Parameter identifiability and model selection for sigmoid population growth models

Sigmoid growth models, such as the logistic, Gompertz and Richards’ models, are widely used to study population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and parameter estimation are critical if...

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Main Authors: Simpson, MJ, Browning, AP, Warne, DJ, Maclaren, OJ, Baker, RE
Format: Journal article
Language:English
Published: Elsevier 2021
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author Simpson, MJ
Browning, AP
Warne, DJ
Maclaren, OJ
Baker, RE
author_facet Simpson, MJ
Browning, AP
Warne, DJ
Maclaren, OJ
Baker, RE
author_sort Simpson, MJ
collection OXFORD
description Sigmoid growth models, such as the logistic, Gompertz and Richards’ models, are widely used to study population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and parameter estimation are critical if these models are to be used to make practical inferences. However, the question of parameter identifiability – whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates – is often overlooked. We use a profile-likelihood approach to explore practical parameter identifiability using data describing the re-growth of hard coral. With this approach, we explore the relationship between parameter identifiability and model misspecification, finding that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards’ models encounter practical non-identifiability issues. This analysis of parameter identifiability and model selection is important because different growth models are in biological modelling without necessarily considering whether parameters are identifiable. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and potentially misleading mechanistic interpretations. For example, using the Gompertz model, the estimate of the time scale of coral re-growth is 625 days when we estimate the initial density from the data, whereas it is 1429 days using a more standard approach where variability in the initial density is ignored. While tools developed here focus on three standard sigmoid growth models only, our theoretical developments are applicable to any sigmoid growth model and any appropriate data set. MATLAB implementations of all software are available on GitHub.
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spelling oxford-uuid:c3f93b0c-959d-4c6d-8346-b2d54f7a03f92023-01-04T07:10:01ZParameter identifiability and model selection for sigmoid population growth modelsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c3f93b0c-959d-4c6d-8346-b2d54f7a03f9EnglishSymplectic ElementsElsevier2021Simpson, MJBrowning, APWarne, DJMaclaren, OJBaker, RESigmoid growth models, such as the logistic, Gompertz and Richards’ models, are widely used to study population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and parameter estimation are critical if these models are to be used to make practical inferences. However, the question of parameter identifiability – whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates – is often overlooked. We use a profile-likelihood approach to explore practical parameter identifiability using data describing the re-growth of hard coral. With this approach, we explore the relationship between parameter identifiability and model misspecification, finding that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards’ models encounter practical non-identifiability issues. This analysis of parameter identifiability and model selection is important because different growth models are in biological modelling without necessarily considering whether parameters are identifiable. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and potentially misleading mechanistic interpretations. For example, using the Gompertz model, the estimate of the time scale of coral re-growth is 625 days when we estimate the initial density from the data, whereas it is 1429 days using a more standard approach where variability in the initial density is ignored. While tools developed here focus on three standard sigmoid growth models only, our theoretical developments are applicable to any sigmoid growth model and any appropriate data set. MATLAB implementations of all software are available on GitHub.
spellingShingle Simpson, MJ
Browning, AP
Warne, DJ
Maclaren, OJ
Baker, RE
Parameter identifiability and model selection for sigmoid population growth models
title Parameter identifiability and model selection for sigmoid population growth models
title_full Parameter identifiability and model selection for sigmoid population growth models
title_fullStr Parameter identifiability and model selection for sigmoid population growth models
title_full_unstemmed Parameter identifiability and model selection for sigmoid population growth models
title_short Parameter identifiability and model selection for sigmoid population growth models
title_sort parameter identifiability and model selection for sigmoid population growth models
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