A generalisation of T-optimality for discriminating between competing models with an application to...

The T-optimality criterion is used in optimal design to derive designs for model selection. To set up the method, it is required that one of the models is considered to be true. We term this local T-optimality. In this work, we propose a generalisation of T-optimality (termed robust T-optimality) that relaxes the requirement that one of the candidate models is set as true. We then show an application to a nonlinear mixed effects model with two candidate non-nested models and combine robust T-optimality with robust D-optimality. Optimal design under local T-optimality was found to provide adequate power when the a priori assumed true model was the true model but poor power if the a priori assumed true model was not the true model. The robust T-optimality method provided adequate power irrespective of which model was true. The robust T-optimality method appears to have useful properties for nonlinear models, where both the parameter values and model structure are required to be known a priori, and the most likely model that would be applied to any new experiment is not known with certainty.