Identifiability methods for biological systems: Determining subsets of parameters through sensitivity analysis, penalty-based optimisation, profile likelihood and LASSO model reduction

Abstract

Parameter estimation for model equations of biological systems can be complicated when some of the parameters are not identifiable. For example this can occur if parameters are very insensitive or if there are correlations between the parameters such that ranges of different parameter values give the same model output. To solve these issues, a logical procedure is suggested which incorporates sensitivity analysis and existing methods for testing for identifiability together with a LASSO based model reduction method for obtaining potential correlations between parameters. This procedure aims to separate the full set of parameters into a subset of identifiable parameters, a subset of insensitive parameters and provide correlations for determining values of non-identifiable parameters. The combined methodology is illustrated through two case studies: A simple two-compartment pharmacokinetic model and a complex kinetic model for the bioproduction of succinic acid from glycerol.