$DESIGN

$DESIGN, $DESI

Instructions for Clinical Trial Design Evaluation and Optimization

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 $DESIGN  Record Options
         [APPROX=[FO|FOI|FOCE|LAPLACE|LAPLACEI]]
         [OFVTYPE=[0|1|2|3|4|5|6|7|8]]
         [OFVDIMSCALED=[0|1]]
         [GROUPSIZE=n]
         [FIMTYPE=[0|1|2|3]]
         [FIMDIAG=[0|1|2|3]]
         [VARCROSS=[0|1]]
         [EOPTD=1]
         [SEED=n]
         [CLOCKSEED=[0|1]]
         [MODE=[0|1|2|3]]
         [DATASIM=[0|1]]
;#  Additional Control Options for $DESIGN
         [SIGL=n]
         [SIGLO=n]
         [ABORT|NOABORT|NOHABORT]
         [MAXEVALS=n]
         [PRINT=n]
         [NUMERICAL|NONUMERICAL]
         [LIKELIHOOD|-2LOGLIKELIHOOD|-2LL]
         [SLOW|NOSLOW|FAST]
         [POSTHOC|NOPOSTHOC]
         [NOPRIOR=[0|1]]
         [FILE=filename]
         [FORMAT|DELIM=s3]
         [FNLETA=n]
;# Options for Setting up Types of Optimal Design
         [NELDER]
         [FEDOROV]
         [RS]
         [STGR]
         [DISCRETE]
         [DISCRETE_RS]
         [DISCRETE_SG]
         [DESEL=label]
         [DESELSTRAT=label]
         [DESELMIN=label]
         [DESELMAX=label]
         [NMIN=label]
         [NMAX=label]
         [STRAT=label]
         [STRATF=label]

;# Example
 $DESIGN APPROX=FOCEI MODE=1 NELDER FIMDIAG=0
         DATASIM=1 GROUPSIZE=32 OFVTYPE=0

The above example will produce the most empirical, clinical trial simulation (CTS) style covariances, complete with simulated ETAs and eps, and standard FIM is assessed. If FIMDIAG>0, then a y-expectation covariance will be evaluated, but mode will be evaluated with the simulated data.

Discussion

The optimal design process can help you in designing or evaluating a clinical trial. It may be desired to evaluate specified time points, or find the optimal time points, dose levels, and number of time points appropriate for a particular sub-design, etc. The design algorithms have been modeled after POPED by Hooker et al., and PFIM by Mentre et al. (see references [22-27]) in Introduction to NONMEM 7.

Another name for the record is $OPTDESIGN, or $OPT.

The following is a brief summary of the options. See Introduction to NONMEM 7 "Clinical Trial Design Evaluation and Optimization" for more details and examples. The options are grouped into the following sections:

$DESIGN Record Options
Additional Control Options for $DESIGN
Options for Setting up Types of Optimal Design

$DESIGN Record Options

APPROX

Default to "FO". The NLME approximation method is specified here. First order (no interaction) is the default, and the appropriate type of covariance matrix is evaluated or used in optimization of the design. Other options are:

FOI: First order interaction with interaction"
FOCE: first order conditional estimation
FOCEI: first order conditional estimation with interaction
LAPLACE: Laplace conditional estimation
LAPLACEI: Laplace conditional estimation with interaction

OFVTYPE

OFVTYPE=1 by default. The objective function types are comparable to those of PopED:

0,1,3,4,5: design type: d-optimality, -log(det(FIM)), where FIM=Fisher Information Matrix (inverse of variance-covariance).
2: design type: a-optimality, -1/tr(1/FIM)
6: design type: ds-optimality, -log(det(FIM))+log(det(FIMunintersting)) To identify parameters as uninteresting, place UNINT at the parameter in the same manner you would place FIX.

To identify parameters as uninteresting, place UNINT at the parameter in the same manner you would place FIX. For example:
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$THETA 0.1 (0.5 UNINT) 0.4 $OMEGA BLOCK(2) 0.1 UNINT ;# Sets entire block "uninteresting" 0.01 0.1
7: design type: r-optimality (relative standard error),-1/tr(sqrt(1/FIM)/Paramer))
8: optimal design type: Individual Bayesian FIM, -log(det(Bayes FIM)), as described in the PFIM 4.0 manual.

In this case, the ETC() are optimized, as listed in the .phi table. The ETC() are the conditional variance-covariances of the individual’s parameters. If just one subject (or subject type) is in the data file, then the criterion is that one subject’s Bayesian FIM. If more than one subject (or subject type), then the Bayesian FIM of all the subjects, averaged together, is the criterion for design.

The change in variances with each printed iteration are listed in the additional raw file (.ext extension by default). The shrinkage information is reported in the main report file, and the individual empirical Bayes variances (ETC()) are reported in the .phi file. For shrinkage information, only the following have meaning:
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EBVSHRINKSD(%) EBVSHRINKVR(%) EPSSHRINKSD(%) EPSSHRINKVR(%)
When OFVTYPE=8, the change of average individual conditional variances (average empirical Bayes conditional variance) with each iteration are shown in the root.bfm file (where root is name of control stream file), and the final one on the -1000000000 line, during an optimization. The RAW file (by default named root.ext) shows only the starting, and final values of the standard errors of population parameters, as extra information.
9: Same as option 2, and using the UNINT filter.
10: Same as option 7, and using the UNINT filter.

OFVDIMSCALED (NM76)

OFVDIMSCALED=0 by default. If OFVDIMSCALED=1, then the objective function is scaled to be per parameter, the dimension of the FIM, as follows:

0,1,3,4,5: design type: D-optimality, -log(det(FIM))/D, where D is the dimension of the FIM.
2: design type: a-optimality, -1/tr(1/FIM)
6: design type: DS-optimality, (-log(det(FIM))+log(det(FIMuninteresting)))/(D-U) where U=number of uninteresting parameters.
7: design type: R-optimality (relative standard error), -1/(tr(sqrt(1/FIM)/Parameter))/D)
8: -log(det(Bayes FIM))/D
9: design type: A-optimality, -1/(tr(1/FIM)/(D-U))
10: -1/(tr(sqrt(1/FIM)/Parameter))/(D-U))

GROUPSIZE

GROUPSIZE=1 by default. The GROUPSIZE is comparable to that of POPED, in which the FIM is multiplied by this number to provide the subject number size of the dataset template. For a template of one subject, GROUPSIZE would then offer the variance-covariance expected from GROUPSIZE number of subjects.

FIMTYPE or FIMDIAG

FIMTYPE or FIMDIAG may be set to the following, and corresponds to fimcalc.type in POPED:

0 (default): Full information matrix Uses finite difference assessment for THETA, OMEGA, and SIGMA variances and covariances. No assumptions are made about whether the approximated variance (C=h*SIGMA*h+g*OMEGA*g, as described in Guide I, section E.2) used in FO is dependent on any THETAs via h and g.
1: Create a block diagonal information matrix of the estimates that assumes there is neglible correlation between THETAs and (OMEGAs,SIGMAs). Also, independence of variance C with respect to THETAs is assumed (that is, h and g’s dependence on theta is ignored) . This is similar to the fim.calc.type=1 option in POPED or the diagonal option in PFIM, and performs finite difference at the y=E(f) position on the thetaxtheta portion of the information matrix (for THETAs that are mu referenced, an analytical evaluation is made, and increases speed considerably), analytical evaluation of (SIGMAS OMEGAS)x(SIGMAS OMEGAS) portion of information matrix, and THETAs x (SIGMAS OMEGAS) cross variances are set to 0.
2: Create a block information matrix, by performing finite difference on the thetaxtheta portion of the information matrix, independence of variance C with respect to THETAs is not assumed (that is, h and g’s dependence on theta is not ignored), performs analytical evaluation of (SIGMAS OMEGAS)x(SIGMAS OMEGAS) portion of information matrix, and THETAs x (SIGMAS OMEGAS) are cross variances set to 0.
3: Create a full information matrix by performing finite difference on the Theta x Theta portion of the information matrix, and on the THETAs x (SIGMAS OMEGAS) portion of the information matrix, and performs analytical evaluation of (SIGMAS OMEGAS)x(SIGMAS OMEGAS) portion of information matrix.

For the film.calc.type=4 equivalent, see VARCROSS below.

With FIMTYPE=1, it is worth while to mu reference all non-fixed THETAs. This will allow analytical evaluation of the thetaXtheta portion of the information matrix, and can provide considerable speed improvement. Even derivatives of mu-referenced THETAs with associated OMEGA() fixed to 0 will be analytically evaluated.

VARCROSS

VARCROSS=0 (default): standard NONMEM residual variance modeling, as in
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$PK … IPRED=F Y=IPRED+EPS(1)+IPRED*EPS(2) … $SIGMA 0.5 0.15
as residual variance
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var=SIGMA(1,1)+IPRED*IPRED*SIGMA(2,2)
To model variance as squared residual standard deviation:
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var=(sqrt(SIGMA(1,1))+IPRED*sqrt(SIGMA(2,2))**2= SIGMA(1,1)+2*sqrt(SIGMA(1,1)*SIGMA(2,2))*IPRED+IPRED*IPRED*SIGMA(2,2)
as in the manner of the PFIM 4.0 software, one would normally model the residual variance using THETAs, such as:
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$PK … IPRED=F W=SQRT(THETA(4))+SQRT(THETA(5))*IPRED Y=IPRED+W*EPS(1) … $SIGMA (1.0 FIXED)
However, when FIMTYPE=1 is used, the theta(4) and theta(5) are not identified as Sigma type parameters, and the appropriate contribution by theta(4) and theta(5) is not estimated. To provide an interpretation of residual variance incorporating the the cross-term
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2*sqrt(SIGMA(1,1)*SIGMA(2,2))*IPRED
model using the SIGMAS as shown in the first example, and set VARCROSS to 1:
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$PK … IPRED=F Y=IPRED+EPS(1)+IPRED*EPS(2) … $SIGMA 0.5 0.15 … $DESIGN … VARCROSS=1 FIMTYPE=1
FIMTYPE=1 VARCROSS=1 is equivalent to fim.calc.type=4 in POPED, and diagonal option in PFIM. Note that the variances are still modeled, rather than the standard deviation form. See ..\examples\optdesign\warfarin_pfim.ctl for an example of its use.
VARCROSS=1: residual Standard Deviation Modeling VARCROSS=1 means to treat the residual variance model in the manner of PFIM 4.0, as described in the manual. FIMTYPE=1 VARCROSS=1 is equivalent to fim.calc.type=4 in POPED, and diagonal option in PFIM.

EOPTD=1

EOPTD=1 by default. For each iteration, this creates a random sample of THETAs, OMEGAs, or SIGMAs, using the prior information. $PRIOR NWPRI prior information is required, and PLEV=0.999 must be specified. Best used with STGR. See example optdesign16.

SEED

Default: 223345. Set the starting seed for any random samples to be created, whether for EOPTD=1, or for FOCE type FIM in creating random ETAs (see below).

CLOCKSEED

CLOCKSEED=0 by default. As of nm75, the actual starting seed will be 10000*(seconds after midnight)+SEED (SEED may be set to 0 for this purpose), if CLOCKSEED=1. This allows a control stream to produce different stochastic results for automated replications, without the need to modify the seed value in the control stream file in each replication.

MODE

Used for specifying data and prediction value type when specifying APPROX=FOCEI. In NONMEM report:

0 (default): FOCEI with data at F(ETAsim), and predicted function evaluated at f(ETAsim), is to be used.
1: FOCEI with data at F(ETAsim), and predicted function evaluated at the mode, f(ETAhat), is to be used (see below). The results are less satisfactory.
2: linearized FOCEI, with data at F(ETAsim)-G*ETAsim, and predicted function at F(ETAsim).
3: Evaluate at F(0) during conditional design assessment.

DATASIM

DATASIM=0 by default. Normally, y-expectation evaluation of the FIM is performed. To actually simulate data, set DATASIM=1, and along with APPROX=FOCEI, this will produce simulated ETAs as well.

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$DESIGN APPROX=FOCEI MODE=1 NELDER FIMDIAG=0 DATASIM=1 GROUPSIZE=32 OFVTYPE=0

produces the most empirical, “clinical trial simulation” (CTS) style covariances, complete with simulated ETAs and eps, and standard FIM is assessed. If FIMDIAG>0, then a y-expectation covariance will be evaluated, but mode will be evaluated with the simulated data.

Additional Control Options

The following options may be set within the $DESIGN record, and they operate exactly as their counterparts in the $EST record. Thus, the following are equivalent:

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  $DESIGN FIMDIAG=1 OFVTYPE=6 APPROX=FO
          MAXEVAL=9999 NOHABORT PRINT=20 SIGL=10 POSTHOC

  $DESIGN FIMDIAG=1 OFVTYPE=6 APPROX=FO
  $EST    MAXEVAL=9999 NOHABORT PRINT=20 SIGL=10 POSTHOC

The options are as follows.

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  SIGL
  SIGLO
  SIGL
  SIGLO
  ABORT/NOABORT/NOHABORT
  MAXEVAL
  MAXEVAL=0 ;# indicates design evaluation (the default)
  MAXEVAL>0 ;# indicates design optimization
  PRINT ;# control iteration printing during optimal design
  NUMERICAL/NONUMERICAL
  -2LL/LIKELIHOOD/LLIKELIHOOD
  SLOW/NOSLOW/FAST
  POSTHOC
  NOPRIOR
  FORMAT
  FILE
  FNLETA

Design evaluation example

The options described above can be used to set up the design criteria, and can be used for finding the best design parameters (optimal design), or for evaluating design parameters proposed by the user (design evaluation). We will consider a simple example of design evaluation, before we consider additional options needed for optimal design. Using the example of ..\examples\optdesign\warfarin_pfim.ctl, note the following record:

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$DESIGN GROUPSIZE=200 FIMTYPE=1 VARCROSS=1

The csv file contains only one subject (that is one subject type), but the subject number size may be specified with GROUPSIZE. Here, you request the variance-covariance one should expect from 200 subjects, all of the one particular subject type (equivalent time values, doses, covariates) defined in the csv file. You can have more than one subject in the csv, each with their own design (different doses, sample times, etc.). Also, by use of STRAT and STRATF (see below), one can desire a specific weighting of each subject type to contribute to the FIM.

FIMTYPE=1 means to evaluate the variance-covariance with the block-diagonal modality. VARCROSS=1 means to treat the residual variance model in the manner of PFIM 4.0, as described in the manual.

The intended result for this problem is essentially the FIM information and its derived components. In warfarin_pfim.coi, is the inverse covariance matrix (the FIM itself), for a sample size of 200 subjects. In the .res file, the -log(det(PFIM)) is given. Also, standard errors are given in report form here. The .ext file has essentially the same information is the .res file, but is in rows-column format. Much of these outputs (.res, .ext., .coi) are already a part of standard NONMEM outputs, they are now just recruited for optimal design and design evaluation.

Note the usual variance-covariance intended for an actual data set is not created, but rather the asymptotic, y-expectation evaluation version, since the $DESIGN record was specified. Much of the control stream setup is as is if one were performing an FO estimation analysis on a real data set, while the addition of the $DESIGN record then re-purposes the analysis for design evaluation (or optimization if MAXEVAL>0).

View the standard error and variance-covariance outputs in the NONMEM report file, .ext file, .cov, .cor, and .coi files. For optimal design, you can view the final optimal design in the final data set, which can be outputted with the $TABLE step (see Examples for Optimal Design).

Options for Setting up Types

The additional options for $DESIGN listed below are for optimizing parts of the design components. For example, the DESEL, DESELSTRAT, DESELMIN, DESELMAX can be specified for all the various design elements that you want optimized. It might be TIME for time samples, AMT for dose, or some type of covariate specific for the problem. Certainly, any combination of covariates can be requested to be optimized.

NELDER: Use Nelder method to search for optimal continuous parameters
FEDOROV: Use to find ideal set of discrete time points from a larger set of possible time points.
RS: Random Search method to find optimal continuous parameters
STGR: Stochastic Gradient method to find optimal continuous parameters
DISCRETE: Find optimal number of time points for each sub-design (subject template), and use NELDER method to find optimal continuous parameters.
DISCRETE_RS: Find optimal number of time points for each sub-design (subject template), and use RS method to find optimal continuous parameters.
DISCRETE_SG: Find optimal number of time points for each sub-design (subject template), and use STGR method to find optimal continuous parameters.

Data items must be specified to be optimized. This is done using the following options:

DESEL=label: The data item (column) that contains the design element (DESEL) values that are to be modified and optimized. For example, TIME column would indicate that you want times to be estimated.
DESELSTRAT=label: The data item (column) indicating stratification. The DESELSTRAT data item should contain integer indices to indicate what values are to be shared, and estimated together. If a record contains a value of 0 in the DESELSTRAT column, then this record is not included in the estimation process, and its value (say its time value in DESEL=TIME column) will not be changed. If the record contains a positive value, say 1, in DESELSTRAT, then all records with the value of 1 in DESELSTRAT will share the same time value (or whatever DESEL selected), estimated together. Those records with value 2 will be another set of records which will share a time value, etc. Thus, within a subject, there may be a PK record and a PD record which should share the same time value. Also, a group of subjects may share the same time values. Within a subject, times will be automatically sorted as they are changed, so that NONMEM's time ordering policy is not violated.
DESELMIN, DESELMAX: the data item (column) containing the minimal/maximal value. You must impose boundaries on the values that are being optimized. That is done with these two data items. Only those records with a stratification value >0 in DESELSTRAT column will require a min and max value, and only those records that define that stratification value for the first time.

All the above four DESEL items must be specified. They may be repeated for as many design elements are to be optimized. For example for times and amounts:

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  DESEL=TIME DESELMMIN=TMIN  DESELMAX=TMAX   DESELSTRAT=TSTRAT
  DESEL=AMT  DESELMIN=AMTMIN DESELMAX=AMTMAX DESELSTRAT=AMTSTRAT

NMIN, NMAX: the name of the data item (column) containing minimal/maximal number of time points to the subject. If NMIN<0 or NMAX<0, then most previous non-negative value is used. The NMIN and NMAX column are only used for the DISCRETE* analyses, to bound the number of time points that may be permitted for a given subject. With DISCRETE*, the total N of time points among all subjects is determined by the total number of time points whose MDV=0 in the starting data set.
STRAT=label: the data item (column) containing grouping or stratification number pertaining to that subject.
STRATF=label: The data item (column) containing starting fraction representation for the stratification value in column STRAT. If STRAT and STRATF are specified, and there is at least one STRAT value >0, then the SRATF values are optimized, and represent the weight to the contribution of that subject to the Information matrix. For STRAT<=0, then their STRATF values are not optimized, and remain fixed at their initial values, but are still used as weights to the information matrix. It is up to the user to ensure that the sum of STRATF values among unique STRAT values sum to 1. If value of STRATF<0.0, then that subject is not included in the assessment.

Additional $COVARIANCE Control Options

$DESIGN sets up the covariance step $COVARIANCE with option MATRIX=R UNCONDITIONAL. To specify additional controls, add in a $COV record, such as:

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$DESIGN FIMDIAG=1 OFVTYPE=6 APPROX=FO MAXEVAL=9999 NOHABORT PRINT=20 SIGL=10 POSTHOC
$COV PRINT=E

Record order

Same as $ESTIMATION or $SIMULATION.

References

Guide Introduction_7