Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences

Murphy, Ryan J.; Maclaren, Oliver J.; Simpson, Matthew J.

doi:10.1098/rsif.2023.0402

Cited by 7 publications

(6 citation statements)

References 102 publications

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“…This result is very different to previous implementation of the PWA workflow for identifiable problems where finite sample coverage properties for parameter confidence intervals are very close to the expected asymptotic result (Simpson and Maclaren 2023 ; Murphy et al. 2024 ).…”

Section: Resultscontrasting

confidence: 99%

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Making Predictions Using Poorly Identified Mathematical Models

Simpson,

Maclaren

2024

Bull Math Biol

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Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self-contained document that can be studied together with relatively straightforward Julia code provided on GitHub. Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly-encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.

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Section: Resultscontrasting

confidence: 99%

“… 2023 ), as well as systems of ODEs and systems of PDEs (Murphy et al. 2024 ), or more complicated mathematical models that encompass biological heterogeneity, such as multiple growth rates (Banks et al. 2018 ).…”

Section: Discussionmentioning

confidence: 99%

Making Predictions Using Poorly Identified Mathematical Models

Simpson,

Maclaren

2024

Bull Math Biol

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“…This gives 4900 / 5000 = 98.00% which, unsurprisingly, exceeds the expected 95% asymptotic result due to the fact that the likelihood function is relatively flat. This result is very different to previous implementation of the PWA workflow for identifiable problems where finite sample coverage properties for parameter confidence intervals are very close to the expected asymptotic result [48, 63].…”

Section: Resultscontrasting

confidence: 99%

“…Unfortunately, however, under these conditions it becomes computationally infeasible to compare with predictions from the gold-standard full likelihood approach so we have not dealt with more complicated models in the current study. While we have focused on presenting ODE-based models with a standard additive Gaussian measurement model, the PWA approach can be applied to more complicated mathematical models including mechanistic models based on PDEs [19, 59], as well as systems of ODEs and systems of PDEs [48], or more complicated mathematical models that encompass biological heterogeneity, such as multiple growth rates [7]. Here we have chosen to work here with Gaussian additive noise because this is by far the most commonly–used approach to relate noisy measurements with solutions of mathematical models [32], but our approach can be used for other measurement models, such as working with binomial measurement models [43,64] or multiplicative measurement models that are often used to maintain positive predictions [48], as well as correlated noise models [40].…”

Section: Discussionmentioning

confidence: 99%

Making predictions using poorly identified mathematical models

Simpson,

Maclaren

2023

Preprint

Self Cite

View full text Add to dashboard Cite

Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self–contained document that can be studied to-gether with relatively straightforward Julia code provided onGitHub. Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly–encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of some parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.

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“…We point out the reader that the assumption of additive Gaussian noise may not be the more appropriate under certain conditions, especially for data close to zero. We highlight that other choices of measurement error model may be considered in order to relax this assumption of additive Gaussian noise (see [ 50 ] for a recent review on the topic). In any case, the method of the profile likelihood analysis here implemented holds when different measurement models are used.…”

Section: Methodsmentioning

confidence: 99%

Structural and practical identifiability of contrast transport models for DCE-MRI

Conte,

Woodall,

Gutova

et al. 2024

PLoS Comput Biol

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Contrast transport models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

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Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences

Cited by 7 publications

References 102 publications

Making Predictions Using Poorly Identified Mathematical Models

Making Predictions Using Poorly Identified Mathematical Models

Making predictions using poorly identified mathematical models

Structural and practical identifiability of contrast transport models for DCE-MRI

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