Software

PopED V1.0: a prototype of D- and ED-optimal experiment design methods

In standard D-optimal design, where information is available only on parameters’ central tendencies, the same sampling times are assigned to each individual, without regard for that individual’s particular time course. However, one can envision situations where this generic sampling schedule is unsuitable for specific individuals in the population. In the population D-optimal designs that we are investigating, sampling schedules can be individualized, mostly based on covariate demographic information, when available. A population design is shown here superimposed to the response of a 12-subject population for a study involving the oral dosing of the anti-asthmatic agent theophylline.

In collaboration with our subcontractors at Gruppo Biomed Mod (University of Padova, Italy), we developed PopED (Population Experiment Design), a standalone software tool that performs D- and ED-optimality calculations for a series of compartmental models commonly used in population pharmacokinetics. This release is intended for Windows based machines and was developed using the Windows 2000 operating system and in the O-Matrix programming environment (Harmonic Software, Seattle, WA). The user will not need to purchase or otherwise run O-Matrix to access PopED’s capabilities: rather, a version of O-Matrix will be bundled with the PopED executable in one single download file. Figure 1, Figure 2, and Figure 3 show various screen shots from PopED, while Figure 4 describes the flowchart of the PopED computational engine. PopED currently accommodates eight pharmacokinetic models of varying complexity, summarized in Table 1. These sample models cover a very large percentage of commonly used pharmacokinetic models.

There are three main functions that the program performs (also shown in the window above, top to bottom):

• Design and Optimization Setup: here the user has the option to modify and select various options for the optimization of the experimental design. These options are:
• Experimental Design Variables, under which various options regarding which variables to optimize can be accommodated (homogeneous groups of individuals, model parameters, sampling patterns, covariates, etc.). The program is designed to make all this accessible to the user.
• Optimization Numerics, where the numerical options for optimization are adjusted. These options are explained in detail in the User Manual, as they are the most common source of confusion for the novice user. The large number of options is due to the fact that PopED includes a random search algorithm, which is a global optimizer.
• Optimization Types, where the kind of variables to be optimized can be selected by the user. Currently available optimization types are:
  • Samples per subject;
  • Sampling schedule;
  • Covariates;
  • Other variables.
• Reporting Options, which can be either graphical or text-based (log file).
  
  
• Design Methods: at the moment, only D- and ED-optimization are available. To the best of our knowledge, PopED is the first software tool to simultaneously provide both these two approaches to optimal experiment design of models involving linear differential equations.
  
  
• Analysis Tools: these include a capability to analyze a given design for optimality (based on Fisher information), or to optimize a design. The former possibility may be important if a design is based on common practice, and the user wishes to analyze its information content. Figure 3 shows parts of a sample optimization output from PopED.

The package can optimally design both the sampling pattern, i.e. the number of samples for each subject, and the sampling schedule, i.e. the location of the sampling times for each subject. It employs refined optimization techniques (adaptive random search and stochastic gradient) to design the sampling schedule and a discrete gradient-like technique to optimize the sampling pattern.

Obtaining PopED: The PopED development team is based at the Division of Pharmacokinetics and Drug Therapy, within the Department of Pharmaceutical Biosciences at Uppsala University. The latest version of PopED can be obtained by downloading it from http://poped.sourceforge.net/

Table 1. A summary of the eight population pharmacokinetic compartmental models accommodated by the PopED software (four structural compartmental models are available, and each can be used with two population models).

Figure 1. PopED startup window. The user has various options, among which loading previous experiments, choosing between D-optimality and ED-optimality and selecting the sampling pattern and the population-level model for the optimal design. The values for the fixed effects can also be entered, together with an initial guess for the sampling schedule.

Figure 2. PopED experimental design variables selection (left) and optimization numerics window (right).

Figure 3. PopED sample result output.

Figure 4. A flowchart with the hierarchical structure and the main modules of PopED. It must be noted that the ED criterion involves the maximization of an expectation function. Since this process is quite time-consuming and would be prohibitive to use at each iteration of the optimization procedure, a simplifying approach has been used, namely the expectation has been approximated by simple averaging. A graphical user interface is also present, to allow the user to set the main program parameters related to model and experiment structure, experiment design and optimization algorithm.