bioprocess optimization

[#1]

Dear Sir,

I am conducting a bioprocess experiment with four factors and one response variable. My goal is to optimize these factor concentrations for future lab studies. In JMP, only two factors were significant (P<0.05), though I also observed some quadratic interactions. When using the Prediction Profiler to maximize desirability, should I remove the non-significant factors first, or should I include both significant and non-significant effects in the final optimization.

also,

When performing model reduction for a bioprocess optimization in JMP, what is the best practice for handling non-significant terms in the Prediction Profiler? My model shows two significant main effects and some quadratic interactions. I am unsure if I should retain the non-interactive, non-significant factors when predicting the maximum desirability, or if keeping them might introduce unnecessary noise into the optimization.

Many thanks in advance for your response.

[#2]

Welcome! I am not sure if there is a simple, general answer to your questions, as the topic of Model Reduction often depends on the specific details of your experiment. I will defer to the DOE and statistics experts to advise on that. 

If you have not seen it already, I would recommend the following resource to learn about how to analyze experiments using Multiple Linear Regression in JMP: Correlation and Regression Tutorial | JMP 

[#3]

You haven't provided enough structure for your experiment.  There is no information on levels or whether you did any repeats or replication? Could you attach the data table? When you say you are trying to optimize, is that really what you want or do you want to select the winner? There is no one right way to analyze the data. Typically you will start DOE analysis with the model you used to select the experiment and perform Fit Model in JMP. There are a number of statistics you use to help reduce or simplify the model, but yes you should simplify the model before using the prediction profiler with confidence. What do you mean by quadratic interactions? you mean something like this: X1*X2^2? If you have interactions, you should be cautious of setting for the main effects.

As a note, Optimization comes after you understand noise in the system.  If you are truly optimizing, then you should have already established the significance of factors. Now you are contour mapping the response surface.

Also, I find it extremely unusual that you have a situation with only 1 response variable. I don't know that I have ever seen this. We live in a multivariate world.

[#4]

As is the answer most of the time in statistics, there is not a one size fit all approach to this very common question. The absolute first thing you should do is fit the full model that your design was based on. Then, instead of just dropping a term because its p-value is less than 0.05, you could look at other model selection criteria that are better for more robust predictions, like AICc and PRESS (both available in JMP). Another option is to look at effect sizes (there is an add-in on JMP marketplace that can help you calculate these) to get a better sense of practical significance, i.e. not just removing a term because its p-value is 0.051 instead of 0.049. Common practice is also to make sure you enforce effect heredity (keep a main effect in the model if its quadratic or an interaction with it is significant, even if the main effect itself is insignificant). It is important to run all your normal diagnostic checks after picking a new model. 

A final important step is to then decide what settings to fix your factors at to optimize your response, especially factors that you did not include in the model. This is a very important step and often needs as much subject matter knowledge as statistical knowledge. In theory, if the data you have in hand suggest that a term does not belong in a model for a given response, then the mean of your response is more or less constant across the space of your studied effect (now this is assuming a lot of things, most notably that the data you collected is representative of your overall population and that there isn't some other factor that describes your process that you might have left out that could be biasing your terms or has an interaction with the effect you left out). So, one could argue to set it at the midpoint of your effect's range. You could set it at a spot that you know your process controls well at (i.e. minimal variation), or at a level that might be cheaper or easier to run. You could choose to just keep in all main effects so that once you optimize with the desirability you get settings for all factors. I have seen any of these approaches and more used.

This is just one stream of thought for dealing with this problem, as I am sure others might have different/additional opinions.