Discussion
Models characterising drug actions and biological systems can have different degrees of complexity. Compartmental models, that also incorporate empirical pharmacodyanmic functions, e.g. the Emax model, for instance, are built chiefly on the observed data with the aim of being utilised for predictions to new scenarios. However, their predictive performance can be limited [18,19,55] when used for extrapolation. Such models when incorporating sufficient population data usually provide good insights for answering many drug development and utilisation questions. However, extrapolating beyond the available data remains problematic. In contrast, QSP models (including PBPK models) are built upon mechanistic knowledge of biological systems and drug actions and therefore allow for predictions of outcomes in previously untested scenarios. Despite the potential benefits of these mechanistic models, the issue of model complexity can make them intractable for many applications. There remains the need for a balance between model usability and complexity. Model-order reduction can act as a bridging approach that provides a means of producing intermediary scale models that bring together the strengths of both simplicity and mechanistic predictive ability. Model-order reduction can also be used to estimate between-subject variability in some parameters using population approach [22] which could then be used to feedback into the original QSP model.
Despite the benefits that model-order reduction provides, careful consideration of the limitations of different methods should be given. Most model-order reduction methods will incur some degree of information loss relative to the full-order model. The greater extent of model reduction means, in most situations, greater loss of information. The optimal balance of the trade-off between model simplicity and accuracy will largely depend on the intended use of the reduced model. It is also important to realise the local nature of many model-order reduction methods, i.e., the reduced model may only be valid for a specific set of parameter values. Of note, most model-order reduction techniques incur a large upfront computational cost for producing a reduced model. This should be balanced against the expected computational speed-up gained by the reduced model in order to determine whether a particular model-order reduction technique is worthwhile.
In this work, we have developed an overall framework for considering various methods of model-order reduction that can be useful in the context of QSP models (figure 2 & table 1). The framework provides a natural categorisation of various methods based on their utility. We hope this can guide modellers to choose the best model-order reduction method that suits their needs.
In summary, model-order reduction can have a significant impact on the future of modelling and simulation in drug development and clinical use [56]. The vast repository of information contained in QSP models can act as source library from which smaller models to describe a specific input-output relationship(s) can be extracted through model-order reduction methods. The existence of automated tools for model-order reduction can streamline the process of model building saving time and effort. It is therefore anticipated that pharmacometricians and clinical pharmacologists would benefit from being familiar with various model-order reduction techniques and there benefits and potential uses.