Question related to DoE for degradation of chemical compounds

[#1]

WARNING: noob question!

I want to use DoE to model the degradation of different compounds we monitor during stability studies. We know that there are three factors influencing degradation (all continuous) but want to extend our understanding to relatively extreme values of these factors. Eventually we want to use the experimental results to model degradation.

What I still have to understand is how time is factored in. Time naturally has an influence, but in all our stability studies only specific time points are sampled and we always use a fixed shelf-life for our product. 

Where do I start? Do I want to model the degradation slope(s) or do I want to model the residual fraction(s) of an active compound after a fixed time? Are there any JMP tutorials I could use? 

[#2]

Do you have JMP Pro? If so, then you can treat the time course as a function. You design the experiment using Custom Design as usual but you use a functional response. See Help > Books > Design of Experiments for more information about this approach.

If you do not have JMP Pro, then you can include Time as a Discrete Numeric factor along with the other stress factors. JMP will add enough powers of Time to the model to justify the levels of time you enter. (Leave them in the model!) Because you expect the stress factors to affect the degradation path (effect of time), you want to cross all the terms for Time with the stress factors. For example, if Temperature is a stress factor in your experiment, then cross Temperature with Time, Time*Time, and so on.

You can also use the Analyze > Reliability and Survival > Degradation platform for such an analysis. See the Help > Books > Reliability and Survival book for more information and examples.

Hope this reply gives you enough to get started. If you have more questions, ask away!

[#3]

Some other thoughts, questions and rants:  I always think about what questions I am trying to answer before deciding what tool to use to answer them.

1. What is a "stability study"?  Not trying to be controversial, but this means different things to different people.

2. How did you determine that the three factors influence degradation?  Are those the only factors?

3. Is the degradation linear or non-linear (this may effect the number of levels you test your factors at.)

4. Just curious as to why you want to use DOE?  Assuming you already have a first order model (by your claim of knowing three variables that have an affect), why not take "data" in a time series and use regression to model that data?

5. How were the specific time points for sampling established?  How was the "fixed shelf-life" established?  The problem with always using the same fixed time points is you may not know what is going on between those times.  It is important to combine scientific hypotheses/theories with sampling concepts.  Is there a reason why those specific time points were chosen?  What does the chemistry suggest?  When you have no rational explanation as to why certain time periods were selected, a random selection is less biased.

6. As far as measurements (Y's), I recommend measuring as many as you can.  Slope of the degradation line, amount of residual material left after specific times, perhaps the area under the curve of the degradation line.  What are the compounds degrading into?  Can this be measured? Since this appears to be some chemical reaction (not being told if it is exothermic or endothermic), perhaps temperature measurements.  Maybe there are other physical attributes that can be measured or observed (e.g., color, viscosity)

[#4]

1. No worries. For us stability is degradation of individual compounds in the product we sell.

2. The three factors + time (i.e. 4 factors actually) were identified by experience and previously also used for modelling of the degradation of at least one compound. Not sure if these are the only factors, but they do make a lot of sense and have high explanatory power.

3. Based on the many stability studies we performed we have no reason to assume non-linear degradation of the compounds we are looking at. The regression residuals typically resemble a normal distribution.

4. We run a lot of stability studies to confirm shelf-life of our products - I am responsible for managing our stability program. These studies are designed following ICH guidelines, which set a very clear standard or template for how to perform these studies.  On the other side we also run a couple of accelerated studies at much higher temperatures on different products, to compare the stabilities of the different products. For the latter experiments we are now also aiming at pushing the other factors to more extreme values. I only started having access to JMP very recently, know that it has DoE functionality and challenged management whether we were getting the most of our accelerated studies. My hypothesis was that the use of DoE would save us cost and time (which; after having read your reply; I suspect may be an incorrect assumption.)

5. Yes, these specific time points were chosen because of ICH guidelines mentioned under 4.. We only want to confirm that our products indeed are stable for at least two years. Sometimes they are stable for a longer period. Usually we run stability studies for 36 months. I think if we resorted to different time points that would put us in conflict with regulatory authorities.

6. We do measure a lot of different physical and chemical parameters, including appearance and viscosity. Storage temperature is controlled, as is relative humidity and sampling times. The slopes of the degradation lines are routinely compiled into plots showing changes in the slopes due to individual factors being changed. JMP in itself already works wonders for us by allowing different grouping, overlays, colors and formats. But what we want is a model, and for this model I presumed DoE would be an adequate start. and yes, degradation is a chemical reaction. I am not sure what role it plays if it is exo- or endothermic for an experimental design.

Just for clarification. since we have established (form our point of view) relevant factors, do you think DoE is overdoing it?

[#5]

@Ressel: I'll only respond to your very last sentence in your latest post asking something akin to '...is DOE overdoing it?'

My stock reply is I can't honestly think of an instance in my 38 years of DOE practice where we felt we were 'overdoing it'. If for no other reason, even IF you do 'understand the relevant factors'...at what level? Do you have a confirmed, verified, system model? If not...then DOE is your most efficient path to this knowledge. And I can't tell you how many times when DOE provided new knowledge wrt to a system's performance that 'the OLD GUARD' had not known or considered. Many an urban manufacturing process myth was busted through use of DOE.

Rant over.

[#6]

Perhaps this forum is not the right place for this discussion, but I do have some follow-up thoughts/questions/rants:

1. I re-read your posts multiple times and I still do not know what a "stability study" is?  Is to answer the question how consistent and predictable is the degradation of the individual compounds?  If so, DOE is not the tool I would recommend.  I would be using directed sampling. No doubt DOE is the most effective tool for understanding causal structure, but it is not very efficient in understanding stability and consistency (where by definition you will need some time series).  Why do you continue to run stability studies?  Are you be concerned you have not identified potential variables that may effect degradation?  Based on your comment about degradation "our products indeed are stable for at least two years. Sometimes they are stable for a longer period", it seems you don't know why?  I'll bet you have some hypotheses. These can be tested very efficiently using DOE.

2. Your understanding of the chemical "reactions" are a function of theoretical chemistry and empirical data (experience).  It might be worthwhile to investigate why the compounds degrade, how can the degradation be mitigated, etc.  This is where DOE can be very effective.  Likely you have certain variables you can manage (control) in your processes.  There are also variables that you choose not to control for whatever reason (noise).  If you would like your processes to be robust to noise, DOE again is the tool of choice.

3. I am not familiar with the ICH requirements, but understand the role regulatory agencies play. I understand these standards must be met,   but these requirements are typically not meant to drive companies to continuously improve.  I could argue these requirements stymie improvement, but that is for another discussion.  If your company policy is to continuously improve, you will have to go above and beyond the minimally acceptable requirements of regulatory agencies.

4.  I'm still a bit confused about your bullet #6. What do you want the model for? For predicting degradation? For identifying where predictor variables need to be set? ...etc Is there any relationship between the different measurements you take (color, viscosity) and degradation?  Have you preformed any multivariate studies?  Why do you control storage temp. and humidity?  How much do these factors affect degradation?  Would you want to have your products be robust to these conditions?

"All models are wrong, some are useful"...G.E.P. Box

[#7]

This forum might be the right place for the discussion you want to have but the originator is simply asking about how to use a designed experiment to determine the effect of conditions on product stability.

This kind of study is done an enormous number of times each day around the world. There are several important guidance documents that have been honed over decades to address the regulatory issues about stability. The originator is using the ICH Q1A and Q1E guidance documents, part of a long standing, global harmonization effort. This guidance applies to pharmaceuticals, biologicals, and diagnostic assay reagents. It is really the same thing as a degradation path if you understand reliability but it is described within the context of these application areas.

There are various modeling schemes that are popular. The goal is to first determine the expiry (i.e., substance re-test date and product shelf-life) and second to determine how the degradation path depends on conditions that might vary over the life time of the material. The simplest experiment is to increase the level of a stress variable. For example, temperature and relative humidity often accelerate the degradation process. This accelerated degradation experiment provides more information about the degradation process. It also provides an answer much more quickly that the real-time stability data through extrapolation.

[#8 · Accepted solution]

I agree with @P_Bartell that a designed experiment is almost always the best way to collect the best data to estimate model parameters. The alternatives are one or more isolated tests or an observational study that either cannot support the model or present issues for the model.

Based on your answers 2 and 3 above, you should only need two levels for the three continuous factors to support the linear effect in the model. Time will use the Discrete Numeric so you can enter the expected time points. An accelerated stability study is difficult to predict a priori but it sounds like you have experience that can guide you with the selection of the time points. Like any continuous factor, time only needs enough levels to support the model. So a linear change over time really only needs two levels. I am aware, though, that most of these studies include many time points between baseline and the end point. You can use a different set of time points if you are not running the Long-Term, Intermediate, or Accelerated protocols. A stress test will necessarily be shorter in duration and depend on the conditions and the stability of a particular product.

As for answer 6, you will use Analyze > Fit Model to specify the terms. You will include terms for the main linear effects of time and the three factors. Your model will not require powers of the factors but you might consider adding interaction effects. For example, the effect of humidity might change at higher temperatures. Also, the acceleration assumes that the degradation over time changes with conditions so you must add terms by crossing time with the factors. I expect that you will find the Prediction Profiler with the selected, fitted model to be very informative. This approach does not fit separate models for different conditions but one model that includes all the factors and levels.

[#9]

Btw, I am not using JMP Pro. I presume that the approach you so kindly described will also work with JMP 14 or 15 (we are upgrading in the coming weeks).

[#10]

That is correct, JMP Pro features are not required for this analysis, although there are such features that apply.