## Ftp.iitm.ac.in

Title Normalised prediction distribution errors for nonlinear mixed-effect models
Author Emmanuelle Comets, Karl Brendel, Thi Huyen Tram Nguyen, France Mentre.

Maintainer Emmanuelle Comets <

[email protected]>
Description Routines to compute normalised prediction distribution
errors, a metric designed to evaluate non-linear mixed effectmodels such as those used in pharmacokinetics and pharmacodynamics
’global.R’ ’NpdeData.R’ ’NpdeRes.R’ ’NpdeObject.R’’func_methods.R’ ’func_plots.R’ ’main.R’ ’zzz.R’
npde-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

dist.pred.sim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

npde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

npde.cens.method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

npde.decorr.method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . npde.graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . npde.save . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . npdeControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . npdeData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NpdeData-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NpdeObject-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NpdeSimData-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . plot.NpdeData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . plot.NpdeObject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . set.plotoptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . showall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . simtheopp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . simvirload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . skewness
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
theopp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . virload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Normalised prediction distribution errors for nonlinear mixed-effectmodels
Routines to compute normalised prediction distribution errors, a metric designed to evaluate non-linear mixed effect models such as those used in pharmacokinetics and pharmacodynamics
See the documentation for npde or autonpde for details. A comprehensive user manual is providedin the inst directory of the package, along with a document illustrating the different graphs andgraphical options. Please refer to these two guides for details, and send all comments and bugreports to Emmanuelle Comets (<

[email protected]>).

Emmanuelle Comets, Karl Brendel and France Mentre
Maintainer: Emmanuelle Comets <

[email protected]>
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F. Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

E. Comets, K. Brendel, and F. Mentre. Computing normalised prediction distribution errors toevaluate nonlinear mixed-effect models: the npde add-on package for R. Computer Methods andPrograms in Biomedicine,90:154–66, 2008.

E. Comets, K. Brendel, and F. Mentre. Model evaluation in nonlinear mixed effect models, withapplications to pharmacokinetics. Journal de la Societe Francaise de Statistique,151:106–28, 2010.

T.H. Nguyen, E. Comets, and F. Mentre. Extension of NPDE for evaluation of nonlinear mixedeffect models in presence of data below the quantification limit with applications to HIV dynamicmodel. Journal of Pharmacokinetics and Pharmacodynamics, in press, 2012.

# x<-autonpde(theopp,simtheopp,1,3,4,boolsave=FALSE)# x$npde
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 thedistribution of npde under the null hypothesis.

number of datasets (defaults to 100 or to the number of replications if it issmaller)
additional arguments. Currently only the value of calc.pd and calc.npde may bepassed on, and will override their corresponding value in the "options" slot ofnpdeObject
an object of class NpdeObject; the ["results"] slot will contain pd and/or npde for a sample of thesimulated datasets (depending on whether calc.pd/calc.npde are ), stored in pd.sim and/or npde.sim
Emmanuelle Comets <

[email protected]>
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F. Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

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 npdeplot(x,plot.type="ecdf",bands=TRUE,approx.pi=TRUE)# defaults to computing the pd and npde for 100 simulated datasets (in the theophylline example, this uses all the simulated datasets)x<-dist.pred.sim(x)# Use the npde from the simulated datasets to obtain a prediction interval on the empirical cdfplot(x,plot.type="ecdf",bands=TRUE,approx.pi=FALSE)
Performs a global test on npde (default) or pd
gof.test.NpdeObject(object, which = "npde",
an object (currently has methods for types numeric, NpdeRes and NpdeObject)
whether the tests should be performed for npde (default), pd or npd (normalisedpd)
whether parametric or non-parametric tests should be applied
additional arguments passed on to the function; special arguments are na.action,which controls how to handle NAs in the results verbose (ifFALSE, suppresses printing of the results) and covsplit which requests thetests to be performed split by categories or quantiles of the data. If covsplitis TRUE, continuous covariates will be split in 3 categories (<Q1, Q1-Q3, >Q3)(see details in the PDF documentation), but this behaviour can be overriden bypassing the argument ncat=XXX where XXX is the number of categories to di-vide the continuous covariates in.

If object is an NpdeObject and an argument covsplit=TRUE is given in . . . , in addition to theglobal descriptive statistics and tests, tests will be performed for each covariate in which.cov. Thisargument can be set in . . . ; barring an explicit specification, the component which.cov of the prefsslot for a NpdeObject object will be used. The default value is which.cov="all", which producestests for each covariate in the dataset. Two additional dataframes will then be present:
cov.stat descriptive statistics and test p-values split by covariate and by categories
cov.p.value p-values split by covariate; for each covariate, two tests are performed: the first test is
a correlation test for continuous covariates and a Chi-square test for categorical covariates; thesecond test is defined using the p-values of the global tests split by each category, and applinga Bonferroni correction to obtain an overall p-value (see PDF documentation for details)
The p.value elements is a named vector with four components:
p.mean p-value for the mean test (Wilcoxon test if parametric=FALSE, Student test if paramet-
p.var p-value for the variance test (parametric=FALSE, Fisher test if parametric=TRUE)
p.dist p-value for the distribution test (XXX if parametric=FALSE, XXX if parametric=TRUE)
p.global p-value for the global test (combination of the mean, variance and distribution tests with
p.value p-values for several tests (see below)
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

K. Brendel, E. Comets, C. Laffont, and F.Mentre. Evaluation of different tests based on obser-vations for external model evaluation of population analyses. Journal of Pharmacokinetics andPharmacodynamics, 37:49–65, 2010.

a numeric vector containing the values whose kurtosis is to be computed. NAvalues are removed in the computation.

If N = length(x), then the kurtosis of x is defined as:
N sumi(xi − mean(x))4(sumi(xi − mean(x))2)( − 2)−
G. Snedecor, W. Cochran. Statistical Methods, Wiley-Blackwell, 1989
Compute normalised prediction distribution errors
These functions compute normalised prediction distribution errors (npde) and optionally predictiondiscrepancies (pd). npde asks the user the name and structure of the files containing the data, usingpdemenu, while autonpde takes these variables and others as arguments.

autonpde(namobs, namsim, iid, ix, iy, imdv = 0, icens =
0, icov = 0, iipred = 0, boolsave = TRUE, namsav ="output", type.graph = "eps", verbose = FALSE,calc.npde=TRUE, calc.pd=TRUE, decorr.method ="cholesky", cens.method = "cdf", units =list(x="",y=""), detect=FALSE, ties=TRUE)
name of the file containing the observed data, or a dataframe containing theobserved data (in both cases, the column containing the various data requiredfor the computation of the pde can be set using the arguments iid,ix and iybelow)
name of the file containing the simulated data, or a dataframe containing thesimulated data (the program will assume that subject ID are in column 1 andsimulated Y in column 3, see User Guide)
name/number of the column in the observed data containing the patient ID; ifmissing, the program will attempt to detect a column named id
name/number of the column in the observed data containing the independentvariable (X); ; if missing, the program will attempt to detect a column named X
name/number of the column in the observed data containing the dependent vari-able (Y); if missing, the program will attempt to detect a column with the re-sponse
name/number of the column containing information about missing data (MDV),defaults to 0 (column not present)
name/number of the column containing information about censored data (cens),defaults to 0 (column not present)
name/number of the column(s) containing covariate information defaults to 0(no covariates)
name/number of the column(s) with individual predictions (ipred), defaults to 0(individual predictions not available)
a list with components x, y and cov (optional), specifying the units respectivelyfor the predictor (x), the response (y), and the covariates (a vector of lengthequal to the number of covariates). Units will default to (-) if not given.

a boolean controlling whether automatic recognition of columns in the datasetis on, defaults to FALSE
a boolean (TRUE if graphs and results are to be saved to a file, FALSE other-wise), defaults to TRUE
name of the files to which results are to be saved (defaults to "output", whichwill produce a file called output.eps (if the default format of postscript is kept,see type.graph) for the graphs and a file called output.npde for the numericalresults (see value)
type of graph (one of "eps","jpeg","png","pdf"), defaults to postscript ("eps")
a boolean (TRUE if npde are to be computed, FALSE otherwise), defaults toTRUE
a boolean (TRUE if pd are to be computed, FALSE otherwise), defaults to TRUE
a character string indicating the method used to handle censored data (see defaults to cdf
a character string indicating the method used to decorrelate observed and sim-ulated data in the computation of npde (see defaults tocholesky
a boolean (if FALSE, the distributions of pd and npde are smoothed by jitteringthe values so that there are no ties), defaults to TRUE
a boolean (TRUE if messages are to be printed as each subject is processed,FALSE otherwise), defaults to FALSE
Both functions compute the normalised prediction distribution errors (and/or prediction discrepan-cies) in the same way. npde is an interactive function whereas autonpde takes all required input asarguments.

When the computation of npde fails because of numerical problems, error messages are printed out,then pd are computed instead and graphs of pd are plotted so that the user may evaluate why thecomputation failed.

The function also prints out the characteristics of the distribution of the npde (mean, variance,skewness and kurtosis) as well as the results of the statistical tests applied to npde. In addition, ifboolsave is TRUE, two files are created:
results file the numerical results are saved in a file with extension .npde (the name of which is given
by the user). The file contains the components id, xobs, ypred, npde, pd stored in columns
graph file the graphs are saved to a file with the same name as the results file, and with extension
Emmanuelle Comets <

[email protected]>
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F. Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

x<-autonpde(theopp,simtheopp,1,3,4,boolsave=FALSE)x
# Calling autonpde with names of files to be read from disk
write.table(theopp,"theopp.tab",quote=FALSE,row.names=FALSE)write.table(simtheopp,"simtheopp.tab",quote=FALSE,row.names=FALSE)x<-autonpde(namobs="theopp.tab", namsim="simtheopp.tab", iid = 1,ix = 3, iy = 4, imdv=0, boolsave = FALSE)
head(x["results"]["res"])
Specifies the method used to handle censored data (data below the limit of quantification LOQ)
More details can be found in the PDF documentation.

The following methods are available in the npde library:
omit pd and npde for censored data will be set to NA
cdf for an observation ycens_ij under the LOQ, a pd_ij will be imputed in the uniform distribution
[0-pLOQ_ij] where pLOQ_ij is the probability that y_ij is below LOQ, according to the model;the predictive distribution will then be used to obtain a corresponding y*_ij. This is alsoperformed for all simulated data, and the npde are then computed on the completed datasetcontaining the observed y_ij for the uncensored data and the y*_ij imputed for the censoreddata. This method is the default.

ipred an observation ycens_ij is replaced by the individual prediction according to the model
(ipred, which must be present in the dataset). Simulated data are left untouched.

ppred an observation ycens_ij is replaced by the population prediction according to the model.

loq an observation ycens_ij is replaced by the value of the LOQ. Simulated data are left untouched.

K. Brendel, E. Comets, C. Laffont, C. Laveille, and F. Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

Specifies the method used to decorrelate observed and simulated data
More details can be found in the PDF documentation.

Decorrelation requires computing the square root of the inverse of the individual variance-covariancematrix Vi. The following methods are available in the npde library:
cholesky decorrelation is performed through the Cholesky decomposition (default)
inverse decorrelation is performed by inverting Vi through the eigen function
polar the singular-value decomposition (svd) is used
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F. Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

Save the graphs for a NpdeObject object to a file
optional arguments to replace options in object
The following options can be changed by passing the appropriate arguments: namsav (string givingthe root name of the files, an extension depending on the type of graph will be added), namgr (stringgiving the full name of the file), type.graph (one of "eps", "pdf", "jpeg", "png")
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

Save the results contained in a NpdeObject object to a file
optional arguments to replace options in object
The following options can be changed by passing the appropriate arguments: namsav (string givingthe root name of the files, an extension .npde will be added), nameres (string giving the full nameof the file)
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

Set, replace and check options for an NpdeObject
npdeControl(boolsave = TRUE, namsav = "output",
type.graph = "eps", verbose = FALSE, calc.npde = TRUE,calc.pd = TRUE, decorr.method = "cholesky", cens.method= "omit", ties = TRUE, sample = FALSE)
whether to save the results (a file containing the numerical results and a file withthe graphs)
the root name of the files to save to (the file with the results will be namedROOTNAME.npde and the graphs will be saved to ROOTNAME.format whereformat is given by the type.graph argument)
type of graph to save to (one of "eps", "pdf", "jpeg", "png")
a boolean; if TRUE, a message is printed as the computation of the npde beginsfor each new subject
the method used to decorrelate simulated and observed data (see
the method used to handle censored data (see
if FALSE, a smoothing will be applied to prediction discrepancies to avoid ties
if TRUE, the test on the pd will be performed after randomly sampling only pdper subject
This function is used to create a NpdeData object, representing a longitudinal data structure, and fillit with data from a dataframe or a file on disk
npdeData(name.data,header=TRUE,sep="",na.strings=c(".","NA"),name.group,
name.predictor,name.response,name.covariates,name.cens,name.miss,name.ipred,units=list(x="",y="",covariates=c()),detect=TRUE,verbose=FALSE)
name of the file containing the observed data, or a dataframe containing theobserved data
strings to be considered as indicating NA
boolean indicating whether the file has a header (mandatory if detect is TRUE)
name/number of the column in the observed data containing the patient ID (ifmissing and detect is TRUE, columns named id, subject or sujet (regardless ofcase) will be assumed to contain this information)
name.predictor name/number of the column in the observed data containing the independent
variable X (if missing and detect is TRUE, columns named xobs, time, dose, x,temps, tim (regardless of case) will be assumed to contain this information)
name/number of the column in the observed data containing the dependent vari-able Y (if missing and detect is TRUE, columns named yobs, response, resp,conc, concentration (regardless of case) will be assumed to contain this infor-mation)
name/number of the column containing information about missing data (MDV)(if missing and detect is TRUE, column called mdv or miss (regardless of case)will be assumed to contain this information)
name/number of the column containing information about censored data (cens)(if missing and detect is TRUE, column with a name containing cens (regardlessof case) will be assumed to contain this information)
name/number of the column(s) containing covariate information (optional)
name/number of the column(s) with individual predictions (ipred) (if missingand detect is TRUE, column with a name containing ipred (regardless of case)will be assumed to contain this information)
a list with components x, y and cov (optional), specifying the units respectivelyfor the predictor (x), the response (y), and the covariates (a vector of lengthequal to the number of covariates). Units will default to (-) if not given.

a boolean controlling whether automatic recognition of columns in the datasetis on, defaults to TRUE
whether to print warning messages, defaults to FALSE (set to TRUE to checkhow data is being handled)
Emmanuelle Comets <

[email protected]>
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F. Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

x<-npdeData(theopp) # Automatic detectionprint(x)x<-npdeData(theopp,name.group="ID",name.predictor="Time",name.response="Conc",name.covariates=c("Wt"),units=list(x="hr",y="mg/L",covariates="kg")) # Explicitprint(x)plot(x)
Class "NpdeData" representing the structure of the longitudinal data
NpdeData objects are typically created by calls to and contain the following slots:
name.data character string giving the name of the dataset
name.group character string giving the name of the grouping term (ID)
name.predictor character string giving the name of the predictor (X)
name.response character string giving the name of the response (Y)
name.cens character string giving the name of the censoring indicator
name.mdv character string giving the name of the missing data indicator
name.covariates vector of character string giving the name(s) of the covariates
name.ipred character string giving the name of the individual predictions
units (optional) a list with the units for X, Y, and covariates
ntot.obs total number of non-missing observations
nind.obs vector of size N giving the number of non-missing observations for each subject
icens index of censored observations (non-missing)
not.miss a vector of boolean indicating for each observation whether it is missing (FALSE) or
npdeData(name.data): Create a new object from dataset name.data
print(npde.data): Prints a summary of object npde.data
show(npde.data): Prints a short summary of object npde.data
showall(npde.data): Prints a detailed summary of object npde.data
plot(npde.data): Plots the data in npde.data. More details can be found in
summary(npde.data): Returns a summary of object npde.data in list format
set.plotoptions(npde.data): Sets options for graphs of npde.data (internal method used in plots)
NpdeObject objects are typically created by calls to or They contain the followingslots:
data an object of class NpdeData, containing the observed data
sim.data an object of class NpdeSimData, containing the simulated data
res an object of class NpdeRes, containing the results
prefs a list of graphical preferences for the plots
show(x): Prints a short summary of object
showall(x): Prints a detailed summary of object
plot(x): Diagnostic and other plots. More details can be found in
summary(x): Returns a summary of object x in list format
gof.test(x, which="npde", parametric=TRUE, .): Returns goodness-of-fit tests
set.plotoptions(x): Sets options for graphs (internal method used in plots)
Class "NpdeSimData" representing the structure of the longitudinaldata
A longitudinal data structure, with simulated data
NpdeSimData objects are created by associating an NpdeData object with matching simulated data,and they contain the following slots.

name.simdata character string giving the name of the dataset
datsim a dataframe containing the simulated data, with columns: idsim (subject id), irsim (replica-
tion index), xsim (simulated x), ysim (simulated response). After a call to or an additional column ydsim (decorrelated replicated data) will be added.

print(npde.simdata): Prints a summary of object npde.simdata
show(npde.simdata): Prints a short summary of object npde.simdata
showall(npde.simdata): Prints a detailed summary of object npde.simdata
unused, here for compatibility with the base plot function
additional graphical parameters to be passed on to the plot
The default plot is a spaghetti plot of all the data, with a line joining the observations for eachsubject. If censored data is present, it is shown with a different symbol and colour.

K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

x<-npdeData(theopp,name.group="ID",name.predictor="Time",name.response="Conc",name.covariates=c("Wt"),units=list(x="hr",y="mg/L",covariates="kg"))plot(x)
Plots the data and diagnostic plots in a NpdeObject object
unused, here for compatibility with the base plot function
additional graphical parameters, which when given will supersede graphicalpreferences stored in the object
K. Brendel, E. Comets, C. Laffont, C. Laveille, and F.Mentre. Metrics for external model evaluationwith an application to the population pharmacokinetics of gliclazide. Pharmaceutical Research,23:2036–49, 2006.

x<-autonpde(theopp,simtheopp,iid="ID",ix="Time", iy="Conc", boolsave=FALSE)plot(x)
This function is used to set options for graphs
an object of class NpdeData or NpdeObject
arguments to replace default arguments (currently ignored)
See documentation for a list of available options.

Emmanuelle Comets <

[email protected]>
Simulated data for the computation of normalised prediction distribu-tion errors
The simtheopp dataset contains 100 simulations using the design of dataset These simu-lations are used to compute npde. The control file used to perform the simulations can be found inthe subdirectory ’doc’ within the library npde.

This data frame contains the following columns:
ID an ordered factor with levels 1, . . . , 12 identifying the subject on whom the observation was
made. The ordering is first by simulation then by increasing time.

xsim time since drug administration when the sample was drawn (hr).

ysim simulated theophylline concentration (mg/L).

See for a description of the original dataset.

The simulated data was obtained using the software NONMEM. A one-compartment model was fitto the data. An exponential interindividual variability was assumed for the three parameters (ab-sorption rate constant ka, volume of distribution V and clearance CL) and a combined additive andproportional residual error model was usd. The estimated parameters were then used to simulate 100datasets with the same structure as the original dataset. Thus, for each observation in the originaldataset, the simulated dataset contains 100 simulations under the model used for the estimation.

This dataset is provided so that users can figure out what type of data is needed for the computationof prediction distribution errors. More information can be found in the User Guide distributed alongwith this package, which contains a run-through of the theophylline example.

Boeckmann, A. J., Sheiner, L. B. and Beal, S. L. (1994), NONMEM Users Guide: Part V, NON-MEM Project Group, University of California, San Francisco.

# Plotting the simulated data for subject 1 in the first simulationplot(ysim[2:12]~xsim[2:12],data=simtheopp,xlab="Time after dose (hr)",ylab="Theophylline concentration (mg/L)",type="l",main="Example of simulated data for subject 1")
# Plotting a 90% prediction interval for the observations in theopp# using the simulated data in simtheopp# note : differences in doses between subjects are not taken into accountdata(theopp)xpl<-c(0,0.25,0.5,1,2,3.5,5,7,9,12,24)xpl1<-list(c(0,0.1),c(0.2,0.4),c(0.5,0.65),c(0.9,1.2),c(1.9,2.2),c(3.4,4),c(4.9,5.2),c(6.9,7.2),c(8.8,9.4),c(11.5,12.2),c(23.7,24.7))
ypl<-cbind(xpl=xpl,binf=xpl,median=xpl,bsup=xpl)for(i in 1:(length(xpl))) {
vec<-simtheopp$ysim[simtheopp$xsim>=xpl1[[i]][1] &simtheopp$xsim<=xpl1[[i]][2]]ypl[i,2:4]<-quantile(vec,c(0.05,0.5,0.95))
}plot(Conc~Time,data=theopp,xlab="Time after dose (hr)",ylab="Theophylline concentration (mg/L)")lines(ypl[,1],ypl[,3],lwd=2)lines(ypl[,1],ypl[,2],lty=2)lines(ypl[,1],ypl[,4],lty=2)
Simulated data for the computation of normalised prediction distribu-tion errors, viral load example
The simvirload dataset contains 1000 simulations using the design of dataset Thesesimulations are used to compute npde.

This data frame contains the following columns:
ID an ordered factor with levels 1, . . . , 50 identifying the subject on whom the observation was
made. The ordering is first by simulation then by increasing time.

ysim simulated viral loads, in base 10 log-scale (cp/L).

See for a description of the original dataset.

The simulated data was obtained using the software R, as described in Nguyen et al. (2011).

Goujard, C., Barrail-Train, A., Duval, X., Nembot, G., Panhard, X., Savic, R., Descamps, D.,Vrijens, B., Taburet, A., Mentre, F., and the ANRS 134 study group (2010). Virological response toatazanavir, ritonavir and tenofovir/emtricitabine: relation to individual pharmacokinetic parametersand adherence measured by medication events monitoring system (MEMS) in naive HIV-infectedpatients (ANRS134 trial). International AIDS Society 2010, Abstr WEPE0094.

Nguyen, T., Comets, E., Mentre, F. (2010). Prediction discrepancies (pd) for evaluation of modelswith data under limit of quantification. 20th meeting of the population approach group in Europe(PAGE), Athens, Greece. Abstr 2182.

a numeric vector containing the values whose skewness is to be computed. NAvalues are removed in the computation.

If N = length(x), then the skewness of x is defined as
G. Snedecor, W. Cochran. Statistical Methods, Wiley-Blackwell, 1989
The theopp data frame has 132 rows and 5 columns of data from an experiment on the pharma-cokinetics of theophylline.

This data frame contains the following columns:
ID an ordered factor with levels 1, . . . , 12 identifying the subject on whom the observation was
made. The ordering is by Time at which the observation was made.

Dose dose of theophylline administered orally to the subject (mg).

Time time since drug administration when the sample was drawn (hr).

Conc theophylline concentration in the sample (mg/L).

Boeckmann, Sheiner and Beal (1994) report data from a study by Dr. Robert Upton of the kineticsof the anti-asthmatic drug theophylline. Twelve subjects were given oral doses of theophyllinethen serum concentrations were measured at 11 time points over the next 25 hours. In the presentpackage npde, we removed the data at time 0.

These data are analyzed in Davidian and Giltinan (1995) and Pinheiro and Bates (2000) using atwo-compartment open pharmacokinetic model.

These data are also available in the library datasets under the name Theoph in a slightly modifiedformat and including the data at time 0. Here, we use the file in the format provided in the NONMEMinstallation path (see the User Guide for that software for details).

Boeckmann, A. J., Sheiner, L. B. and Beal, S. L. (1994), NONMEM Users Guide: Part V, NON-MEM Project Group, University of California, San Francisco.

Davidian, M. and Giltinan, D. M. (1995) Nonlinear Models for Repeated Measurement Data, Chap-man & Hall (section 5.5, p. 145 and section 6.6, p. 176)
Pinheiro, J. C. and Bates, D. M. (2000) Mixed-effects Models in S and S-PLUS, Springer (AppendixA.29)
#Plotting the theophylline dataplot(Conc~Time,data=theopp,xlab="Time after dose (hr)",ylab="Theophylline concentration (mg/L)")
Simulated HIV viral loads in HIV patients
This is simulated data, based on real data obtained in a phase II clinical trial supported by the FrenchAgency for AIDS Research, the COPHAR 3-ANRS 134 trial (Goujard et al., 2010). The originalstudy included 35 patients, who received a once daily dose containing atazanavir (300 mg), ritonavir(100 mg), tenofovir disoproxil (245 mg) and emtricitabine (200 mg) during 24 weeks. Viral loadswere measured 6 times over a treatment period of 24 weeks (day 0, 28, 56, 84, 112, 168).

The datasets were generated in a simulation study designed to evaluate the new method proposedto handle BQL data (Nguyen et al., 2011). Data was simulated using a simple bi-exponential HIVdynamic model describing the two-phase decline of viral load during anti-retroviral treatment.

The virload data frame has 300 rows and 4 columns of data. The dataset was then censored attwo different LOQ levels (LOQ=20 or 50~copies/mL) to generate two datasets containing differentproportions of BQL data, creating the data frames virload20 andvirload50 respectively.

This data frame contains the following columns:
ID an ordered factor with levels 1, . . . , 50 identifying the subject on whom the observation was
made. The ordering is by Time at which the observation was made.

Time time since the beginning of the study (days).

Log_VL logarithm (base 10) of the viral load (copies/L).

cens indicator variable (cens=1 for censored data, cens=0 for observed data)
Goujard, C., Barrail-Train, A., Duval, X., Nembot, G., Panhard, X., Savic, R., Descamps, D.,Vrijens, B., Taburet, A., Mentre, F., and the ANRS 134 study group (2010). Virological response toatazanavir, ritonavir and tenofovir/emtricitabine: relation to individual pharmacokinetic parametersand adherence measured by medication events monitoring system (MEMS) in naive HIV-infectedpatients (ANRS134 trial). International AIDS Society 2010, Abstr WEPE0094.

Nguyen, T., Comets, E., Mentre, F. (2010). Prediction discrepancies (pd) for evaluation of modelswith data under limit of quantification. 20th meeting of the population approach group in Europe(PAGE), Athens, Greece. Abstr 2182.

#Plotting the dataplot(Log_VL~Time,data=virload,xlab="Time (d)",ylab="Viral loads, base 10 logarithmic scale
plot(Log_VL~Time,data=virload50,xlab="Time (d)",ylab="Viral loads, base 10 logarithmic scale
[<-,NpdeData-method (NpdeData-class),
plot,NpdeObject (NpdeObject-class), plot.NpdeData, plot.NpdeObject, print,NpdeData-method (NpdeData-class),
set.plotoptions, set.plotoptions,NpdeData-method
showall, showall,NpdeData-method (showall), showall,NpdeObject-method
showall,NpdeSimData-method (showall), showall.NpdeData (showall), showall.NpdeObject (showall), showall.NpdeRes (showall), showall.NpdeSimData (showall), simtheopp, simvirload, skewness, summary,NpdeData-method

Source: ftp://ftp.iitm.ac.in/cran/web/packages/npde/npde.pdf

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