Compute confidence interval on model predictions

Hello,

I fitted three model parameters to data, and I was able to retrieve the optimization results and get the confidence intervals on both parameters and model predictions, as explained in PredictionConfidenceInterval - Object containing confidence interval results for model predictions - MATLAB

I also performed simulations for other individuals using the same model and the same fitted model parameters, but with some parameters (not the fitted ones) defined individually. I ran a groupsimualtion for this, and I would like to compute the uncertainty on these simulations, based on the uncertainty of the fitted parameter, but I was unsuccessful so far...

Is there a way to compute the confidence interval on model predictions, using different simulation settings (i.e. individual or variant) than for model fitting?

Thanks in advance!

[Torsten]

I also performed simulations for other individuals using the same model and the same fitted model parameters, but with some parameters (not the fitted ones) defined individually.

So in the original model, the extra parameters were absent or were they set to fixed (mean) values ?

Can you explain more about the type of model in question ?

You also read the below page ? I doesn't answer your question about extra parameters, but is quite helpful to understand and interprete the fitting results.

https://uk.mathworks.com/help/curvefit/confidence-and-prediction-bounds.html

[Justine]

Thank you for your answer!

The model was built in Simbiology, and it is a PBPK model. The extra parameters existed in the original model, but they were fixed to different values indeed. Now I am using the exact same model structure, kept the fitted parameter from the original model, but using slightly different value of physiological parameters to model several individuals.

I hope this clarifies a bit the context.

[dpb]

I am not familiar with what a PBPK model is, but I think if I interpret the above reply to @Torsten that the fixed parameters are the same set but just want to use different values for them, then one assumes there is no uncertainty in those parameters. For the revised model, one would then have to recompute the residuals from the fitted data set to obtain a revised Jacobean of the error of the model with the changed parameters and use it to then recalculate the confidence intervals.

Answer 1

[nws]

Yes, this is possible, but it usually cannot be done directly from the original predictionConfidenceInterval result once the simulation settings have changed.

In your case, the model structure and fitted parameters remain the same, but the physiological parameters are changed to represent different individuals. The uncertainty on predictions can still be evaluated by propagating the uncertainty of the fitted parameters through each of these new individual simulations.

A practical approach is to:

1. Use the uncertainty information from the fitted parameters obtained during model fitting.
2. Re-run simulations for each individual with their specific physiological parameter values.
3. Propagate the fitted-parameter uncertainty through those simulations, for example by sampling parameter values within their estimated uncertainty range and simulating repeatedly.
4. Derive prediction intervals from the resulting spread in simulated profiles.

One important point is that this gives prediction uncertainty due to the fitted parameters only. If you also want to account for uncertainty in the individual physiological parameters, that would need to be included separately.

[Justine]

Many thanks! Your answer helped me find a way out, with a "Generate Samples -> Simulation " program in the simbiology analyzer.