Methods for optimising designs with a fixed number of clusters

[AngusMcLure]

This is probably a useful tool (when the cluster locations are fixed due to practical considerations), however will require rethinking the optimisation process. When the number of clusters is not fixed, there is an optimal pool and sample size per cluster that is optimal (i.e. minimizes cost per unit of Fisher information [FI]) regardless of the objective (e.g. target power, effect size to be detected). However, when the number of clusters is fixed we need to find the cheapest design that satisfies some kind of inequality.

Possible approach that simplifies:

• Get user to specify goal (type I and II error rates, effect size)
• Convert this into minimum FI required per cluster
• Call a function that iterates over cluster-level designs that achieve the minimum FI to find the one that minimizes costs
  • This perhaps can be made more efficient by noting that FI monotonically increases with certain inputs (e.g. number of pools per site) so we can set bounds on designs that have to be considered