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 with the multiarmed bandit approach and a randomized 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.

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Model‐based geostatistical design involves the selection of locations to collect data to minimize an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which, for geostatistical studies, could be to minimize the prediction uncertainty at unobserved locations. In this paper, we propose a new approach to design such studies via a loss function derived through considering the entropy about the model predictions and the parameters of the model. The approach includes a multivariate extension to generalized linear spatial models, and thus can be used to design experiments with more than one response. Unfortunately, evaluating our proposed loss function is computationally expensive so we provide an approximation such that our approach can be adopted to design realistically sized geostatistical studies. This is demonstrated through a simulated study and through designing an air quality monitoring program in Queensland, Australia. The results show that our designs remain highly efficient in achieving each experimental objective individually, providing an ideal compromise between the two objectives. Accordingly, we advocate that our approach could be adopted more generally in model‐based geostatistical design.

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