Chapter 7. Optimal Design of Experiments in Pharmaceutical Applications

Valerii Fedorov^[]

^[] Valerii Fedorov is Group Director, Research Statistics Unit, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, USA.

Robert Gagnon ^[]

^[] Robert Gagnon is Associate Director, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, USA.

Sergei Leonov^[]

^[] Sergei Leonov is Director, Research Statistics Unit, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, USA.

Yuehui Wu ^[]

^[] Yuehui Wu is Senior Statistician, Research Statistics Unit, Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals, USA.

In this chapter we discuss optimal experimental designs for nonlinear models arising in various pharmaceutical applications and present a short survey of optimal design methods and numerical algorithms. We provide SAS code to implement optimal design algorithms for several examples:

• quantal models such as logistic models for analyzing success or failure in dose-response studies

• multi-parameter continuous logistic models in bioassays or pharmacodynamic studies, including models with unknown parameters in variance

• beta regression model

• models with multiple responses, for example, measuring both efficacy and safety in dose response studies, or pharmacokinetic models with multiple samples per subject

• models with cost constraints.

For all examples, we use a first-order optimization algorithm in the space of information matrices. A short survey of other software tools for constructing optimal model-based designs is provided.