CONVERGENCE, SAMPLING AND TOTAL ORDER ESTIMATOR EFFECTS ON PARAMETER ORTHOGONALITY IN GLOBAL SENSITIVITY ANALYSIS
Authors: Saxton Harry , Xu Xu , Schenkel Torsten , Clayton Richard H. , Halliday Ian 
Published: March 2024

Abstract

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.

Research Highlights

We conduct a heuristic investigation utilising 2 physiologically intuitive, highly nonlinear and stiff, lumped parameter models.

The Janon and Jansen estimators emerge as optimal choices for calculating parameter orthogonality, as they are insensitive to sampling methodologies and measurement types.

The Janon and Jansen estimators prove to have the most efficient convergence rates in calculating total order indices.

The convergence rate of an estimator appears to be decisive in its ability to truthfully and uniformly recover true indices and orthogonality.

Our methods provide putative best practice for practical identifiability investigations.

Author Summary

In order to gain a new insight into biological systems one often uses a mathematical model to predict possible responses from the system of interest. One vital step when using such models is knowledge of the uncertainty associated with a model response given a change in the inputs provided to the model. Utilising two non-linear and stiff cardiovascular models as test cases we investigate the effects of different choices made when quantifying the uncertainty in a mathematical model. Leveraging efficient solving of the mathematical model we are able to 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. Without this, identifying inputs of a model become uncertain, or clinically, non patient specific. Our detailed study provides a workflow and advice for mathematical models of biological systems thus ensuring a true interpretation of the uncertainty associated with model inputs.