Conditional Robust Calibration (CRC): a new computational Bayesian methodology for model parameters estimation and identifiability analysis

Abstract

Computational modeling is a remarkable and common tool to quantitatively describe a biological process. However, most model parameters, such as kinetics parameters, initial conditions and scale factors, are usually unknown because they cannot be directly measured.\n\nTherefore, key issues in Systems Biology are model calibration and identifiability analysis, i.e. estimate parameters from experimental data and assess how well those parameters are determined by the dimension and quality of the data.\n\nCurrently in the Systems Biology and Computational Biology communities, the existing methodologies for parameter estimation are divided in two classes: frequentist methods and Bayesian methods. The first ones are based on the optimization of a cost function while the second ones estimate the posterior distribution of model parameters through different sampling techniques.\n\nIn this work, we present an innovative Bayesian method, called Conditional Robust Calibration (CRC), for model calibration and identifiability analysis. The algorithm is an iterative procedure based on parameter space sampling and on the definition of multiple objective functions related to each output variables. The method estimates step by step the probability density function (pdf) of parameters conditioned to the experimental measures and it returns as output a subset in the parameter space that best reproduce the dataset.\n\nWe apply CRC to six Ordinary Differential Equations (ODE) models with different characteristics and complexity to test its performances compared with profile likelihood (PL) and Approximate Bayesian Computation Sequential Montecarlo (ABC-SMC) approaches. The datasets selected for calibration are time course measurements of different nature: noisy or noiseless, real or in silico.\n\nCompared with PL, our approach finds a more robust solution because parameter identifiability is inferred by conditional pdfs of estimated parameters. Compared with ABC-SMC, we have found a more precise solution with a reduced computational cost.