Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis

Dynamical system models typically involve numerous input parameters whose “effects” and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators’ role in recovering “true” effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.Author summary: In order to gain new insight into a biological system, one often uses mathematical models to predict possible responses from the system. One vital step when using such models is to gain knowledge of the uncertainty associated with the model responses, for any input changes. Utilising two non-linear and stiff cardiovascular models as test cases, we investigate the effects of different choices made when quantifying the uncertainty of mathematical models. Leveraging efficient solving of the mathematical model, we show that in order to truly quantify the effects of inputs on a set of outputs, one must ensure converged estimates of the inputs’ influence. Our detailed study provides a robust workflow of good modelling practice for biological systems, thus ensuring a true interpretation of the uncertainty associated with model inputs.