Linear compartmental models: input-output equations and operations that preserve identifiability

TL;DR

This paper investigates how the identifiability of linear compartmental models is affected by adding or removing components, using algebraic and combinatorial methods to analyze input-output equations and submodel properties.

Contribution

It provides new insights into when model identifiability is preserved under modifications, clarifies input-output equations, and introduces conditions based on submodel structures.

Findings

Identifiability preservation depends on output-reachable submodels.

Clarified the determinantal formula for input-output equations.

Proved conditions under which adding/removing components preserves identifiability.

Abstract

This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submodels. We look specifically at linear compartmental models and investigate when identifiability is preserved after adding or removing model components. In particular, we examine whether identifiability is preserved when an input, output, edge, or leak is added or deleted. Our approach, via differential algebra, is to analyze specific input-output equations of a model and the Jacobian of the associated coefficient map. We clarify a prior determinantal formula for these equations, and then use it to prove that, under some hypotheses, a model's input-output equations can be understood in terms of certain submodels we call "output-reachable". Our proofs use algebraic and combinatorial techniques.