A latent variable approach to account for correlated inputs in global sensitivity analysis

Abstract

In drug development decision-making is often supported through model-based methods, such as physiologically-based pharmacokinetics (PBPK). Global sensitivity analysis (GSA) is gaining use for quality assessment of model-informed inference. However, the inclusion and interpretation of correlated factors in GSA has proven an issue. Here we developed and evaluated a latent variable approach for dealing with correlated factors in GSA. An approach was developed that 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. The latent variable approach was applied to a set of algebraic models and a case from PBPK. Then, this method was compared to Sobol’s GSA assuming no correlations, Sobol’s GSA with groups and the Kucherenko approach. For the latent variable approach, GSA was performed with Sobol’s method. By using the latent variable approach, it is possible to devise a unique and easy interpretation of the sensitivity indices while maintaining the correlation between the factors. Compared methods either consider the parameters independent, group the dependent variables into one unique factor or present difficulties in the interpretation of the sensitivity indices. In situations where GSA is called upon to support model-informed decision-making, the latent variable approach offers a practical method, in terms of ease of implementation and interpretability, for applying GSA to models with correlated inputs that does not violate the independence assumption. Prerequisites and limitations of the approach are discussed.

A two-stages global sensitivity analysis by using the δ sensitivity index in presence of correlated inputs: application on a tumor growth inhibition model based on the dynamic energy budget theory

“…Ignoring known correlations between model inputs may dramatically alter the model simulations and, consequently, the GSA results [ 28 , 31 , 40 , 44 ]. However, the field of GSA in presence of correlated inputs is still embryonic [ 31 , 39 – 41 ].…”

“…When this hypothesis is violated (i.e., in presence of correlated inputs), the variance decomposition of model output is not unique [ 34 ]. Different extensions of the variance-based GSA method have been proposed to deal with dependent inputs [ 38 – 40 ], but the meaning of their results is not easy to interpret [ 38 , 41 – 43 ].…”

Developing Clinically Relevant Dissolution Specifications (CRDSs) for Oral Drug Products: Virtual Webinar Series

“…Further, the wider adoption of advanced simulation methods in pharmaceutics modelling, such as global sensitivity analysis, allows more systematic interrogation of the impact of information on simulation outputs. This is to inform model development and generation of data [ 76 , 77 ].…”