Abstract: Models with shared parameters arise quite naturally in the biological sciences and we use optimal design theory to construct c-optimal approximate designs for estimating one or more functions of the model parameters in two regression models with shared parameters. We assume sample sizes for the two groups are fixed and establish equivalence theorems to confirm the optimality of the design. As applications, we consider the parallel dose response model, the EMAX model and the Exponential model, each with shared parameters. The methodology is general and can be applied to other models or design problems. For example, we show the theoretical framework can be directly extended to the case when we are interested to find a c-optimal design to estimate the mean difference between the expected responses at an extrapolated dose for a nonlinear model, or when the total sample size for the whole study is fixed, and we wish to determine the optimal proportions of observations to allocate to the two groups, or we have multivariate responses.

Key words and phrases: Approximate design, equivalence theorem, group comparison, L-optimal design.