Help to design a complex DoE on Formulation Buffer Screening

[#1]

I'm planning to optimise a formulation for a liquid drug product. We have a starting material that is in a certain buffer with some excipients and would like to find out, if there is even a better formulation buffer for this drug product regarding stability. 
I want to test:
- Different pH ranges (pH 5, 6, 7, but the pH levels are set by different buffer systems (pH 5 = acetate buffer, pH 6 = histidine buffer, etc).
- Two different surfactants with a fixed concentration (surfactant A, surfactant B and no surfactant)
- One or two different sugars with a fixed concentration (sugar A, possibly sugar B and no sugar)
- A concentration range of salt (100 mg/L to a maximum of 300 mg/L)
- Two concentration levels of the starting material (= drug): low and high concentration

I have difficulties in finding the right factor types: pH: categorial or discrete numeric?; concentration of starting material: continuous or categorial or discrete numeric? 

And what design type to use, either screening design, custom design or easy design? If I should include center points and replicates? 
We will do the buffer screening in a 96-well format, so we can do maximum 96 experiment runs- but of course less would be better. The experiments are not automated, means that the pipetting will be done by an operator. 

Thanks for any hints & input. 

[#2]

Hi,

as most of the time there are different ways to tackle this.

Do you expect the buffer system to be relevant for your outcome/response or is it only relevant to achieve our desired pH level? If it might effect your stability I would prefer adding the buffer as categorical. If only the resulting pH is relevant then discrete numeric for pH might be better here.

If your starting material can be changed freely between high and low than I would simply make it continuous in the range you choose.  

Above 6 factors it is usually recommend to start with a screening design type. Due to the combination of factors, levels and many categorical factors you are working with, you might want to look into the Custom Design Platform which enables you to build screening designs as well as more complex optimization designs dependent on your model choice. A more guided approach will be the EasyDOE Platform. 

Adding replicates to the design is always a good idea since they help with error estimation and enable the lack of fit test. Adding some might be possible since you are not super restricted when it comes to the number of runs. 

Lets see what other might recommend.

-Jonas

[#3]

Hi Jonas,

Thank you very much for your response and input - I really appreciate it! Yes, I also expect that the buffer system influences the stability of the material, depending on factors like its ionic strength. I recently used the custom design tool in JMP to create a screening design and ended up with 72 conditions. I’ll be running the experiments soon and am eager to see the results.

Thanks, 

[#4]

This can get a little tricky, but here are some ways to handle your situation:

• Buffer: include a Buffer Type (with 2 or 3 levels, depending on the number of buffers you want to investigate), and pH with levels (-1, 0, 1) for (low, middle, high).  Most buffers can accommodate a range of pHs, but as you stated, the pH range the buffer is effective depends on the pKa of the buffer (e.g. histidine buffer can typically be adjusted to a pH between 5-7 and still be an effective buffer).  So the actual pH levels in the experiment will depend on the experiment, but just model it as low/middle/high pH within the buffer.     Make sure when you build the DOE and do modeling, include the interaction effect between the buffer type and pH level. 
• For the remaining factors, a mixture modeling approach would work well.  You would have to rethink what the experimental factors are, though.  For example, instead of Sugar A, Sugar B, No Sugar, you would have a factor that is "proportion in solution that is Sugar A" and "proportion in solution that is Sugar B".  And you could even include experiments that both sugars that way.  It would still allow you to estimate the effect of each sugar individually (with an appropriate design.  For this approach you would have 5 factors, each a proportion of the overall formulation, and the Custom DOE platform could fit this model (including any constraints on the formulation factors)
  • Surfactant 1 Component amount
  • Surfactant 2 Component amount
  • Sugar A component amount
  • Sugar B component amount
  • Salt component amount
  • Drug component amount
  • Buffer solution amount (note, this ends up being a slack factor, but you should probably include this also in the design
• An alternative, but more complicated approach, is to use "conditional" models where you have a factors like
  • Sugar A:  one binary (0, 1) discrete numeric factor that indicates if sugar A is in the mixture or not, and then another factor for the amount of Sugar A in the mixture.  
  • Sugar B:  same as above for Sugar A
  • Same for the two surfactants, 

I recommend the 1st approach.  It is a little more abstracted away from how people typically talk about the make up of a formulation, but it is mathematically easier to generate a design and do the analysis on that type of experiment.  

[#5]

Hey, 

Thanks for your suggestion! It sounds interesting and indeed a bit tricky. I'm still new to JMP and not very familiar with DoE and its features yet. However, I'll definitely keep your suggestion in mind as I continue to improve my understanding.

Cheers,