14 Experimental design

Experimental design techniques are useful to assess what type of experiments or studies should be conducted to ensure an adequate level of information in the observed data to address the question(s) of interest. In this chapter we discuss and exemplify some of these techniques

14.1 Use of PopED

PopED is a well known optimal experimental design software that can be used both for population and individual studies based on nonlinear mixed-effect models. Methods, underlying PopED are described in Nyberg et al. (2012) and Foracchia et al. (2004). PopED is available as an R package on CRAN. The installer of IQR Tools will install the correct version automatically.

PopED comes with great flexibility for defining models and design specifications. However, the use is made overly complicated by a not well thought through R based interface to functions. The user either needs to be a PopED specialist or he/she will most likely make more or less critical mistakes, leading to wrong results and interpretations.

In order to make the important functionality of this optimal experiment design package available in a much more seamless manner, an interface between IQR Tools and PopED was developed. It benefits from the already available, intuitive, description of models and from the intuitive and easy to setup NLME model specification in IQR Tools. The user is not required to re-code models or NLME model specifications to use PopED. The same objects are used as if a user would like to perform a parameter estimation task.

The approach employed is to convert the IQR Tools model and design specifications to a PopED database. In the current version then standard PopED functions can be used on this database object. In a future version of IQR Tools dedicated functions will be provided to encapsulate the PopED functions, ensuring the easy creation of powerful and report-ready output in terms of tables and graphics.

Below an example for an IQR Tools run with PopED is given, which is based on an example model in the PopED R package. The same example is repeated in native PopED syntax. The results of both approaches are identical. The reader of this documentation can decide freely which syntax is easier to understand, review, validate, and re-use.

14.1.1 PopED / IQR Toolsinterface

We will consider a one compartment first order absorption PK model with a direct response, inhibitory IMAX, model as PD. This model in the IQRmodel syntax is available here. In a first step this model is loaded into R:

The study design to be evaluated is defined as a list with the named elements time, dosing, groupsize. The example implements a parallel design with three arms/groups with same observation times between groups and observables. N=4 subjects per group. Each group obtains a different dose (20, 40, and placebo).

The model specification for the NLME model is defined in an identical fashion as if the user would like to generate a NONMEM, MONOLIX, or NLMIXR model with IQRtools. The modelSpec variable defined below is a list whose construction is aided by the function modelSpec_IQRest():

The IQR Tools function IQRpopEDdb() takes as required input arguments the structural model, the desired design, and the NLME model specification modelSpec and converts this information to a PopED database object.

This PopED database object then can be used with standard PopED functions. To perform model predictions, design evaluations, etc. In a soon to be available IQR Tools version proper IQR Tools functionality will be provided to simplify the evaluation of designs, etc.

The main result of the above design evaluation are the predicted relative standard errors for the different parameters. Results for this example are shown below. The output is still fairly cryptic, as based on PopE functionality and also might require some further post-processing.

##    bpop[1]    bpop[2]    bpop[3]    bpop[5]    bpop[6]    bpop[7] 
##  18.144697  22.274804   9.626962  15.824337  22.126141  88.275210 
##     D[1,1]     D[2,2]     D[3,3]     D[5,5] 
##  87.071162 130.774210  57.766256  49.274222

PopED results can also be plotted, using PopED functionality.

This conlcudes the example for the current IQR Tools / PopED interface. We still have some work to do to provide adequate functionality to post-process PopED output to produce reasonably nice tables and graphics that are more informative. Stay tuned … it will come in one of the next IQR Tools versions!

In the following section the same example as the one above is shown in native PopED syntax.

14.1.2 Same example in PopED

In this section, the example from the previous section, conducted with the IQR Tools interface to PopED, is performed in the native PopED syntax. The example code was taken from the examples in the PopED package on CRAN.

In a first step the model prediction function needs to be defined. This can be done using ODEs or in this case by the analytic solution. Compare this model specification to that one here. It is far easier to make a mistake in the approach below:

In a second step parameters and their transformation needs to be defined. For more information, please see the PopED documentation.

In a third step the residual error model function is defined. Again, the interested reader is referred to the PopED documentation for further clarification.

The create.poped.database() function in PopED then is used to combine the above information and to define the design to be evaluated.

Once this is completed, we execute the same functions as in the previous IQR Tools / PopED example.

The results are basically identical to the previous example. The observed small differences stem from the fact that in this native PopED example an analytic solution was used, while in the other example the model was implemented using ordinary differential equations and the solutions to the model were integrated numerically.

##    bpop[1]    bpop[2]    bpop[3]    bpop[5]    bpop[6]    bpop[7] 
##  18.156519  22.290494   9.625457  15.824391  22.126653  88.276094 
##     D[1,1]     D[2,2]     D[3,3]     D[4,4] 
##  87.119440 130.861826  57.763841  49.274240

Same plot as in previous example:

14.2 Use of profile likelihood

Example to be added … soon!