  This article proposes a novel adaptive design algorithm that can be used to
find optimal treatment allocations in N-of-1 clinical trials. This new
methodology uses two Laplace approximations to provide a computationally
efficient estimate of population and individual random effects within a
repeated measures, adaptive design framework. Given the efficiency of this
approach, it is also adopted for treatment selection to target the collection
of data for the precise estimation of treatment effects. To evaluate this
approach, we consider both a simulated and motivating N-of-1 clinical trial
from the literature. For each trial, our methods were compared to the
multi-armed bandit approach and a randomised N-of-1 trial design in terms of
identifying the best treatment for each patient and the information gained
about the model parameters. The results show that our new approach selects
designs that are highly efficient in achieving each of these objectives. As
such, we propose our Laplace-based algorithm as an efficient approach for
designing adaptive N-of-1 trials.
