A latent variable approach to account for correlated inputs in global sensitivity analysis with cases from pharmacological systems modelling

TL;DR

This paper introduces a latent variable method to handle correlated inputs in global sensitivity analysis, improving interpretability for pharmacological models with interdependent parameters.

Contribution

The paper proposes a novel latent variable approach for GSA that explicitly accounts for correlated inputs, enhancing analysis accuracy in pharmacological systems modeling.

Findings

The latent variable approach effectively models input correlations in GSA.

Compared to existing methods, it offers easier implementation and interpretation.

Application to pharmacokinetic models demonstrates its practical utility.

Abstract

In pharmaceutical research and development decision-making related to drug candidate selection, efficacy and safety is commonly supported through modelling and simulation (M\&S). Among others, physiologically-based pharmacokinetic models are used to describe drug absorption, distribution and metabolism in human. Global sensitivity analysis (GSA) is gaining interest in the pharmacological M\&S community as an important element for quality assessment of model-based inference. Physiological models often present inter-correlated parameters. The inclusion of correlated factors in GSA and the sensitivity indices interpretation has proven an issue for these models. Here we devise and evaluate a latent variable approach for dealing with correlated factors in GSA. This approach describes the correlation between two model inputs through the causal relationship of three independent factors: the latent variable and the unique variances of the two correlated parameters. Then, GSA is performed with the classical variance-based method. We applied the latent variable approach to a set of algebraic models and a case from physiologically-based pharmacokinetics. Then, we compared our approach to Sobol's GSA assuming no correlations, Sobol's GSA with groups and the Kucherenko approach. The relative ease of implementation and interpretation makes this a simple approach for carrying out GSA for models with correlated input factors.