Screening design for computer experiments: metamodelling of a deterministic mathematical model of the mammalian circadian clock

Computer simulations are faster and cheaper than physical experiments. Still, if the system has many factors to be manipulated, experimental designs may be needed in order to make computer experiments more cost‐effective. Determining the relevant parameter ranges within which to set up a factorial experimental design is a critical and difficult step in the practical use of any formal statistical experimental planning, be it for screening or optimisation purposes. Here we show how a sparse initial range finding design based on a reduced multi‐factor multi‐level design method—the multi‐level binary replacement (MBR) design—can reveal the region of relevant system behaviour. The MBR design is presently optimised by generating a number of different confounding patterns and choosing the one giving the highest score with respect to a space‐spanning criterion. The usefulness of this optimised MBR (OMBR) design is demonstrated in an example from systems biology: A multivariate metamodel, emulating a deterministic, nonlinear dynamic model of the mammalian circadian clock, is developed based on data from a designed computer experiment. In order to allow the statistical metamodel to represent all aspects of the biologically relevant model behaviour, the relevant parameter ranges have to be spanned. The use of an initial OMBR design for finding the widest possible parameter ranges resulting in a stable limit cycle for the mammalian circadian clock model is demonstrated. The same OMBR design is subsequently applied within the selected, relevant sub‐region of the parameter space to develop a functional metamodel based on PLS regression. Copyright © 2010 John Wiley & Sons, Ltd.