdf" && length(npdeObject["sim.data"]["icens"])>0 && length(npdeObject["sim.data"]["datsim"]$ysim.imp)==0) {
# cat("With the cdf method, the imputation step needs to be performed before a call to dist.pred.sim() is made. Please use computepd(x) first.\n")
# return(npdeObject)
# }
nrep<-npdeObject["sim.data"]["nrep"]
if(missing(nsamp)) nsamp<-min(100,nrep)
# Extracting non-missing data
keep<-npdeObject["data"]["not.miss"]
tabsim<-npdeObject["sim.data"]["datsim"][keep,] # simulated data
# if(npdeObject["options"]$cens.method=="cdf" && !is.na(grep("ysim.imp",colnames(tabsim)))) yobs<-matrix(tabsim[,"ysim.imp"], ncol=nrep) else yobs<-matrix(tabsim[,"ysim"],ncol=nrep)
# Use original simulations to compute the PI under the model
idsim<-tabsim$idsim
ysim<-yobs<-matrix(tabsim[,"ysim"],ncol=nrep)
colnames(yobs)<-paste("sim",1:nrep,sep="")
if(nsamp<nrep) {
isample<-sort(sample(1:nrep,nsamp))
yobs<-yobs[,isample]
}
idobs<-npdeObject["data"]["data"][keep,npdeObject["data"]["name.group"]]
pd<-npde<-matrix(nrow=0,ncol=nsamp,dimnames=list(NULL,colnames(yobs)))
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
ysuj<-yobs[idobs==isuj,]
if(calc.pd) {
pdsuj<-c()
# compute pdsim_ij
for(i in 1:nsamp) {
tcomp<-apply(matsim,2,"<",ysuj[,i])
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
# pdsim_ij will be within the sequence seq(0,1-1/nrep,1/nrep) by construction
pdsuj<-c(pdsuj,ycal)
}
# If ties: add 1/(2*nrep) to center the distribution to 1/2*nrep ; 1-1/2*nrep
# else add U(0,1/nrep)
if(npdeObject["options"]$ties)
pdsuj<-pdsuj+1/(2*nrep)
else
pdsuj<-pdsuj+runif(length(pdsuj),0,1/nrep)
pd<-rbind(pd,matrix(pdsuj,ncol=nsamp))
}
if(calc.npde) {
y<-calcnpde.sim(ysuj,matsim,nrep,npdeObject["options"]$method)
if(y$xerr==0) {
pde<-y$pde
if(npdeObject["options"]$ties)
pde<-pde+1/(2*nrep)
else
pde<-pde+runif(length(pde),0,1/nrep)
npde<-rbind(npde,qnorm(pde))
} else {
cat("Problem computing npde for subject",isuj,"\n")
return(npdeObject)
}
}
}
# Saving results
if(calc.pd) npdeObject["results"]["pd.sim"]<-pd
if(calc.npde) npdeObject["results"]["npde.sim"]<-npde
return(npdeObject)
}
calcnpde.sim<-function(yobs,matsim,nrep,decorr.method) {
# yobs: matrix with data treated as observed (1 column=1 set of data=1 'subject')
# matsim: simulated data to be used to decorrelate
# returns decorrelated yobs* for each 'subject'
#variance-covariance matrix computed depending on "method"
varsim<-cov(t(matsim))
moysim<-rowMeans(matsim)
#computing V-1/2
xerr<-0
if(length(moysim)>1) {
y<-switch(decorr.method,
cholesky=decorr.chol(varsim),
polar=decorr.polar(varsim),
inverse=decorr.inverse(varsim))
if(y$xerr==0) ymat<-y$y else xerr<-y$xerr
} else ymat<-1/sqrt(varsim)
pde<-yobs
if(xerr==0) {
#decorrelation of the simulations & the observations
decsim<-t(ymat)%*%(matsim-moysim)
decobs<-t(ymat)%*%(yobs-moysim)
#Computing the pde
for(i in 1:dim(yobs)[2]) {
tcomp<-apply(decsim,2,"<",decobs[,i])
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
pde[,i]<-ycal
}
}
return(list(xerr=xerr,pde=pde))
}
####################################################################################
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########### Compute Probability of being under the LOQ, for all observations
#' Compute P(y_ij<LOQ) for all observations
#'
#' For each observation in the dataset, computes the probability to be below LOQ
#' using the simulations under the model. This is generally performed automatically.
#'
#'
#' @usage compute.ploq(npdeObject)
#' @param npdeObject an object returned by a call to \code{\link{npde}} or \code{\link{autonpde}}
#' @return an object of class NpdeObject with a component ploq in the ["results"] slot
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @keywords internal
compute.ploq<-function(npdeObject) {
# For each observation, computes the probability of being LOQ under the model
### when the data has different LOQ values, the LOQ is taken to be the smallest LOQ
### p_LOQ is computed as the % of simulated values under the LOQ
if(length(npdeObject["data"]["icens"])==0)
return(npdeObject)
ploq<-c()
ploqfull<-rep(NA,dim(npdeObject["data"]["data"])[1])
tab<-npdeObject["data"]["data"][npdeObject["data"]["not.miss"],] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][npdeObject["data"]["not.miss"],] # corresponding simulated data
yobs<-tab[, npdeObject["data"]["name.response"]]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
if(length(npdeObject["data"]["loq"])>0) {
loq<-npdeObject["data"]["loq"]
if(npdeObject@options$verbose) cat("Computing p(y<LOQ) using LOQ=",loq,"\n")
} else {
yloq<-npdeObject["data"]["data"][npdeObject["data"]["icens"], npdeObject["data"]["name.response"]]
if(length(unique(yloq))==1) {
if(npdeObject@options$verbose) cat("Same LOQ for all missing data, loq=",loq,"\n")
loq<-unique(yloq)
} else {
loq<-min(unique(yloq))
if(npdeObject@options$verbose) cat("Computing p(y<LOQ) for the lowest LOQ, loq=",loq,"\n")
}
npdeObject["data"]["loq"]<-loq
}
for(isuj in unique(npdeObject["data"]["data"][,"index"])) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
tcomp<-apply(matsim,2,"<",loq)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
ploq<-c(ploq,ycal)
}
ploqfull[npdeObject["data"]["not.miss"]]<-ploq
npdeObject["results"]["ploq"]<-ploqfull
#saving pd
invisible(npdeObject)
}
########### Compute pd
#' Internal functions used to compute prediction discrepancies
#'
#' Functions used by \code{npde} and \code{autonpde} to compute prediction
#' discrepancies (not intended for the end-user).
#'
#' These functions are normally not called by the end-user.
#'
#' @usage computepd(npdeObject,...)
#' @param npdeObject an object of class NpdeObject
#' @param \ldots additional options to modify
#' @return an object of class NpdeObject; the results slot will now include prediction discrepancies (pd) as well as model predictions (ypred) obtained as the mean of the simulated data for each observation
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @keywords internal
computepd<-function(npdeObject,...) {
npdeObject@options<-replace.control.options(npdeObject@options,...)
if(npdeObject["options"]$cens.method=="omit" | length(npdeObject["data"]["icens"])==0)
object<-computepd.omit(npdeObject) else {
if(npdeObject["options"]$cens.method=="cdf") {
if(length(npdeObject["results"]["ploq"])==0)
npdeObject<-compute.ploq(npdeObject)
object<-computepd.cdf(npdeObject)
}
if(npdeObject["options"]$cens.method %in% c("ipred","ypred"))
object<-computepd.replace(npdeObject)
if(npdeObject["options"]$cens.method=="fix")
object<-computepd.replace(npdeObject,...)
if(npdeObject["options"]$cens.method=="loq") {
if(length(npdeObject["data"]["loq"])==0)
npdeObject<-compute.ploq(npdeObject)
object<-computepd.replace(npdeObject)
}
}
return(object)
}
# Functions to sort the lines/columns of a matrix
linesort<-function(mat) {
for(i in 1:dim(mat)[1])
mat[i,]<-sort(mat[i,])
return(mat)
}
colsort<-function(mat) {
for(i in 1:dim(mat)[2])
mat[,i]<-sort(mat[,i])
return(mat)
}
computepd.omit<-function(npdeObject) {
# Preparing vectors for the different results
ypredfull<-pdfull<-rep(NaN,dim(npdeObject["data"]["data"])[1])
ycomp<-npdeObject["data"]["data"][,npdeObject["data"]["name.response"]]
# Extracting only non-missing and non-censored data
if(length(npdeObject["data"]["icens"])==0) keep<-npdeObject["data"]["not.miss"] else keep<-(npdeObject["data"]["not.miss"] & npdeObject["data"]["data"][,npdeObject["data"]["name.cens"]]==0)
# missing and censored data = NaN in complete data
ycomp[!keep]<-NaN
tab<-npdeObject["data"]["data"][keep,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][keep,] # corresponding simulated data
yobs<-tab[,npdeObject["data"]["name.response"]]
idobs<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
ysuj<-yobs[idobs==isuj]
# Compute ypred
ypred<-rowMeans(matsim)
ypredall<-c(ypredall,ypred)
# compute pd_ij
tcomp<-apply(matsim,2,"<",ysuj)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
if(npdeObject["options"]$ties) {
ycal[!is.na(ycal) & ycal==0]<-1/(2*nrep)
ycal[!is.na(ycal) & ycal==1]<-1-1/(2*nrep)
} else {
idx<-which(!is.na(ycal) & ycal>0 & ycal<1)
ycal[!is.na(ycal) & ycal==0]<-runif(sum(ycal==0),0,1/nrep)
ycal[!is.na(ycal) & ycal==1]<-runif(sum(ycal==0),1-1/nrep,1)
ycal[idx]<-ycal[idx]+runif(length(idx),0,1/nrep)
}
pd<-c(pd,ycal)
}
pdfull[keep]<-pd
ypredfull[keep]<-ypredall
# Saving results
if(length(npdeObject["results"]["res"])==0) { # create data.frame res
res<-data.frame(ypred=ypredfull,ycomp=ycomp,pd=pdfull)
npdeObject["results"]["res"]<-res
} else { # append to data.frame res
npdeObject["results"]["res"]$ypred<-ypredfull
npdeObject["results"]["res"]$ycomp<-ycomp
npdeObject["results"]["res"]$pd<-pdfull
}
return(npdeObject)
}
computepd.replace<-function(npdeObject,fix=NULL) {
# Preparing vectors for the different results
ypredfull<-pdfull<-rep(NaN,dim(npdeObject["data"]["data"])[1])
ycomp<-npdeObject["data"]["data"][,npdeObject["data"]["name.response"]]
# Extracting only non-missing data
keep<-npdeObject["data"]["not.miss"]
# missing data = NaN in complete data
ycomp[!keep]<-NaN
tab<-npdeObject["data"]["data"][keep,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][keep,] # corresponding simulated data
yobs<-tab[,npdeObject["data"]["name.response"]]
icens<-tab[,npdeObject["data"]["name.cens"]]
idobs<-tab[,npdeObject["data"]["name.group"]]
if(npdeObject["options"]$cens.method=="fix" & !is.null(fix))
yobs[icens==1]<-fix
if(npdeObject["options"]$cens.method=="ipred")
yobs[icens==1]<-tab[icens==1,npdeObject["data"]["name.ipred"]]
if(npdeObject["options"]$cens.method=="loq")
yobs[icens==1]<-npdeObject["data"]["loq"]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
ysuj<-yobs[idobs==isuj]
# Compute ypred
ypred<-rowMeans(matsim)
ypredall<-c(ypredall,ypred)
if(npdeObject["options"]$cens.method=="ypred") ysuj[icens[idobs==isuj]==1]<-ypred[icens[idobs==isuj]==1]
# compute pd_ij
tcomp<-apply(matsim,2,"<",ysuj)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
if(npdeObject["options"]$ties) {
ycal[!is.na(ycal) & ycal==0]<-1/(2*nrep)
ycal[!is.na(ycal) & ycal==1]<-1-1/(2*nrep)
} else {
idx<-which(!is.na(ycal) & ycal>0 & ycal<1)
ycal[!is.na(ycal) & ycal==0]<-runif(sum(ycal==0),0,1/nrep)
ycal[!is.na(ycal) & ycal==1]<-runif(sum(ycal==0),1-1/nrep,1)
ycal[idx]<-ycal[idx]+runif(length(idx),0,1/nrep)
}
pd<-c(pd,ycal)
}
pdfull[keep]<-pd
ypredfull[keep]<-ypredall
if(npdeObject["options"]$cens.method=="ypred")
ycomp[npdeObject["data"]["icens"]]<-ypredfull[npdeObject["data"]["icens"]]
if(npdeObject["options"]$cens.method %in% c("ipred","fix","loq")) {
ycomp[npdeObject["data"]["icens"]]<-yobs[icens==1]
}
# Saving results
if(length(npdeObject["results"]["res"])==0) { # create data.frame res
res<-data.frame(ypred=ypredfull,ycomp=ycomp,pd=pdfull)
npdeObject["results"]["res"]<-res
} else { # append to data.frame res
npdeObject["results"]["res"]$ypred<-ypredfull
npdeObject["results"]["res"]$ycomp<-ycomp
npdeObject["results"]["res"]$pd<-pdfull
}
return(npdeObject)
}
computepd.cdf<-function(npdeObject) {
# Censored observation
### cdf: replace pd_ij with random sample from a uniform distribution [0-p_LOQ_ij], where p_LOQ_ij is the probability of being under the LOQ (==previous computation of pd_ij because y_ij=censoring value)
# Preparing vectors for the different results
ypredfull<-pdfull<-rep(NaN,dim(npdeObject["data"]["data"])[1])
ycomp<-npdeObject["data"]["data"][,npdeObject["data"]["name.response"]]
# Indicators for censored data to be imputed
not.miss<-npdeObject["data"]["not.miss"]
# missing data = NaN in complete data
ycomp[!not.miss]<-NaN
tab<-npdeObject["data"]["data"][not.miss,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][not.miss,] # corresponding simulated data
yobs<-tab[,npdeObject["data"]["name.response"]]
ycens<-tab[,npdeObject["data"]["name.cens"]]
ploq<-npdeObject["results"]["ploq"][not.miss]
loq<-npdeObject["data"]["loq"]
has.cens<-(length(loq)>0)
idobs<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
# ECO ici comment gerer les indices proprement ?
# Compute prediction discrepancies
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
# compute pd_ij
tcomp<-apply(matsim,2,"<",yobs[idobs==isuj])
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
pdsuj<-ycal<-rowMeans(tcomp)
ploq.suj<-ploq[idobs==isuj]
# impute pd_ij for censored data
iobs.loq<-which(ycens[idobs==isuj]==1)
if(length(iobs.loq)>0)
pdsuj[iobs.loq]<-runif(length(iobs.loq),0,ploq.suj[iobs.loq])
# Compute ypred
ypred<-rowMeans(matsim)
ypredall<-c(ypredall,ypred)
# If we plan to compute npde afterwards, we need to impute observed & simulated data under the LOQ; for simulated data, we first need to impute pd in the same way
isim.loq<-which(matsim<loq,arr.ind=TRUE)
if(npdeObject["options"]$calc.npde & (dim(isim.loq)[1]+length(iobs.loq))>0) {
# when pd=k/K, jitter by imputing an observation to a value between ysim(k) (kth simulated value) and ysim(k+1)
matsort<-linesort(matsim)
if(!npdeObject["options"]$ties) {
# Pb of jittering when the imputed pd is 1 (k=K) because no ysim(K+1)
ncol<-dim(matsort)[2]
matsort<-cbind(matsort,matsort[,ncol]*2-matsort[,(ncol-1)])
}
if(length(iobs.loq)>0){
ids1<-trunc(pdsuj[iobs.loq]*nrep)+1
if(!npdeObject["options"]$ties) {
yobs.imp<-yobs[idobs==isuj]
for(j in 1:length(iobs.loq)) yobs.imp[iobs.loq[j]]<-runif(1, matsort[iobs.loq[j],ids1[j]],matsort[iobs.loq[j],(ids1[j]+1)])
yobs[idobs==isuj]<-yobs.imp
} else {
yobs.imp<-yobs[idobs==isuj]
yobs.imp[iobs.loq]<-diag(matsort[iobs.loq,ids1,drop=F])
yobs[idobs==isuj]<-yobs.imp
}
}
# saving the imputed data for simulations in the simulated dataset
if(dim(isim.loq)[1]>0) {
pdsim.imp<-runif(dim(isim.loq)[1],0,ploq.suj[isim.loq[,1]])
ids2<-trunc(pdsim.imp*nrep)+1
isim.repl<-isim.loq
if(!npdeObject["options"]$ties) {
ids2[ids2>=nrep]<-nrep-1
isim.repl[,2]<-ids2
isim.repl2<-isim.repl
isim.repl2[,2]<-isim.repl2[,2]+1
matsim[isim.loq]<-runif(dim(isim.loq)[1], matsort[isim.repl], matsort[isim.repl2])
} else {
isim.repl[,2]<-ids2
matsim[isim.loq]<-matsort[isim.repl]
}
ysim[idsim==isuj & ysim<loq]<-matsim[isim.loq]
}
}
pd<-c(pd,pdsuj)
}
# Dealing with extreme values of pd & smoothing if !(npdeObject["options"]$ties)
if(npdeObject["options"]$ties) {
pd[pd==0]<-1/(2*nrep)
pd[pd==1]<-1-1/(2*nrep)
} else {
idx<-which(pd>0 & pd<1)
pd[pd==0]<-runif(sum(pd==0),0,1/nrep)
pd[pd==1]<-runif(sum(pd==1),1-1/nrep,1)
pd[idx]<-pd[idx]+runif(length(idx),0,1/nrep)
}
if(npdeObject["options"]$calc.npde) {
ycomp[not.miss]<-yobs
npdeObject["sim.data"]["datsim"][not.miss,"ysim.imp"]<-ysim
}
ypredfull[not.miss]<-ypredall
pdfull[not.miss]<-pd
# Saving results
if(length(npdeObject["results"]["res"])==0) { # create data.frame res
res<-data.frame(ypred=ypredfull,ycomp=ycomp,pd=pdfull)
npdeObject["results"]["res"]<-res
} else { # append to data.frame res
npdeObject["results"]["res"]$ypred<-ypredfull
npdeObject["results"]["res"]$ycomp<-ycomp
npdeObject["results"]["res"]$pd<-pdfull
}
return(npdeObject)
}
########### Compute npde
#' Internal functions used to compute normalised prediction distribution errors (npde)
#'
#' Functions used by \code{npde} and \code{autonpde} to compute prediction
#' discrepancies (not intended for the end-user).
#'
#' These functions are normally not called by the end-user.
#'
#' @usage computenpde(npdeObject,...)
#' @param npdeObject an object of class NpdeObject
#' @param \ldots additional options to modify
#' @return an object of class NpdeObject; the results slot will now include prediction discrepancies (npde) as well as decorrelated observed data, while the sim.data slot will now include decorrelated simulated data
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @keywords internal
computenpde<-function(npdeObject,...) {
npdeObject@options<-replace.control.options(npdeObject@options,...)
if(npdeObject["options"]$cens.method=="cdf" & length(npdeObject["data"]["icens"])>0 & length(npdeObject["results"]["res"]$ycomp)==0) {
cat("With method",npdeObject["options"]$cens.method,"prediction discrepancies need to be computed first \n")
npdeObject<-computepd(npdeObject)
}
if(npdeObject["options"]$cens.method=="omit" | length(npdeObject["data"]["icens"])==0)
object<-computenpde.omit(npdeObject) else
object<-computenpde.loq(npdeObject)
return(object)
}
computenpde.omit<-function(npdeObject) {
# Compute (normalised) prediction distribution errors omitting BQL
# Preparing vectors for the different results
# Indicators for censored data to be imputed
if(npdeObject["options"]$cens.method=="omit" & length(npdeObject["data"]["icens"])>0) {
tab<-npdeObject["data"]["data"]
not.miss<-(tab[,npdeObject["data"]["name.miss"]]==0 & tab[,npdeObject["data"]["name.cens"]]==0)
} else not.miss<-npdeObject["data"]["not.miss"]
tab<-npdeObject["data"]["data"][not.miss,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][not.miss,] # corresponding simulated data
ypred<-pde<-rep(NA,dim(tab)[1])
yobs.all<-ydobs<-tab[,npdeObject["data"]["name.response"]]
npdefull<-ydobsfull<-rep(NA,dim(npdeObject["data"]["data"])[1])
ydsimfull<-rep(NA,dim(npdeObject["sim.data"]["datsim"])[1])
id<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
xerr<-0
ysim<-ydsim<-tabsim$ysim
idsim<-tabsim$idsim
# computing pde
for(isuj in unique(id)) {
yobs<-yobs.all[id==isuj]
matsim<-matrix(ydsim[idsim==isuj],ncol=nrep)
x<-calcnpde(isuj,yobs,matsim,nrep,npdeObject["options"]$method, npdeObject["options"]$verbose)
if(x$xerr>0) {
xerr<-x$xerr
break
}
pde[id==isuj]<-x$pde
ydsim[idsim==isuj]<-x$ydsim
ydobs[id==isuj]<-x$ydobs
ypred[id==isuj]<-x$ypred
}
if(xerr>0) {
cat("The computation of the pde has failed for subject",isuj,"because \n")
if(xerr==1) {
if(npdeObject["options"]$method=="cholesky") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
if(npdeObject["options"]$method=="inverse") cat("the covariance matrix of the simulated data could not be diagonalised through eigen().\n")
if(npdeObject["options"]$method=="polar") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
}
if(xerr==2) cat("the covariance matrix of the simulated data could not be inverted.\n")
cat("This usually means that the covariance matrix is not positive-definite, or that is is poorly conditioned.\n")
cat("This can be caused by simulations widely different from observations (in \n")
cat("other words, a poor model).\n")
cat("We suggest to plot a prediction interval from the simulated data to check\n")
cat("whether the simulations are reasonable, and to consider prediction\n")
cat("discrepancies.\n")
cat("Prediction discrepancies will now be computed.\n")
break
}
# saving pde
if(xerr==0) {
if(npdeObject["options"]$ties) {
pde[pde==0]<-1/(2*nrep)
pde[pde==1]<-1-1/(2*nrep)
} else {
idx<-which(pde>0 & pde<1)
pde[pde==0]<-runif(sum(pde==0),0,1/nrep)
pde[pde==1]<-runif(sum(pde==1),1-1/nrep,1)
pde[idx]<-pde[idx]+runif(length(idx),0,1/nrep)
}
npde<-qnorm(pde)
npdeObject["results"]["xerr"]<-xerr
npdefull[not.miss]<-npde
ydobsfull[not.miss]<-ydobs
ydsimfull[not.miss]<-ydsim
if(length(npdeObject["results"]["res"])==0) {
res<-data.frame(npde=npdefull,ydobs=ydobsfull)
npdeObject["results"]["res"]<-res
} else {
npdeObject["results"]["res"]$ydobs<-ydobsfull
npdeObject["results"]["res"]$npde<-npdefull
}
npdeObject["sim.data"]["datsim"]$ydsim<-ydsimfull
if(!npdeObject["options"]$calc.pd) {
ypredfull<-npdefull
ypredfull[not.miss]<-ypred
npdeObject["results"]["res"]$ypred<-ypredfull
}
} else {
npde<-rep(NA,length(pde))
npdeObject["options"]$calc.pd<-TRUE
}
return(npdeObject)
}
computenpde.loq<-function(npdeObject) {
# Compute (normalised) prediction distribution errors in the presence of BQL data
# ECO TODO: securiser ici, faire test
if(length(npdeObject["data"]["icens"])>0 & length(npdeObject["results"]["res"]$pd)==0) {
cat("Please compute prediction discrepancies first \n")
return(npdeObject)
}
# Preparing vectors for the different results
# Indicators for censored data to be imputed
not.miss<-npdeObject["data"]["not.miss"]
tab<-npdeObject["data"]["data"][not.miss,] # non-missing data
tabsim<-npdeObject["sim.data"]["datsim"][not.miss,] # corresponding simulated data
ycens<-tab[,npdeObject["data"]["name.cens"]]
ypred<-pde<-rep(NA,dim(tab)[1])
if(npdeObject["options"]$cens.method%in% c("ipred","ypred","cdf"))
yobs.all<-ydobs<-npdeObject["results"]["res"][not.miss,"ycomp"] else
yobs.all<-ydobs<-tab[,npdeObject["data"]["name.response"]]
npdefull<-ydobsfull<-rep(NA,dim(npdeObject["data"]["data"])[1])
ydsimfull<-rep(NA,dim(npdeObject["sim.data"]["datsim"])[1])
loq<-npdeObject["data"]["loq"]
has.cens<-(length(loq)>0)
id<-tab[,npdeObject["data"]["name.group"]]
nrep<-npdeObject["sim.data"]["nrep"]
xerr<-0
ysim<-tabsim$ysim
idsim<-tabsim$idsim
ypredall<-pd<-c()
if(npdeObject["options"]$cens.method=="cdf") ydsim<-tabsim$ysim.imp else ydsim<-ysim
# computing pde
for(isuj in unique(id)) {
yobs<-yobs.all[id==isuj]
matsim<-matrix(ydsim[idsim==isuj],ncol=nrep)
x<-calcnpde(isuj,yobs,matsim,nrep,npdeObject["options"]$method, npdeObject["options"]$verbose)
if(x$xerr>0) {
xerr<-x$xerr
break
}
pde[id==isuj]<-x$pde
ydsim[idsim==isuj]<-x$ydsim
ydobs[id==isuj]<-x$ydobs
ypred[id==isuj]<-x$ypred
}
if(xerr>0) {
cat("The computation of the pde has failed for subject",isuj,"because \n")
if(xerr==1) {
if(npdeObject["options"]$method=="cholesky") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
if(npdeObject["options"]$method=="inverse") cat("the covariance matrix of the simulated data could not be diagonalised through eigen().\n")
if(npdeObject["options"]$method=="polar") cat("the Cholesky decomposition of the covariance matrix of the simulated data could not be obtained.\n")
}
if(xerr==2) cat("the covariance matrix of the simulated data could not be inverted.\n")
cat("This usually means that the covariance matrix is not positive-definite, or that is is poorly conditioned.\n")
cat("This can be caused by simulations widely different from observations (in \n")
cat("other words, a poor model).\n")
cat("We suggest to plot a prediction interval from the simulated data to check\n")
cat("whether the simulations are reasonable, and to consider prediction\n")
cat("discrepancies.\n")
cat("Prediction discrepancies will now be computed.\n")
break
}
# saving pde
if(xerr==0) {
# Dealing with extreme values of npde & smoothing if !(npdeObject["options"]$ties)
if(npdeObject["options"]$ties) {
pde[pde==0]<-1/(2*nrep)
pde[pde==1]<-1-1/(2*nrep)
} else {
idx<-which(pde>0 & pde<1)
pde[pde==0]<-runif(sum(pde==0),0,1/nrep)
pde[pde==1]<-runif(sum(pde==1),1-1/nrep,1)
pde[idx]<-pde[idx]+runif(length(idx),0,1/nrep)
}
npde<-qnorm(pde)
npdeObject["results"]["xerr"]<-xerr
npdefull[not.miss]<-npde
npdeObject["results"]["res"]$npde<-npdefull
ydobsfull[not.miss]<-ydobs
ydsimfull[not.miss]<-ydsim
npdeObject["results"]["res"]$ydobs<-ydobsfull
npdeObject["sim.data"]["datsim"]$ydsim<-ydsimfull
} else {
npde<-rep(NA,length(pde))
npdeObject["options"]$calc.pd<-TRUE
}
return(npdeObject)
}
########### Compute npde - decorrelation methods
calcnpde<-function(isuj,yobs,matsim,nrep,decorr.method,verbose) {
# matsim: simulated data, with BQL data replaced (depending on method)
# matsim: simulated data, raw
if (verbose) cat("Computing the npde for subject ",isuj,"\n")
#Computing decorrelated ysim* and yobs* for subject isuj
#variance-covariance matrix computed using the cov function
#Computing ypred
varsim<-cov(t(matsim))
moysim<-rowMeans(matsim)
#computing V-1/2 with Cholesky
xerr<-0
if(length(moysim)>1) {
y<-switch(decorr.method,
cholesky=decorr.chol(varsim),
polar=decorr.polar(varsim),
inverse=decorr.inverse(varsim))
if(y$xerr==0) ymat<-y$y else xerr<-y$xerr
} else ymat<-1/sqrt(varsim)
if(xerr==0) {
#decorrelation of the simulations
decsim<-t(ymat)%*%(matsim-moysim)
decobs<-t(ymat)%*%(yobs-moysim)
ydsim<-c(decsim)
#decorrelation of the observations
ydobs<-decobs
#Computing the pde
tcomp<-apply(decsim,2,"<",decobs)
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
pde<-ycal
}
return(list(xerr=xerr,pde=pde,ydsim=ydsim,ydobs=ydobs,ypred=moysim))
}
decorr.chol<-function(x) {
xerr<-0
xmat<-try(chol(x))
if(is.numeric(xmat)) {
ymat<-try(solve(xmat))
if(!is.numeric(ymat))
xerr<-2
} else
xerr<-1
return(list(y=ymat,xerr=xerr))
}
decorr.inverse<-function(x) {
xerr<-0
var.eig<-eigen(x)
xmat<-try(var.eig$vectors %*% diag(sqrt(var.eig$values)) %*% solve(var.eig$vectors))
if(is.numeric(xmat)) {
ymat<-try(solve(xmat))
if(!is.numeric(ymat))
xerr<-2
} else
xerr<-1
return(list(y=ymat,xerr=xerr))
}
decorr.polar<-function(x) {
xerr<-0
xmat<-try(chol(x))
if(is.numeric(xmat)) {
svdec<-svd(xmat)
umat<-svdec$u %*% t(svdec$v)
vmat<-t(umat) %*% xmat
ymat<-try(solve(vmat))
if(!is.numeric(ymat))
xerr<-2
} else
xerr<-1
return(list(y=ymat,xerr=xerr))
}
########### Compute distribution of pd/npde under the model, using simulations
#' Compute distribution of pd/npde using simulations
#'
#' This function is used to built the distribution of pd/npde using the simulations under the model. The default is to build only the distribution of pd, and to sample from N(0,1) when building the distribution of npde under the null hypothesis.
#'
#' @aliases dist.pred.sim calcnpde.sim
#' @usage dist.pred.sim(npdeObject,nsamp, ...)
#' @param npdeObject an object returned by a call to \code{\link{npde}} or \code{\link{autonpde}}
#' @param nsamp number of datasets (defaults to 100 or to the number of replications if it is smaller)
#' @param \dots additional arguments. Currently only the value of calc.pd and calc.npde may be passed on, and will override their corresponding value in the "options" slot of npdeObject
#' @return an object of class NpdeObject; the ["results"] slot will contain pd and/or npde for a sample of the simulated datasets (depending on whether calc.pd/calc.npde are ), stored in pd.sim and/or npde.sim
#' @author Emmanuelle Comets <emmanuelle.comets@@bichat.inserm.fr>
#' @seealso \code{\link{npde}}, \code{\link{autonpde}}
#' @references K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.
#' Mentre. Metrics for external model evaluation with an application to the
#' population pharmacokinetics of gliclazide. \emph{Pharmaceutical Research},
#' 23:2036--49, 2006.
#' @export
#' @examples
#'
#' data(theopp)
#' data(simtheopp)
#' x<-autonpde(theopp,simtheopp,1,3,4,boolsave=FALSE)
#' # Use random samples from N(0,1) to obtain a prediction interval on the empirical cdf of the npde
#' plot(x,plot.type="ecdf",bands=TRUE,approx.pi=TRUE)
#' # defaults to computing the pd and npde for 100 simulated datasets (here, all the simulated datasets)
#' x<-dist.pred.sim(x)
#' # Use the npde from the simulated datasets to obtain a prediction interval on the empirical cdf
#' plot(x,plot.type="ecdf",bands=TRUE,approx.pi=FALSE)
dist.pred.sim<-function(npdeObject,nsamp, ...) {
args1<-match.call(expand.dots=TRUE)
i1<-match("calc.pd",names(args1))
calc.pd<-NA
if(!is.na(i1)) calc.pd<-as.logical(as.character(args1[[i1]]))
if(is.na(calc.pd)) calc.pd<- npdeObject["options"]$calc.pd
i1<-match("calc.npde",names(args1))
calc.npde<-NA
if(!is.na(i1)) calc.npde<-as.logical(as.character(args1[[i1]]))
if(is.na(calc.npde)) calc.npde<- npdeObject["options"]$calc.npde
if(!calc.pd & !calc.npde) {
cat("At least one of calc.pd or calc.npde must be TRUE.\n")
return(npdeObject)
}
# ECO not necessary since we're not using the imputed data... why not ??? maybe should ?
# if(npdeObject["options"]$cens.method=="cdf" && length(npdeObject["sim.data"]["icens"])>0 && length(npdeObject["sim.data"]["datsim"]$ysim.imp)==0) {
# cat("With the cdf method, the imputation step needs to be performed before a call to dist.pred.sim() is made. Please use computepd(x) first.\n")
# return(npdeObject)
# }
nrep<-npdeObject["sim.data"]["nrep"]
if(missing(nsamp)) nsamp<-min(100,nrep)
# Extracting non-missing data
keep<-npdeObject["data"]["not.miss"]
tabsim<-npdeObject["sim.data"]["datsim"][keep,] # simulated data
# if(npdeObject["options"]$cens.method=="cdf" && !is.na(grep("ysim.imp",colnames(tabsim)))) yobs<-matrix(tabsim[,"ysim.imp"], ncol=nrep) else yobs<-matrix(tabsim[,"ysim"],ncol=nrep)
# Use original simulations to compute the PI under the model
idsim<-tabsim$idsim
ysim<-yobs<-matrix(tabsim[,"ysim"],ncol=nrep)
colnames(yobs)<-paste("sim",1:nrep,sep="")
if(nsamp<nrep) {
isample<-sort(sample(1:nrep,nsamp))
yobs<-yobs[,isample]
}
idobs<-npdeObject["data"]["data"][keep,npdeObject["data"]["name.group"]]
pd<-npde<-matrix(nrow=0,ncol=nsamp,dimnames=list(NULL,colnames(yobs)))
# Loop on isuj
for(isuj in unique(idobs)) {
matsim<-matrix(ysim[idsim==isuj],ncol=nrep)
ysuj<-yobs[idobs==isuj,]
if(calc.pd) {
pdsuj<-c()
# compute pdsim_ij
for(i in 1:nsamp) {
tcomp<-apply(matsim,2,"<",ysuj[,i])
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
# pdsim_ij will be within the sequence seq(0,1-1/nrep,1/nrep) by construction
pdsuj<-c(pdsuj,ycal)
}
# If ties: add 1/(2*nrep) to center the distribution to 1/2*nrep ; 1-1/2*nrep
# else add U(0,1/nrep)
if(npdeObject["options"]$ties)
pdsuj<-pdsuj+1/(2*nrep)
else
pdsuj<-pdsuj+runif(length(pdsuj),0,1/nrep)
pd<-rbind(pd,matrix(pdsuj,ncol=nsamp))
}
if(calc.npde) {
y<-calcnpde.sim(ysuj,matsim,nrep,npdeObject["options"]$method)
if(y$xerr==0) {
pde<-y$pde
if(npdeObject["options"]$ties)
pde<-pde+1/(2*nrep)
else
pde<-pde+runif(length(pde),0,1/nrep)
npde<-rbind(npde,qnorm(pde))
} else {
cat("Problem computing npde for subject",isuj,"\n")
return(npdeObject)
}
}
}
# Saving results
if(calc.pd) npdeObject["results"]["pd.sim"]<-pd
if(calc.npde) npdeObject["results"]["npde.sim"]<-npde
return(npdeObject)
}
calcnpde.sim<-function(yobs,matsim,nrep,decorr.method) {
# yobs: matrix with data treated as observed (1 column=1 set of data=1 'subject')
# matsim: simulated data to be used to decorrelate
# returns decorrelated yobs* for each 'subject'
#variance-covariance matrix computed depending on "method"
varsim<-cov(t(matsim))
moysim<-rowMeans(matsim)
#computing V-1/2
xerr<-0
if(length(moysim)>1) {
y<-switch(decorr.method,
cholesky=decorr.chol(varsim),
polar=decorr.polar(varsim),
inverse=decorr.inverse(varsim))
if(y$xerr==0) ymat<-y$y else xerr<-y$xerr
} else ymat<-1/sqrt(varsim)
pde<-yobs
if(xerr==0) {
#decorrelation of the simulations & the observations
decsim<-t(ymat)%*%(matsim-moysim)
decobs<-t(ymat)%*%(yobs-moysim)
#Computing the pde
for(i in 1:dim(yobs)[2]) {
tcomp<-apply(decsim,2,"<",decobs[,i])
if(!is.matrix(tcomp)) tcomp<-t(as.matrix(tcomp))
ycal<-rowMeans(tcomp)
pde[,i]<-ycal
}
}
return(list(xerr=xerr,pde=pde))
}
####################################################################################
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