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,

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

Thanks,
Ben

[#3]

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%.

[#4]

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

[#5]

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.

[#6]

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

[#7]

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.

[#8]

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.

[#9]

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.