Predicting degradation data

[#1]

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!

[#2]

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.

[#3]

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.