Optimal designs are crucial when conducting efficient experiments that make the most of available resources. These designs allow scientists to study parameters with comparable precision to non-optimal designs, but with fewer experimental runs, as the number of levels for each factor is usually limited to 2 or 3. This, of course, is particularly useful when you already have some information about your system, as you can then set your factor levels to areas of the space where you are likely to find a response.
To generate an optimal design, you need to provide a model, a design criterion, a run budget, and whichever constraints might be applicable to the system you’re studying. We go into more statistical detail for optimal designs in this document, but for now it is useful to focus on the model and design criterion, usually identified by single letters (D, I, A or G, for e.g.).
When calculating an optimal design, you first decide what it is you want to learn from the biological system you are studying. Do you only care about identifying:
Main effects, e.g. those factors that are independently having an impact on your system or not.
Main effects and two factor interactions, e.g. that are independently having an impact on your system and the factors that interact with one another to impact your system.
Up to quadratic effects, e.g. the effects mentioned above plus quadratic effects, or effects that have curvature in the response.
Identifying up front what you want to learn will impact the calculation of your optimal design and how the different factors and their levels are paired up to best suit the type of model you intend to fit when you get to analysing your data. The model type also influences the type of optimality criteria you might want to use.
Synthace supports two types of optimality criteria: D-Optimal designs, and I-Optimal designs. Usually, the first are intended for screening and exploration, while the latter are used for optimization experiments.
In Synthace, however, we wanted to make the process of choosing your optimal design easier, and therefore made it so that it is dictated by the choice of the model itself: if you choose a Main Effects only model, or one that includes up to two factor interactions, we assume you are screening and therefore calculate a D-optimal design. But if you choose a model that includes quadratic effects, we assume you are optimizing and accordingly pick an I-optimal design.
Considering that calculating Optimal designs is typically more computationally expensive, there are some restrictions on the size of the design supported by Synthace. The three different options are then:
“Main Effects only”, useful for initial screening, which is available if you have less than 20 factors with 2 levels each.
“Up to Two-Factor Interactions", which includes all two factor interactions as well as main effects, and are the best choice for initial screening. These are supported for up to 12 factors with 2 levels each, or 9 factors with 3 levels.
“Up to Quadratic Effects”, useful for optimisation, which is available for up to 8 factors with 3 levels each.
In summary, Optimal designs are incredibly powerful when screening or optimising, when you already have some prior knowledge of the system you are studying. We hope this clarifies how these designs can be useful and how they are implemented in Synthace.
To learn more about the statistics behind optimal designs, click here.
To learn how to calculate an optimal design in Synthace, click here.
To learn about other design types, click here.