OPTIMAL-DESIGN - A COMPUTER-PROGRAM TO STUDY THE BEST POSSIBLE SPACING OF DESIGN POINTS FOR MODEL DISCRIMINATION

Optimal design is largely concerned with selecting design points so as to maximise the precision of parameter estimates once the correct mod el has been identified. Often, however, a priority is that the correct model has first to be identified from a set of candidate models, and this procedure requires a different set of design criteria. We suppose that a decision haste be made on statistical grounds between acceptin g either a correct model g(2)(x, Theta) or a deficient model g(1)(x, P hi), using goodness of fit criteria. where weighting is dictated by a weighting function w(x) and spacing is specified by a spacing function f(x). We describe, for the first time, the choice of spacing function required to generate points which are uniformly spaced with respect t o the y axis (Uniform-Y design). Then we introduce appropriate norms S -n,(Theta), Q(Theta) and R(n), to quantify the effects of alternative choices of spacing, density and number of design points on the probabi lity of correct model identification. Typical problems of this general type in biochemistry, for example, would be determining the correct n umber of classes of receptors in a ligand binding experiment, or fixin g the number of exponential components in a pharmacokinetic experiment . A computer program which performs the necessary calculations For the se and similar problems is described, and illustrated by analysing som e typical test cases. Results From our extended investigations are als o summarised, leading to more general conclusions as to the best spaci ng and density of design points for optimal model discrimination. We a lso prove the remarkable and previously unsuspected Fact that, in diff erentiating two site cooperative ligand binding from one site, the two best designs give identical parameter estimates for the deficient mod el but are not actually equivalent from the point of view of model dis crimination.