Source-linked AI summary
SIAN: software for structural identifiability analysis of ODE models
Hoon Hong, Alexey Ovchinnikov, Gleb Pogudin, Chee Yap
TL;DR
ODE parameter values may not be uniquely recoverable even from continuous, noise-free data, making it useful to check identifiability before experiments. SIAN assesses identifiability for ODE models and assigns parameter and initial-condition labels with a user-specified correctness probability. The paper presents SIAN as able to assess individual parameters and initial conditions, including cases where other tools report that they cannot solve a model.
Problem
ODE model structure can make a parameter impossible to recover uniquely even from continuous, noise-free data, so identifiability is useful to assess before parameter estimation.
Source: §1 · p. 1Method
SIAN is MAPLE software that analyzes rational-function ODE systems and assigns identifiability labels to unknown parameters and initial conditions using a user-specified correctness probability.
Source: §3 · p. 2Results
Takeaways & Limitations
Structural identifiability can be checked a priori, before conducting potentially costly experiments.
Source: §1 · p. 1The stated input specification uses rational functions with complex coefficients, although other function types can also be handled.
Source: §3 · p. 2
Abstract
from arXiv · showhide
Biological processes are often modeled by ordinary differential equations with unknown parameters. The unknown parameters are usually estimated from experimental data. In some cases, due to the structure of the model, this estimation problem does not have a unique solution even in the case of continuous noise-free data. It is therefore desirable to check the uniqueness a priori before carrying out actual experiments. We present a new software SIAN (Structural Identifiability ANalyser) that does this. Our software can tackle problems that could not be tackled by previously developed packages.
1 Introduction
Biological ODE models use unknown parameters that may represent important mechanisms or intervention targets, and these parameters are commonly estimated by fitting experimental data. But model structure can make unique recovery impossible even with continuous, noise-free data, so global identifiability can be checked before experiments.
1 Introduction
- ODE parameters are commonly estimated by fitting model predictions to experimental data with minimal error.The approach is often framed statistically as maximum likelihood or Bayesian inference.Source: §1 · p. 1
- A parameter may be impossible to recover uniquely from continuous, noise-free data because of the model’s structure.Global identifiability asks whether the value can be uniquely recovered under that ideal-data assumption.Source: §1 · p. 1
- Checking structural global identifiability before experiments can reveal whether parameter estimation can guarantee the correct value.The paper notes that experiments may be costly and describes SIAN as software for assessing identifiability in ODE models, based on the algorithm in [Hong et al., 2018].Source: §1 · p. 1
2 Existing software for structural identifiability
Global identifiability is challenging, while local identifiability is more tractable and can be assessed by existing tools. However, locally identifiable parameters need not be globally identifiable, and existing global-identifiability packages have stated scope or input conditions.
2 Existing software for structural identifiability
- Local identifiability means identification in a neighborhood, or, for polynomial systems, identification up to finitely many options.ObservabilityTest and EAR are described as fast and reliable tools for assessing local identifiability.Source: §2 · p. 1
- Real-life systems can have parameters that are locally but not globally identifiable, motivating software that assesses global identifiability.The passage cites [Thomaseth and Saccomani, 2018, Section 4],, and Supplementary Materials A.1.Source: §2 · p. 2
- DAISY and COMBOS use input-output equations and assess global identifiability for systems with the solvability property.[Hong et al., 2018, Example 6] discusses that property.Source: §2 · p. 2
- GenSSI 2.0 uses generating series and conditions its global-identifiability check on an extra input: the truncation order.[Hong et al., 2018, Example 7] discusses the truncation order’s effect on algorithm output.Source: §2 · p. 2
3 Features
SIAN is MAPLE software for assessing identifiability in ODE systems with rational-function dynamics, unknown parameters, and unknown initial conditions. It assigns identifiability labels with a user-specified correctness probability and offers parallel execution and per-parameter assessment, including for initial conditions.
3 Features
- SIAN takes an ODE system with state variables, experimenter-chosen inputs, outputs, unknown parameters, and unknown initial conditions as input.The dynamics and output functions are rational functions in the states, parameters, and inputs with complex coefficients; other function types can also be handled.Source: §3 · p. 2
- SIAN is a Monte Carlo randomized algorithm whose user-specified probability p sets the minimum probability that its assigned labels are correct.The user chooses 0 < p < 1.Source: §3 · p. 2
- For each parameter or initial condition, SIAN labels it globally identifiable when all solutions with the same input and output have the same value.The definition applies to almost every solution of the system.Source: §3 · p. 2
- SIAN distinguishes locally but not globally identifiable parameters, which have finitely many possible values, from non-identifiable ones, which have infinitely many.Both labels are defined for almost every solution among solutions with the same input and output.Source: §3 · p. 2
- SIAN can be parallelized to use a multicore computing environment.Source: §3 · p. 2
- SIAN assesses identifiability for each individual parameter and for initial conditions, whose identifiability is often called observability.Source: §3 · p. 2
4 Performance and Applications
The performance section compares SIAN with COMBOS, DAISY, and GenSSI on benchmark problems and presents runtimes. The supplied passages identify the runtime table and experimental software and hardware settings, but do not provide its cell values.
4 Performance and Applications
- The comparison used a 96-CPU, 2.4 GHz computer running CentOS 6.9; SIAN used MAPLE 2017 with p = 0.99, GenSSI used Matlab R2017a, and DAISY was version 1.9.The reported runtimes are elapsed time.Source: §4 · p. 3
- Table 1 presents runtimes in minutes for benchmark problems compared across SIAN, COMBOS, DAISY, and GenSSI.The section identifies these tools as the global-identifiability software compared.Source: Table 1 · p. 3, §4 · p. 3
- Table footnotes report that GenSSI 2.0 could not find an explicit solution in one case and COMBOS could not solve or accept a model in another.Source: §4 · p. 3
Supplementary materials SIAN: software for structural identifiability analysis of
The supplement recalls SIAN’s MAPLE input-output specification and randomized identifiability labels. It also contains illustrative examples and benchmark-problem descriptions.
Supplementary materials SIAN: software for structural identifiability analysis of
- The supplement contains three illustrative examples from the paper and descriptions of the benchmark problems used in Section 4.Source: Supplementary materials SIAN: software… · p. 5
- SIAN takes state, input, output, parameter, and initial-condition vectors, with rational-function model components; other function types can also be handled.The supplement identifies the software as written in MAPLE.Source: Supplementary materials SIAN: software… · p. 5
- For each parameter or initial condition, SIAN reports global, local-but-not-global, or no identifiability, with labels correct at least with user-specified probability p.SIAN is a Monte Carlo randomized algorithm.Source: Supplementary materials SIAN: software… · p. 5
A.1 Chemical reaction
The two examples show SIAN identifying locally but not globally identifiable parameters in a chemical reaction model and globally identifiable quantities in a ruminal lipolysis model. The latter illustrates converting exponential terms to rational dynamics.
A.1 Chemical reaction
- In the chemical reaction example, all parameters and initial values are locally identifiable, but only x*C is globally identifiable.The set {k1,k2} is recoverable, but either value may correspond to k1 or k2, a slow-fast ambiguity [12, Equation (1.3)].Source: §A.1 · p. 6
- For the chemical reaction model, separate measurements of εA and εC are redundant because both are globally identifiable from y1 and y2.Source: §A.1 · p. 7
A.2 Ruminal lipolysis
- Replacing k1e^-k3t with x5 and adding x5'=-k3x5 rewrites the ruminal lipolysis system using rational functions; models (4) and (5) are equivalent in identifiability.Source: §A.2 · p. 7
- All parameters and initial conditions of ruminal lipolysis model (5), and consequently model (4), are globally identifiable.Source: §A.2 · p. 8
A.3 Goodwin oscillator
The Goodwin oscillator illustrates locally but not globally identifiable parameters and a software-based way to analyze their non-uniqueness. The analysis also aims to handle systems whose right-hand sides are not rational functions of the parameters.
A.3 Goodwin oscillator
- The section uses the oscillator to show that locally but not globally identifiable parameters occur in small real-life systems.It also states an aim of handling systems whose right-hand sides are not rational functions of the parameters.Source: §A.3 · p. 8
- The analysis concludes that a, A, α, γ, x*_2, and x*_3 are non-identifiable.It reasons that non-identifiability of a follows from that of x*_3, given the global identifiability of x*_4 and σ, and then extends the conclusion to A.Source: §A.3 · p. 9
- To investigate non-uniqueness, the authors seek changes of variables and parameters that preserve outputs while changing a parameter's value.For this example, the proposed change swaps β and δ while leaving the other variables and parameters unchanged except x2.Source: §A.3 · pp. 9–10
- The pair {β,δ} is identifiable, but observations cannot distinguish which value is β and which is δ.SIAN's intermediate results expose this ambiguity; a change swapping β and δ preserves the output.Source: §A.3 · p. 9
B Benchmarks
The benchmarks section compares SIAN with GenSSI 2.0, COMBOS, and DAISY using runtime results. It specifies the correctness probability for results reported later in the section.
B Benchmarks
- The section compares SIAN, GenSSI 2.0, COMBOS, and DAISY on benchmark problems using runtime results.Table 1 is identified as reporting runtimes in minutes.Source: B Benchmarks · p. 10, Table 1 · p. 10
- Results presented in the rest of the section are computed with probability of correctness p = 0.99.The table notes cases where GenSSI 2.0 cannot find an explicit solution and COMBOS reports that a model may be incorrectly entered or unsolvable by its algorithms.Source: B Benchmarks · p. 10
B.1 Chemical Reaction
This benchmark describes a reduced fully processive, n-site phosphorylation network. The reported analysis finds all its parameters and initial conditions globally identifiable.
B.1 Chemical Reaction
- The benchmark system is a reduced fully processive, n-site phosphorylation network.Its listed outputs are y1 = x2 and y2 = x3.Source: §B.1 · p. 11
- The passage identifies benchmark input files for DAISY, COMBOS, and GenSSI 2.0 in the Supplementary Data.The listed files are ChemicalReactionNetwork.txt for DAISY and COMBOS, and CRN.m for GenSSI 2.0.Source: §B.1 · p. 11
- All parameters μ and initial conditions x* are globally identifiable for the chemical reaction network.The system corresponds to a reduced fully processive, n-site phosphorylation network.Source: §B.1 · p. 11
B.2 HIV
The appendix applies identifiability analysis to four biological models, reporting which parameters and initial conditions are globally identifiable, locally but not globally identifiable, or non-identifiable.
B.2 HIV
- For HIV, a, b, d, h, q, u, w* and z* are globally identifiable, while β, λ, c, k, x*, y* and v* are non-identifiable.Source: §B.2 · p. 12
B.3 SIRS with forcing
- For the forced SIRS model, b0, g, µ, ν, s*, i* and r* are globally identifiable; M is locally but not globally identifiable; b1, x*1 and x*2 are non-identifiable.Source: §B.3 · p. 13
B.4 Cholera
- For the cholera SIWR model, all parameters µ and initial conditions x* are globally identifiable.Source: §B.4 · p. 13
B.5 Protein Complex (NFκB)
- The NFκB result reports global identifiability for parameters and initial values, with an exception among the initial values.Source: §B.5 · p. 15
B.6 Pharmacokinetics
The section considers a simplified pharmacokinetics model and reports that all its parameters and initial values are globally identifiable.
B.6 Pharmacokinetics
- The tested pharmacokinetics system is a simplified version of a model arising in pharmacokinetics.Source: §B.6 · p. 15
- The initial-condition vector is specified as x* = (x*1, x*2, x*3, x*4).Source: §B.6 · p. 15
- All parameters µ and initial values x* in the pharmacokinetics model are globally identifiable.Source: §B.6 · p. 15