topic Re: Predicting degradation data in Discussions

Predicting degradation data

UrsulaOrsolya — Thu, 07 May 2026 08:22:13 GMT

What modeling approach can predict 24‑month concentration from previous degradation data with different initial values?

There is degradation data measured over time (ex. up to 24 months) for several batches/samples.
Each batch starts at a different initial concentration at release, and not all batches are measured at all time points (there are missing observations for later time points). All measurements were performed using the same measurement parameters. We want to predict the concentration at 24 months, assuming a hypothetical release value of 80%, even though all of the observed batches start above 85%. The goal is to use all available data simultaneously to create a model, even though some time points are missing for certain batches.

The Repeated Measures Degradation platform did not allow for the use of Arrhenius equation without X variable (which was not available because the same measurement parameters were used). Other models did not fit well for the available data.

Thank you in advance!

Re: Predicting degradation data

Ben_BarrIngh — Thu, 07 May 2026 09:28:03 GMT

Hi @UrsulaOrsolya,

Could you provide the equation/formula you were using for this that were failing?

Thanks,
Ben

Re: Predicting degradation data

UrsulaOrsolya — Thu, 07 May 2026 10:54:52 GMT

Thank you for the response! This is where I am currently at. I created a separate coloumn in tha data for temperature (25 C for all data points). But I am unsure how to use this to predict for the hypothetical release value of 80%.

Re: Predicting degradation data

Ben_BarrIngh — Thu, 07 May 2026 12:31:50 GMT

Hi Ursula,

Just to clarify, what is the target ('reference' in JMP) temperature you're aiming for with the Modified Arrhenius? With just a single temperature it becomes difficult to correctly estimate parameters.

When you say you're looking at 80% - is this as a spec limit to cross? Or are you looking for what the value would be at 24 months?

Thanks!
Ben

Re: Predicting degradation data

MathStatChem — Thu, 07 May 2026 12:36:15 GMT

It looks like the degradation follows a non-linear model, so I would recommend you try the Fit Curve platform. Since you don't have varying temperature or other accelerating conditions, repeated measures degradation doesn't really work for this.

Another option is the linearize the data (maybe by taking the log of the data) and fit a linear regression model to the data. You can use predictions from that and do the reverse transform to get predictions.

Re: Predicting degradation data

MathStatChem — Thu, 07 May 2026 12:40:08 GMT

Exponential 3P or Mechanistic Growth models seem to fit this data well:

Re: Predicting degradation data

Ben_BarrIngh — Thu, 07 May 2026 12:46:42 GMT

Hi @UrsulaOrsolya, I've attached your data table back with a script saved using Fit Curve - because you're not exploring different temperatures it might be better to fit a first-order rate equation and use the profiler to identify the likely response at X months.

Re: Predicting degradation data

UrsulaOrsolya — Thu, 07 May 2026 13:27:48 GMT

We would like to predict the value at 24 months for a hypothetical sample that would have has an initial (release) value of 80% (so at 0 month). A confidence interval would also be useful. The temperature itself is not important for us, because all samples were stored under identical conditions.

Re: Predicting degradation data

UrsulaOrsolya — Thu, 07 May 2026 13:36:21 GMT

Thank you for your help! This approach does not fully meet our objective, as the curve is fitted to the entire dataset without accounting for the fact that degradation behavior may differ depending on the initial value. It is important to consider that samples with different starting points at time zero may degrade somewhat differently over time. The aim is to know what might happen if we would start a 80% at 0 months.

Re: Predicting degradation data

UrsulaOrsolya — Fri, 08 May 2026 10:04:53 GMT

Thank you for the suggestion! My aim would be something like this but with confidence intervals:

So I would like to find a general formula based on the measured data and then use it for the hypothetical sample that starts at 80% at 0 months (batch 5).

I am not sure how to use the Fit Curve platform for this purpuse. Do you have any tips?

Re: Predicting degradation data

rcast15 — Fri, 08 May 2026 12:57:39 GMT

Hi @UrsulaOrsolya,

I do not believe you would be able to get what you are looking for directly in the fit curve platform. What I would suggest is the following:

1. Save the parametric prediction formula using the model that @Ben_BarrIngh fit in his attached JMP file.

2. Next, use the nonlinear platform with your raw data and parametric prediction formula.

3. Lock your a parameter to 80, which is parameterized as your initial value in the First Order with Limits model we fit. Then hit go. Click the confidence interval button so the algorithm gives you CI for your b and c parameter. Then open up the prediction profiler.

Then if you want, you can save this prediction formula and its associated confidence/prediction intervals.

I should add this is a fairly brute force way to acquire this prediction in JMP and what I think would be a more statistically sound way to get what you want is to use R or Python to fit a bayesian nonlinear model which would allow you to 1. account for any correlation between your starting value and the degradation rate and 2. Use your batch-to-batch variability and MCMC sampling to make predictions for future unobserved batches at any given initial value.

Re: Predicting degradation data

MathStatChem — Fri, 08 May 2026 16:43:53 GMT

after you have fit the model, you can save prediction formulas to the data table with Std Error prediction formula. You would need to do a little math in another formula column to put a confidence interval for the mean prediction. A simple approach would be to just multiply the Std Error by 2, which would be an approximate 95% confidence half-width. If you then want to make predictions at a given timepoint for a given batch, then add a row to the table and set the batch id and timepoints, and the prediction formulas will calculate for that condition.