Robustness of optimal design of fMRI experiments with application of a genetic algorithm.

In this paper we apply the genetic algorithm developed by Kao et al. (2009) to find designs which are robust against misspecification of the error autocorrelation. Two common optimality criteria, the A-optimality criterion and the D-optimality criterion, based upon a general linear model are employed to obtain locally optimal designs for a given value of the autocorrelation. The maximin criterion is then used to obtain designs which are robust against misspecification of the autocorrelation. Furthermore, robustness depending on the choice of optimality criterion is evaluated. We show analytically and empirically that the A- and D-optimality criterion will result in different optimal designs, e.g. with different stimulus frequencies. Optimal stimulus frequency for the A-optimality criterion has been derived by Liu et al. (2004) whereas we derive here the optimal stimulus frequency for the D-optimality criterion. Conclusions about the robustness of an optimal design against misspecification of model parameters and choice of optimality criterion are drawn based upon our results.