A generalisation of T‐optimality for discriminating between competing models with an application to pharmacokinetic studies

Abstract

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.

Experiment design for nonparametric models based on minimizing Bayes Risk: application to voriconazole$$^{1}$$

“…The D-optimal designs do not enjoy this same property. However, several extensions relevant to model discrimination have been developed (cf., Atkinson et al [2], Vajjah and Duffull [53]).…”

“…This comparison is not intended to be exhaustive as other experiment design methods are possible. Comparisons with methods such as D s optimal design (Goodwin and Payne [21]), T-optimal design (Atkinson et al [2] Vajjah and Duffull [53]), alternative robust D-optimal designs [22][36], and Bayesian design (Chaloner and Verdinelli [12], Ryan et al [42]), are left for future studies.…”

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

“…We are encouraged by SIP methodology and plan to test its ability to find optimal discrimination designs more broadly in more complicated problems. For example, a good test case is to find robust T-optimal designs where we do not require one of the two models to be fully known [44]. Mathematical programming tools such as SIP and Semi-definite programming have already been commonly and effectively used by engineers for decades but not by statisticians.…”

Using animal instincts to design efficient biomedical studies via particle swarm optimization

“…For example, Li and Balakrishnan [17] and Konstantinou et al [18] assumed technical conditions to arrive at the theoretical descriptions of the optimal designs. PSO can find optimal designs that satisfy the technical conditions and also able to find optimal designs when the conditions do not apply, suggesting that PSO can find optimal designs for a wider class of problems [46, 47, 48, 49]. …”