Driving the Model to Its Limit: Profile Likelihood Based Model Reduction

PLoS One. 2016 Sep 2;11(9):e0162366. doi: 10.1371/journal.pone.0162366. eCollection 2016.


In systems biology, one of the major tasks is to tailor model complexity to information content of the data. A useful model should describe the data and produce well-determined parameter estimates and predictions. Too small of a model will not be able to describe the data whereas a model which is too large tends to overfit measurement errors and does not provide precise predictions. Typically, the model is modified and tuned to fit the data, which often results in an oversized model. To restore the balance between model complexity and available measurements, either new data has to be gathered or the model has to be reduced. In this manuscript, we present a data-based method for reducing non-linear models. The profile likelihood is utilised to assess parameter identifiability and designate likely candidates for reduction. Parameter dependencies are analysed along profiles, providing context-dependent suggestions for the type of reduction. We discriminate four distinct scenarios, each associated with a specific model reduction strategy. Iterating the presented procedure eventually results in an identifiable model, which is capable of generating precise and testable predictions. Source code for all toy examples is provided within the freely available, open-source modelling environment Data2Dynamics based on MATLAB available at http://www.data2dynamics.org/, as well as the R packages dMod/cOde available at https://github.com/dkaschek/. Moreover, the concept is generally applicable and can readily be used with any software capable of calculating the profile likelihood.

MeSH terms

  • Algorithms
  • Computer Simulation*
  • Models, Biological*
  • Nonlinear Dynamics
  • Software*
  • Systems Biology / methods*

Grant support

This work was supported by the German Ministry of Education and Research through the grants LiSyM (Grant No. 031L0048), LungSys II (Grant No. 0316042G), ReelinSys (Grant No. 0316174C), SBEpo (Grant No. 0316182B), IMOMESIC (Grant No. 031A604B). This work was also supported by the EU-IMI grant MIP-DILI (Grant No. 115336) and the DFG grant FOR1202 (TP7, Grant No. TI315/10-1). Merrimack Pharmaceuticals provided support in the form of salaries for author AR, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of author AR are articulated in the ‘author contributions’ section.