Reducing structural non-identifiabilities in upstream bioprocess models using profile-likelihood

Process models are increasingly used to support upstream process development in the biopharmaceutical industry for process optimization, scale-up and to reduce experimental effort. Parametric unstructured models based biological mechanisms are highly promising, since they do not require large amounts of data. The critical part in the application is the certainty of the parameter estimates, since uncertainty of the parameter estimates propagates to model predictions and can increase the risk associated with those predictions. Currently Fisher-Information-Matrix based approximations or Monte-Carlo approaches are used to estimate parameter confidence intervals and regularization approaches to decrease parameter uncertainty. Here we apply profile likelihood to determine parameter identifiability of a recent upstream process model. We have investigated the effect of data amount on identifiability and found out that addition of data reduces non-identifiability. The likelihood profiles of non-identifiable parameters were then used to uncover structural model changes. These changes effectively alleviate the remaining non-identifiabilities except for a single parameter out of 21 total parameters. We present the first application of profile likelihood to a complete upstream process model. Profile likelihood is a highly suitable method to determine parameter confidence intervals in upstream process models and provides reliable estimates even with non-linear models and limited data.