Abstract
Here, we address the issue of experimental design for animal and crop disease transmission experiments, where the goal is to identify some characteristic of the underlying infectious disease system via a mechanistic disease transmission model. Design for such non-linear models is complicated by the fact that the optimal design depends upon the parameters of the model, so the problem is set in simulation-based, Bayesian framework using informative priors. This involves simulating the experiment over a given design repeatedly using parameter values drawn from the prior, calculating a Monte Carlo estimate of the utility function from those simulations for the given design, and then repeating this over the design space in order to find an optimal design or set of designs.
Here we consider two agricultural scenarios. The first involves an experiment to characterize the effectiveness of a vaccine-based treatment on an animal disease in an in-barn setting. The design question of interest is on which days to make observations if we are limited to being able to observe the disease status of all animals on only two days. The second envisages a trial being carried out to estimate the spatio-temporal transmission dynamics of a crop disease. The design question considered here is how far apart to space the plants from each other to best capture those dynamics. In the in-barn animal experiment, we see that for the prior scenarios considered, observations taken very close to the beginning of the experiment tend to lead to designs with the highest values of our chosen utility functions. In the crop trial, we see that over the prior scenarios considered, spacing between plants is important for experimental performance, with plants being placed too close together being particularly deleterious to that performance.
Optimal design for linear models with correlated observations
