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.Comment: Minor changes to text. Additional results in supplementary material.
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