How to design a screening DOE for continuous factors that includes 3 levels (zero, intermediate, high concentration)?

[#1]

Hi all,

I am trying to design a screening DOE for multiple continuous biological factors for which I suspect a biphasic relationship between the factors and the outcome (= viability): I first expect a positive correlation up until a certain concentration after which I expect a negative correlation due to toxicity at higher concentrations. How can I take this biphasic association into account when designing a classical screening DOE? Or do I need to choose a custom design to be able to include 3 levels for each factors: (1) concentration 0 , (2) high concentration, (3) intermediate concentration?

Thank you for your help.

Kind regards,

Sara

[#2]

With the information you've provided, you can go either way. A 2 level only design would need to include some center points to see if the curvature in the response is present in the system. So it's really a 3 level design no matter what you do. The optimal design approach is more model centric so you can define the model first and then let JMP figure out the optimal design. Either way can work. Perhaps other considerations may lead you down a certain path?

1. Noise factors affecting the response in the system?

2. Variation in the response across the inference space? My past experience says cell viability studies can be highly variable?

3. Disallowed/undesirable treatment combinations?

4. Restrictions on resources so there might be an upper limit to the number of runs in the design?

[#3]

Hi @SaraA,

Welcome in the Community !

The situation you're describing seems to imply a certain amount of curvature on the response.

Depending on the number of independent factors you have (and type(s) : only numerical continuous ?), constraints, experimental budget available, ... I would recommend to try a :

• Definitive Screening Design, very powerful screening design for several continuous numerical factors (recommended for 5+ factors, below 5 factors it may not be very economical/efficient to use it), using three levels for continuous factors and which may be able to detect main effects, interactions and quadratic effects. However, you need to check that you don't have constraints in your experimental space that won't allow certain combinations (else use the next following design recommandation),
• D-Optimal design (Custom Design), flexible designs where you have full flexibility on the assumed model and terms included. For example, if you want to have middle levels for each factor, you can include quadratic terms in the model as "Necessary" or "If Possible" (depending on your experimental budget and need/precision to estimate quadratic terms). Custom designs also enable to take into account various factors type (including mixture, categorical, covariate, ...) and are very helpful in the presence of disallowed combinations or experimental restrictions.

Both designs can use blocking, to help reduce noise in presence of known and controllable nuisance factors (time, different operators, ...). You can create several designs and compare them using the Compare Designs platform, to better assess the pros and cons of each approach/design.

If you can provide more information on the number of factors, ranges, constraints (if present), experimental budget, ..., I may have other advices or recommendations, and other Community members can also join the discussion

I hope this first answer may help you,

[#4]

Hi Victor,

Thank you so much for your reply, this is very helpful.

I have a total of nine factors I would like to screen for and I want to include a maximum of 54 runs. I do not have any constraints with regard to certain combinations - all combinations are technically possible.

Previously, for similar experiments testing the effect of different biological compounds on cell viability, I used a Plackett-Burman design first for the screening, followed by a full factorial design for optimization. However, these designs do not allow to include center points. The definitive screening design sounds like an attractive alternative. Are there any disadvantages of using a definitive screening design when compared to a classical Plackett-Burman design? The definitive screening design might also be cost-effective by performing only one DOE instead of two. Or is it still recommended to perform an optimization design afterwards?

Thank you!

Sara

[#5 · Accepted solution]

Hi @SaraA,

Glad that these first suggestions might work for you.

If you plan to create a Definitive Screening Design for 9 continuous factors, the recommended "default" run size is 25, which is very economical compared to your allowed experimental budget. But you can still add more runs to enable higher precision in the estimation of coefficients, and/or allow an easier detection of quadratic effects, and compare the benefits of adding more runs in your design with the platform Compare Designs.

The DSD is a very interesting option when/if possible, as it allows precise main effects estimation (main effects are completely unbiased, not correlated with any 2-factors interactions or quadratic effects), and they can also identify factors having a nonlinear effect on the response (since 3 levels are used for each factor). There are a lot of other benefits compared to classical screening designs listed here : Overview of Definitive Screening Designs

You can also use Blocking with DSD, for example if you want to take into consideration random variability from different plates used, so this makes DSDs a very efficient screening design choice.

Even if DSDs have very interesting design properties, I would probably not stop at this stage, as there are several ways you might need more information (and you have an allowed experimental budget that allows more in-depth study of the factors):

• Perhaps you may have to refine the factors ranges, in order to focus on a narrower experimental space of interest ?
• DSDs are still screening designs, so once main effects are identified with high confidence, you may want to confirm other effects that might have been detected during this first screening stage (2-factors interactions, quadratic effects) ?
• Finally, in the case of a predictive model, it might be interesting to add validation runs and/or other "training" runs (perhaps in a Space-Filling way), so that you can confirm and/or refine your model ?

It all depends on your objectives, requirements and experimental budget/constraints, and which precision you may need to reach a certain understanding of the system.
I hope this complementary answer will help you,

[#6]

Hi @Victor_G 

When attempting to design my experiment using the DSD I do not see where I can add replicate runs? Is this not indicated for a DSD?

Thank you

Sara

[#7]

After you've added the factors, you get the following screen.  You can add blocks.  These are replicates.