LikelihoodProfiler.jl: A Unified Package for Practical Identifiability Analysis and Confidence Intervals Estimation
Ivan Borisov1, Aleksandr Demin1, Evgeny Metelkin1
1InSysBio
Introduction. Practical identifiability addresses the crucial question of how well a model (particularly Systems Biology/Quantitative Systems Pharmacology (SB/QSP) model) is determined by the available experimental data. Noisy or incomplete experimental data may result in uncertainty in parameters estimations, which is typically described by confidence intervals (CI) and confidence regions (CR). CI/CR estimation based on profile likelihood methods is preferred to other practical identifiability methods such as Monte Carlo simulation due to its reliability [1]. Moreover, the profile likelihood approach is readily extended to analyze not only the unknown parameters but also the model’s states and predictions, which makes it of utmost importance for the SB/QSP fields. Objectives. LikelihoodProfiler.jl proposes a single interface to different profile likelihood methods and constitutes a unified open-source package for practical identifiability analysis in Julia. Methods. LikelihoodProfiler.jl package provides a single interface to various methods of profile likelihood-based practical identifiability: - Confidence intervals by Constrained Optimization method (CICO) originally implemented in the package [2] and other methods to estimate parameters CI without restoring the full shape of the likelihood profile. - Optimization-based likelihood profiles. The classical stepwise optimization procedure with fixed or adaptive stepping to restore the shape of the profile for a given parameter. - Integration-based approach to compute likelihood profiles by solving the system of differential equations. - Hybrid approach, which performs both differential equations integration and optimization steps to increase the accuracy in estimation of the profile. Proposed methods can be used to analyze both parameters and model’s states or predictions. LikelihoodProfiler.jl interface supports modeling format of the Julia SciML ecosystem. This facilitates the integration of LikelihoodProfiler.jl into existing model analysis and simulation pipelines shipped in the SciML packages. And, vice versa, such compatibility enables LikelihoodProfiler.jl to reuse the functionality from third-party packages, which support the SciML format: HetaSimulator, SBML, PEtab models, etc. Results. The computational efficiency of LikelihoodProfiler.jl was tested on a number of benchmark models. LikelihoodProfiler.jl methods are based on the Julia SciML package ecosystem [3], which empowers profile likelihood methods with access to various top-of-the-line optimizers, differential equations solvers, automatic differentiation backends, etc. Also, LikelihoodProfiler.jl utilizes Julia distributed features and can speed up profiles' computation by parallel setup. Variability of profiling methods together with unique features of Julia and SciML make LikelihoodProfiler.jl applicable and efficient to study practical identifiability of large-sale SB/QSP models. Conclusion. LikelihoodProfiler.jl can be used as a unified package for practical identifiability for complex computationally demanding SB/QSP models. It implements the state-of-the-art methods for profile likelihood analysis and CI estimation in a single Julia-based interface. The package is open-source and freely available on GitHub [4]. The results of LikelihoodProfiler.jl analysis can be used to further reduce the complexity and eliminate model’s uncertainty by implementing identifiable parametrizations and model reduction techniques.
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