Efficient inference and identifiability analysis for differential equation models with random parameters

TL;DR

This paper introduces a flexible likelihood-based framework for inference and identifiability analysis of differential equation models with biologically heterogeneous parameters, improving understanding of variability sources in biological data.

Contribution

It develops a novel moment-matching approach for models with random parameters, enabling efficient analysis of heterogeneity in biological systems.

Findings

Framework applicable to various models with random parameters

Allows both frequentist and Bayesian identifiability analysis

Computational cost comparable to non-heterogeneous models

Abstract

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.