7.10. Summary

Design optimization is a critical aspect of experimentation; this is particularly true in pharmaceutical applications. There are many barriers to routine application of optimal design theory. Among these is the lack of software. For the mathematically simplest cases, namely linear models where the parameters are independent of the variance function, many software packages are available for finding optimal designs (see Section 7.1.6). However, as models increase in complexity, the availability of software for solving optimal design problems drops off dramatically and pharmaceutical researchers often find it frustrating. Some academic labs have created software that supports selected optimal designs (see Section 7.1.6) but a general software package accessible to researchers in the pharmaceutical industry is not currently available. To this end, we have created a series of powerful modules that are based on SAS software for constructing optimal experimental designs for a large number of popular non-linear models. Although we focus on D-optimal designs, the same algorithm can be used for constructing other types of optimal designs, in particular A-optimal designs after minor changes.

In this chapter, we provide a brief introduction to optimal design theory, and we also discuss optimal experimental designs for nonlinear models arising in various pharmaceutical applications. We provide several examples and the SAS code for executing these examples is included. The examples increase in complexity as the chapter moves forward. The first example generates D-optimal designs for quantal models; subsequent examples, in order, generate D-optimal designs for continuous logistic models, logistic regression models with unknown parameters in the variance function, the beta regression model, models with binary response, bivariate probit models for correlated binary responses, and pharmacokinetic models with multiple measurements per patient, with or without cost constraints. The most important hurdle in contructing these designs is the computation of the Fisher information matrix, and storage/retrieval of these matrices and associated design points. As designs increase in complexity, computation time is increased in order to handle the necessary calculations and storage/retrieval.